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Title: Rules and Examples of Perspective proper for Painters and Architects, etc. - In English and Latin: Containing a most easie and - expeditious method to delineate in perspective all designs - relating to architecture
Author: Pozzo, Andrea
Language: English
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Rules and Examples of
PERSPECTIVE
_PROPER FOR_
Painters and Architects, etc.
In English and Latin;
_Containing a most easie and expeditious Method to_
_DELINEATE in PERSPECTIVE_
All DESIGNS relating to ARCHITECTURE,
_AFTER A NEW MANNER_,
Wholly free from the Confusion of Occult Lines:
_BY THAT GREAT MASTER THEREOF_,
ANDREA POZZO, _Soc. Jes._
_Engraven in 105 ample folio Plates, and adorn’d with 200
Initial Letters to the Explanatory Discourses:
~Printed from Copper-Plates~ on y^{e} best Paper_
By John Sturt.
Done into English from the Original Printed at Rome 1693 in
Lat. and Ital.
_By M^{r} John James of Greenwich._
[Illustration]
LONDON:
PRINTED by Benj. Motte, MDCCVII.
_Sold by John Sturt in Golden-Lion-Court in_
Aldersgate-Street.
PERSPECTIVA
PICTORUM
_ET_
ARCHITECTORUM,
_ANDREÆ PUTEI,
E SOCIETATE JESU._
In quâ docetur Modus expeditissimus Delineandi
Opticè omnia quę pertinent ad Architecturam.
[Illustration]
LONDINI:
Juxta Exemplar ROMÆ excusum, MDCXCIII.
_Ex Sculpturâ Joannis Sturt, et ejusd. Curâ adornata_:
TYPIS Benj. Motte, MDCCVII.
[Illustration]
[Illustration]
TO
Her most Sacred Majesty,
QUEEN ANNE.
_May it please your Majesty!_
_The Condescension of the late Emperor of ~Germany~ to patronize this
~WORK~ in the ~Original~, could not have incited me to the Presumption
of laying the ~Translation~ at Your Royal Feet; had not the ~Art~ of
~PERSPECTIVE~, of which it treats, been so nearly ally’d to the Noble
Arts of ~PAINTING~ and ~ARCHITECTURE~. The ~First~ of these Your Majesty
has been pleas’d to honour, as well in expressing a Satisfaction with the
Performances, as in extending Your Royal Munificence to that great Master
thereof, Signor ~Verrio~._
_AND although Affairs of higher Consequence have hitherto deferr’d Your
Majesty’s Commands for Raising ~WHITE-HALL~ from its Ruins; yet has not
~Architecture~ been without Encouragement, under ~Your Majesty’s~ Most
Auspicious Reign: Witness the great Dispatch lately given to those Noble
Fabricks of S. ~PAUL’s~, ~Greenwich~-Hospital, and ~Blenheim~._
_THESE seem to presage, that a Time is coming, when, through the
Blessing of Peace, and the Happy Influence of Your Majesty’s Government;
~WHITE-HALL~ shall become a Structure worthy its Great ~Restorer~, and
its Name as much Celebrated among ~Palaces~, as Your Royal Vertues
are Illustrious among ~Princes~: When Your Majesty’s Subjects shall
exert themselves as much to their Country’s Honour, in the ~Arts~ of
~Design~, and ~Civil Architecture~; as they have already done in the ~Art
Military~, and ~Personal Valour~._
_PRELIMINARY to such Happy Season, I presume this ~Art of Perspective
made Practicable~, may not be improper; being One of the most Useful,
though hitherto the most Obscure and Confus’d, of all the Lineary Arts.
I therefore, with all Submission, beg Leave to supplicate Your Majesty’s
Pardon for this Address, and Your Gracious Protection of this Specimen
of ~English~ Graving; to which if ~Your Majesty~ vouchsafe ~Your~ Royal
~PATRONAGE~, it will effectually animate the future Endeavours of,_
May it please Your Majesty!
_Your Most Obedient Subject_,
J. STURT.
PREFACE TO THIS TRANSLATION.
NOTWITHSTANDING the _Art_ of PERSPECTIVE must be acknowledg’d so
highly and indispensably requisite in the Practice of _Painting_,
_Architecture_, and _Sculpture_; that in the First of these especially,
nothing commendable can be perform’d without its Assistance: Yet such
have been the Difficulties and Obscurities met with in the first
Attempts, and so great the Perplexity and Confusion of Lines in the
Practice thereof; that the best Instructions, hitherto made _English_,
have invited very few to such a Prosecution of this Study, as might
render their Performances of this kind, truly valuable.
’TIS something unaccountable, that, among so many learned Persons as have
handled this Subject, _Priests_, _Architects_, and _Painters_; very few,
if any of them, have given Directions proper for shunning that Disorder
and Confusion of Lines, which, in most Instances, must necessarily
attend the Execution of their Rules: In all or most of which, the whole
Space for the Performance is confin’d between the Lines of the Plan and
Horizon; which, where the Scale is small, and the Height of the Eye not
very much advanc’d, renders the Work exceedingly confus’d; and where
those Lines are coincident, (which frequently happens) the Method becomes
utterly impracticable.
THIS Author’s great Experience in the Practice of _Perspective_, having
furnish’d him with excellent RULES for Shortning the Work, and Obviating
the foremention’d Difficulties; he has here very generously imparted
them, and especially the latter, in the Tenth and Eleventh Figures.
And tho’ on Perusal of the first three or four Plates, this Method may
possibly seem the same that some others have before made use of; yet
whoever shall diligently observe and copy the Rules and Examples of the
succeeding Figures, must necessarily acknowledge the great Advantage this
has in a Perspective-Plan and Upright, clear and distinct; whence the
finish’d Piece is deduc’d, without the least Incumbrance of the Work.
The Explanations of the Rules here given, are short and instructive;
and the Architectonical Designs produc’d to exemplify them, Noble and
Magnificent.
THE Manner of Designing, where the Perspective is drawn on several
Ranges of Frames one behind the other, and such Scenes of Theaters whose
Grooves lie oblique to the middle Line, is also here laid down: And by
our Author’s Method, _Horizontal Perspective_, or that of Ceilings, is
render’d less difficult than the _Vertical_, or that against an upright
Wall. Upon the whole, nothing seems wanting that may make a Work of this
nature complete; unless what concerns Designs which are either Circular,
or abound with many Columns: For the Performance whereof, the Author, as
he promises in the Sixty-fifth Figure, has, in a SECOND Volume, given
a Rule more proper for the purpose; which also may possibly be made
_English_ in due time, if this Part meet with Encouragement.
WHAT the Author once intended should make a Part of that Second Volume,
he afterwards inserted in the Ninety-third and following Figures of
this Book: In the last of which, particular Notice should be taken of
his Conclusion; _That if_ Painters _would not run into inextricable
Errors, they ought as strictly to observe the Rules of_ Perspective, _in
designing the Figures of Men and Animals; as they do in painting Columns,
Cornices, or other Parts of Architecture_.
THAT none therefore be discourag’d in their first Attempts, through the
Brevity or Silence of our Author; (who, writing in a Country where the
Principles of this Art are more generally known than with Us, had no
need to insist so long on some things, as might be thought necessary to
_Beginners_) we shall endeavour to speak as plainly as we can to a point
or two, most liable to be misunderstood, or to prove a Stumbling-Block at
the Entrance; and then add a Word of Advice to such as shall attempt the
putting these Rules in Execution.
THE Author, in both his Explanations of the first Plate, has given some
Account of what he would have his Reader understand, by _Designing in
Perspective_; and a right Conception of this point being of great Use to
facilitate the Work, we thought it not improper, to describe something
more particularly, what is meant by the Art _Perspective_: but shall at
present speak only of That, which, whether Vertical or Horizontal, is
receiv’d on a Flat and Even Superficies; This being of much the more
general Use, and, when rightly understood, renders the Difficulties of
the Circular or Irregular Surfaces, easy and familiar.
PERSPECTIVE is the Art of Delineating, on a flat Superficies, as a
Wall, Ceiling, Canvas, Paper, or the like, the Appearances of Objects,
as seen from One determinate Point: For tho’ in Works of great Length,
Two, Three, or more Points of Sight are sometimes made use of; yet such
may more properly be said to be Several Views conjoin’d, than One Piece
of Perspective: Of which see the Author’s Opinion, at the End of this
Treatise.
IN Perspective, the Eye of the Beholder is esteem’d a Point, from whence
Rays are suppos’d to proceed to every Angle of the Object. The Wall or
Canvas to be painted (which we shall here call the _Section_) is imagin’d
to intervene at right Angles to the Axis of the said Rays, and, by
dissecting them, to receive the Appearance of the Object, in greater or
less Proportion, as the Section is more or less remote from the Point of
Sight. Our Author’s Rule is, That the Distance of the Eye ought to be
equal to the greatest Extent of the Object, whether in Length or Height:
As, to view a Building that is a hundred Foot long, and fifty high; he
would have the Distance a hundred Foot: To view a Tower sixty Foot wide,
and a hundred and fifty Foot high; the Distance should be a hundred and
fifty Foot. This Distance is not strictly to be understood of the Space
between the Eye and the Object, but of the Space between that and the
Section, the Plan of which our Author calls the Line of the Plan, or
Ground-line; for it’s often requisite, that the Section be plac’d at some
Distance before the Object, on account of Projectures of Cornices, and
other Parts of the Work that advance, as in the Eighth Figure.
THE Place of the Eye, with respect to its Height above the Ground,
ought to be such, as is most natural and agreeable to the Object. Thus
in _Architecture_, the Basements and inferior Parts of a Building are
improper to be set above the Eye, and their Cornices and Entablatures
have but an ill Effect when below it. _General_ Perspectives indeed
require the Sight to be taken at a Birds View; and on other Occasions
the Place of the Eye may be vary’d: but the best and most general Rule
is, not to exceed five or six Foot Height above the Ground. The Height
of the Eye above the Ground, thro’ which a Line is drawn, call’d the
_horizontal_ Line, is set on by the same Scale of Proportion, as the
Design bears to the real Work; and the Point of Sight so plac’d therein,
as may render the Object most agreeable. From the Point of Sight, either
on one or both sides in the horizontal Line, you are to set, by the same
Scale, the Distance you stand from the Section. And by means of these
Points of Sight and Distance, and the Measures of the Parts brought on
the Lines of the Plan and Elevation of the Section, by the same Scale;
all the Examples of this Volume are reduc’d into Perspective; as is
manifest on Inspection of the Figures.
WHAT we would add, by way of Advice, is,
I. THAT you very carefully observe, what the Author understands by
_Breadth_, _Length_, and _Height_, in his Explanation of the Fifth Plate,
before you proceed to practise on any Figure; otherwise you’ll certainly
misunderstand him; especially in the Third Figure.
II. THAT the Rules of the Tenth and Eleventh Figures be particularly
regarded, for avoiding Confusion in the Plans and Uprights.
III. THAT from the Disposition of the Perspective-Plans and Uprights,
with respect to the finish’d Pieces in the Twelfth and many following
Figures, you would observe, with what Dispatch the said Pieces may,
without the Help of Compasses, be delineated by your Drawing-Square;
_viz._ the Perpendiculars from the Perspective-Plan, and the level Lines
from the Perspective-Upright, or Section.
IV. THAT you would accustom yourself in Works that have many Lines, to
make the Perspective-Plans and Uprights for each Part distinct, so as to
prevent all Danger of Confusion. Thus you may have one Plan and Upright
for the Basement of a Building; and when that is drawn on your finish’d
Piece, remove them, and place those of the Body of the House; and when
that’s complete, do so by the _Attick_, &c. always observing so to place
the Plan below, and the Upright on one side of your neat Draught, that
your Drawing-Square may command each of them; which will mightily shorten
your Work.
V. THAT the Author’s Advice of taking the Figures in Course, be strictly
follow’d in the Practice; which will be a great means to render the Whole
easy and pleasant.
THIS is the Sum of what we thought most proper to advertise you; and
have only this farther to request, That if any Mistakes may have escap’d
the Press undiscover’d, as we well hope there are few or none, you will
favourably correct and pardon them.
MONITA ad TYRONES.
_Concinnitatem ac symmetriam opticæ delineationes ædificiorum habere
nequeunt, nisi utramque mutuentur ab Architectura. Proinde necesse
est, ut in istius graphide ac intelligentia te aliquandiu exerceas,
donec uniuscujusque elevationis vestigium formare didiceris, ex eoque
eruere sectionem totius longitudinis, ut in Opere toto videre est,
præsertim figuris sexagesimaoctava & septuagesima. Siquidem ex vestigio
& ex sectione derivatur in opticas imagines congrua rerum singularum
profunditas._
_Subjiciam his consilium summi momenti; videlicet, egregiè intelligas
oportet figuram secundam, priusquam progrediaris ad tertiam, idemque
de cæteris dictum velim; nam singulas eo disposuimus ordine, ut quæ
præcedit, necessaria sit ad percipiendas eas quæ sequuntur. Si aliqua
sint in explicatione, quæ initio non intelligas, ipsum schema sæpius
diligenter inspicies; ac vicissim si aliqua desint in schematibus, ex
declarationibus ea supplebis. Lapsus verò quos deprehenderis, facilè pro
tua benignitate, mihi, ut spero, condonabis._
ADVICE to BEGINNERS.
The Perspective of Structures here treated of, can have no Grace or
Proportion, without the Help of Architecture. ’Tis therefore absolutely
necessary, that you employ yourself for some time in Drawing, and the
Study of that Art; till you can readily describe the Plan of any Upright,
and from thence project the Section or Profile, as is shewn through the
whole Course of this Work; and more particularly, in the Sixty-eighth and
Seventieth Figures: Forasmuch as the proper Depth of each Part of the
Perspective, is determin’d by the Plan and Profile thereof.
I shall add this one thing more, which is indeed of the last Importance;
to wit, that you endeavour to understand the Second Figure throughly,
before you proceed to the Third; and so of the rest: they being dispos’d
in such Order, that the Knowledge of the preceding Figure is always
necessary to a right Understanding of that which follows. If you meet
with any thing which at first seems difficult in the Description, a
diligent Inspection of the Figure may relieve you: And on the other
hand, if you find not in the Figure every thing you desire, you may have
Recourse to the Explanation. What Errours you discover in the Work, I
hope you’ll generously overlook and pardon.
AD
Lectorem Perspectivæ studiosum.
_Ars Perspectiva, oculum, licet sagacissimum inter sensus nostros
exteriores, mirabili cum voluptate decipit; eademque necessaria est iis,
quibus in pingendo, tum singulis figuris positionem ac deformationem
suam congruè tribuere, tum colores & umbras, magis vel minus intendere
aut remittere, prout oportet, curæ est. Ad id autem sensim sine sensu
illi perveniunt, qui solo studio Graphidis non contenti, singulis
Architecturæ Ordinibus exactè deformandis assueverint. Nihilominus,
inter multos qui opus hujusmodi magno impetu aggressi hucusque fuerunt,
paucos numeramus, qui animum ipso statim initio non desponderint, ob
magistrorum librorumque penuriam, ordinatè ac perspicuè docentium opticas
projectiones, à principiis hujus artis, usque ad omnimodam perfectionis
consummationem. Quum autem sentiam, longâ multorum annorum exercitatione,
me non minimam facilitatem in hac disciplina mihi parasse: censeo
Studiosorum voluntati me satisfacturum, eorumque profectui consulturum,
si methodos expeditissimas in lucem proferam, ad singulorum Architecturæ
Ordinum opticas delineationes perficiendas, adhibitâ communi regulâ, ex
qua omnia linearum occultarum offendicula sustulimus. Deinde, si tempus
& vires ad aliud Opus conscribendum Bonitas Divina dederit, projectiones
quascunque absolvemus regulâ qua in præsentia uti soleo, ac multò
facilior & universalior est regula communi & vulgata, quamvis hæc sit
fundamentum alterius. Itaque, Lector studiose, constanti animo negotium
tuum suscipe; ac lineas omnes tuarum operationum, ad verum oculi punctum
ducere, ad gloriam scilicet DEI O.M. tecum omninò decerne. Sic votis
honestissimis, ut auguror tibi ac spondeo, feliciter potieris._
TO
The Lovers of Perspective.
The Art of PERSPECTIVE does, with wonderful Pleasure, deceive the Eye,
the most subtle of all our outward Senses; and is very necessary to be
known of all, who in Painting would give a due Place and Proportion to
their Figures, and more or less Strength requisite to the Lights and
Shades of the Picture. This might be insensibly attain’d, if Persons, not
content with the Study of Drawing only, would accustom themselves exactly
to delineate the several Orders of Architecture. Nevertheless, among
many who have hitherto vigorously undertaken this Work, there have been
but very few, who have not been in a manner quite discourag’d, through
want of Masters and Books to teach them clearly and methodically the
Rules of Perspective-Projections, from the first Principles of the Art,
to the entire Perfection thereof. Wherefore, apprehending that by long
and constant Practice in Works of this kind, I had acquir’d a Method
to facilitate the same; I judg’d it might be for the Satisfaction and
Advantage of the Studious, to publish the shortest way for designing in
Perspective the several Orders of Architecture, by a common and easy
Rule, free from the Incumbrances of occult Lines. But if it please God
to give me Life and Health to compose another Book, I shall therein shew
the Method of putting Works into Perspective by the Rule I make use of at
present, which is more easy and general than the common way, though this
be the Foundation of the other. Therefore, Reader, my Advice is, that
you chearfully begin your Work, with a Resolution to draw all the Lines
thereof to that true point, the Glory of GOD; and I durst predict, and
promise you good Success in so honourable an Undertaking.
THE
Approbation of this Edition.
At the Request of the Engraver, We have perus’d this Volume of
PERSPECTIVE; and judge it a WORK that deserves Encouragement, and very
proper for Instruction in that ART.
_Chr. Wren_,
_J. Vanbrugh_,
_N. Hawksmoor_.
[Illustration]
POZZO’s
ARCHITECTURE IN PERSPECTIVE.
[Illustration: FIG. I.]
FIGURA PRIMA.
Explicatio linearum Plani & Horizontis, ac Punctorum Oculi & Distantiæ.
_Ut principia Perspectivæ faciliùs intelligas, pono tibi ob oculos
Templum, in cujus interiori facie, præter cætera, pingendum sit aliquid
ad Perspectivam pertinens. Templi hujus vestigium geometricum est ~A~,
elevatio geometrica in longum est ~B~, in latum est ~C~. In ~A~ est locus
Hominis aspicientis lineam ~DE~, cui paries pingendus incumbit. In ~B~
idem Homo ex eâdem distantiâ intuetur lineam ~FG~, quæ refert elevationem
parietis. In figura ~C~ supponimus Hominem consistere è regione ipsius
parietis: easdemque proportiones mensuratum translatas esse ex vero
pariete in figuram ~C~, quæ ipsum in parvo repræsentat._
_Prima ergo linea ~HI~ dicitur linea terræ vel plani, ex quâ incipit,
eidemque incumbit ædificium. Secunda linea ~NON~ priori parallela,
dicitur horizontalis, in quâ ponitur ~O~ punctum oculi, & ~N~ punctum
distantiæ. Duo autem puncta distantiæ à nobis posita sunt, ut unum
adhibeas ex quâ parte volueris; nam ad figuras opticè contrahendas
sufficit unum punctum distantiæ: nec fieri potest ulla optica delineatio,
quin primo loco designentur duæ parallelæ, una plani seu terræ, altera
horizontis, notando in lineâ horizontis, punctum oculi, seu opticum,
& punctum distantiæ. Porrò unam eandemque rem triplici Schemate
repræsentare oportuit, ut videas, locum ex quo aspicienda est figura ~C~
esse punctum ~N~ unius ex rectis ~NO~, quam concipere debemus veluti
normaliter infixam in ~O~; ac distantiam inter ~O~ & ~N~ eandem esse
debere cum distantiâ inter ~A~ & ~DE~, inter ~B~ & ~GF~._
_In picturis multum spatii occupantibus, punctum oculi poni solet
in medio lineæ horizontalis: atque ubi altitudo picturæ sit major
latitudine, distantia ~NO~ fiet æqualis altitudini. Si latitudo picturæ
sit major altitudine, distantia ~NO~ fiet æqualis latitudini; ita
enim unico intuitu totum picturæ spatium comprehendi poterit. Porrò
quamvis eadem distantia diverso modo adhibeatur in vestigio ~A~, & in
elevationibus ~B~ & ~C~; nihilominus sectiones visualium cum pariete
vestigii ~A~, & elevationis ~B~, omninò conspirant cum sectionibus
visualium figuræ ~C~._
_Jam si velimus ut spectatori in ~A~ & ~B~ paries depictus videatur
distare à lineis ~DE~ & ~GF~, quanta est longitudo quadrati ~P~, cujus
elevatio est ~Q~; ex punctis ~A~ & ~B~ fiant visuales ad puncta extrema
quadrati, notando sectiones visualium cum pariete ~DE~ & ~GF~, qui ab
aliis vocatur velum, vitrum diaphanum, sectio, tela, vel tabula. Invenies
autem, lineas ~RS~ ac ~TV~ esse æquales, ac similiter lineas ~XZ~ & ~YK~;
& sic de aliis._
The First Figure.
_Explication of the Lines of the Plan and Horizon, and of the Points of
the Eye and of the Distance._
That you may the better understand the Principles of Perspective, here
is presented to your View a Temple, on the inner Wall of which, amongst
other things, one would paint something in Perspective. The Geometrical
Plan of this Church is A, the Geometrical Elevation, or Upright,
lengthwise is B, breadthwise is C. In A is the Place from whence a Man
beholds the Line DE, which is the Plan of the Wall that is to be painted:
In B the same Man, from the same Distance, looks upon the Line FG, that
represents the Elevation of the Wall. In Fig. C, the Man is supposed to
stand opposite to the said Wall; and this Figure contains, in Little, the
very same Proportions of Measures transferr’d from the real Wall.
The first Line therefore HI is call’d the Ground-line, or Line of the
Plan, at which the Edifice begins, and on which it stands. The second
Line NON, parallel to the former, is call’d the Horizontal Line, wherein
is plac’d O the Point of the Eye, and N the Point of the Distance. Two
Points of Distance are here laid down, that you may make use of which you
please; for that on one Side only is sufficient for the fore-short’ning
Figures in Perspective: Neither can any Optick Delineation, or
Perspective, be described, without first making two Parallels; one of the
Plan, or Ground-line, the other of the Horizon; marking, in the Line of
the Horizon, the Point of the Eye, or Sight, and the Point of Distance.
It was thought besides expedient to put one and the same Thing into three
Schemes or Designs, to let you see, that the Place, from which the Figure
C is to be look’d upon, is the Point N, one of the right Lines NO, which
must be conceived as fixt at right Angles into O; the Distance ON being
the same as that between A and DE in the Plan, or between B and GF in the
Upright.
In Pictures taking up a great deal of Room, the Point of Sight ought to
be made in the middle of the Horizontal Line; and where the Height of
the Picture happens to be greater than the Breadth, the Distance NO
must be made equal to the Height. If the Breadth of the Picture exceed
the Height, the Distance NO must be made equal to the Breadth: For so
will the Extent of the Picture be the better comprehended, or receiv’d,
at one View. And altho’ the same Distance may seem to be used in a
different manner in the Plan A, and in the Elevation B, from what it is
in C; nevertheless the Sections of the visual Rays, with the Wall of the
Plan A, and of the Elevation B, have a perfect Correspondence with the
Sections of those of the Figure C.
Now, if to the Spectator in A and B, we would have the farthest Part of
the Work seem to recede from the Lines DE and GF, as much as the Square
P does, whose Elevation is Q; draw from the Points A and B, the visual
Rays to the extreme Points of the Square P and Q; noting the Sections
they make with the Walls DE and GF; which by some is call’d the Veil,
Transparent Medium, Section, Cloth, or Table: and you’ll find RS equal to
TV, XZ equal to YK; and so of the rest.
[Illustration: FIG. II.]
FIGURA Secunda.
Modus delineandi opticè Quadratum.
_Ante descriptionem opticam quadrati ~A~, quod fingimus delineatum esse in
papyro separatâ, ducendæ sunt duæ lineæ parallelæ; altera plani, altera
horizontis, ut jam docuimus; notando in linea horizontis punctum oculi
~O~, & punctum distantiæ ~E~. Tum translatâ in lineam plani latitudine
ac longitudine ipsius quadrati ~A~, ita ut linea ~CB~ sit æqualis
latitudini, & ~DC~ sit æqualis longitudini. Ex punctis ~B~ & ~C~ fiunt
visuales ~BO~, ~CO~ ad punctum oculi; ex puncto ~D~ fit recta ~DE~ ad
punctum distantiæ. Demum ubi visualem ~CO~ secat recta ~DE~, fit ~GF~
parallela ad ~CB~; habesque quadratum opticè contractum._
_Compendium temporis & laboris facies, præsertim in schematibus quæ
abundant lineis, si chartulam in medio complicaveris, eademque utaris, ut
latitudinem ac longitudinem quadrati transferas in lineam plani._
The Second Figure.
_Manner of delineating a ~Square~ in Perspective._
Before the _Square_ A, which is supposed to be drawn on a separate Paper,
can be laid down in Perspective, two parallel Lines must be drawn; one of
the Plan, the other of the Horizon, as is already intimated; noting in
the Horizontal Line the Point of Sight O, and the Point of Distance E.
Then, when the Length and Breadth of the Square A shall be transferr’d
into the Line of the Plan, so that the Line CB be equal to the Breadth,
and DC be equal to the Length, let the visual Lines BO, CO be drawn from
the Points B and C to the Point of Sight O, and the right Line DE from
the Point D to the Point of Distance. Lastly, where the Line DE cuts the
Visual CO, make GF parallel to CB: and you have the _Square_ Optically
contracted, or fore-shorten’d in Perspective.
To spare Time and Pains, especially in Figures that abound in Lines, fold
your Paper in the middle, and make use of it to transfer the Breadth and
Length of the Square, into the Line of the Plan.
[Illustration: FIG. III.]
FIGURA TERTIA.
Optica delineatio rectanguli, alterâ parte longioris.
_Latitudo ~BC~ rectanguli ~A~ ponatur in linea plani, adhibito circino,
vel chartulâ complicatâ; & ex punctis ~B~ & ~C~ fiant visuales ad ~O~,
punctum perspectivæ. Tum papyro ex altera parte iterum complicatâ,
notetur longitudo ~CD~ rectanguli; ducendo tum rectam ~DE~ ad punctum
distantiæ, tum rectam ~FG~ parallelam ad ~BC~, quæ complebit opticam
delineationem rectanguli._
_Altera figura ostendit complicationem cruciformem papyri, quæ adhiberi
potest in delineandis rectangulis, seu latitudo eorum sit major
longitudine, aut vice versâ; seu latitudo & longitudo sint æquales._
The Third Figure.
_The Delineation of an Oblong ~Square~ in ~Perspective~._
Let the Breadth BC of the Square A, be plac’d in the Line of the Plan,
by the Compass, or a folded Paper, and from the Points B and C, make the
Visuals to the Point of Sight O. Then fold your Paper cross-wise, and
mark CD the Length of the Square, drawing the Line DE to the Point of
Distance, and the Line FG parallel to BC, which will complete the Optick
Delineation of the oblong Square.
The other Figure shews the Folding of the Paper cross-wise, which is of
ready use in delineating Squares, whose Breadth exceeds their Length, or
_vice versâ_; or whose Length and Breadth are equal.
[Illustration: FIG. IV.]
FIGURA QUARTA.
Optica descriptio quadrati duplicis.
_Iam incipies frui compendio papyri complicatæ. Nam eam admovendo lineæ
plani, nullo negotio notare poteris puncta ~1~, ~2~, ~3~, ~4~, ~5~, ~6~,
linearum visualium, quæ ducentur ad ~O~ punctum perspectivæ. Exinde
complicatâ rursum chartulâ in crucem ad ~P~, notabuntur hæc puncta; ~7~,
coincidens cum puncto ~6~, nisi quadratum distet à linea plani; ~8~, ~9~,
~10~. Ductis autem rectis ex ~8~, ~9~, ~10~, ad punctum ~E~, ubi secant
visualem ~6~, ~7~, ~O~ fient parallelæ, eritque completa delineatio._
_In medio quadrati ~B~, aliud quadratum facilè describetur, ducendo
diagonales seu diametros ab angulo ad angulum, ut in figura._
The Fourth Figure.
_The Optical Delineation of a double Square._
Here you’ll find the Advantage of your folded Paper; for, applying it
to the Line of the Plan, you readily mark the Points 1, 2, 3, 4, 5, 6,
of the visual Lines, which must be drawn to the Point of Sight O. Then
folding the Paper cross-wise, as in P, you mark the Points 7, 8, 9,
10, placing the Point 7 on that of 6, unless you would have the Square
removed within the Line of the Plan. Then from 8, 9, 10, drawing Lines
to the Point of Distance E; where they intersect the Line 6, 7, O, draw
Parallels to the Line of the Plan; and your Work is done.
Within the Square B, you may easily inscribe another Square, by help of
the Diagonals; as may be seen in the Figure.
[Illustration: FIG. V.]
FIGURA QUINTA.
Vestigia quadratorum, cum elevationibus.
_Suppositis iis quæ jam diximus de Contractione optica Quadratorum,
notandum est, vestigium primi Quadrati distare à linea plani spatio ~BA~
opticè contracto; quia linea ~BD~ habet à visuali ~AO~, distantiam ~BA~.
Eodem modo Quadratum secundum distat à linea plani spatio ~EA~, & sic
deinceps._
_Velim observes, in omnibus his Quadratis lineas longitudinis esse partes
visualium, lineas vero latitudinis esse parallelas lineæ plani, & in
primo Quadrato duci ex punctis, in quibus lineæ ~BD~, ~CD~, tendentes ad
punctum distantiæ, secant visualem ~AO~._
_Sub singulis vestigiis Quadratorum, delineavimus alia omnino similia,
per quæ parvo labore fient tres bases, erigendo ad libitum duas primas
perpendiculares æquales; ac ducendo tum duas visuales ad punctum oculi
~O~, tum reliquas, ut in figura. Supponendum est autem, geometricam
altitudinem cujuslibet rei desumi ex lineis normalibus ad lineam plani;
quemadmodum latitudo & longitudo geometrica desumuntur ex eadem linea
plani._
_Tres aliæ bases inferiores formantur sine lineis occultis ex vestigio &
ex elevatione longitudinis opticè deformatis, adhibendo solas altitudines
ac latitudines angulorum. Nomine altitudinis intelligimus distantiam
cujuslibet anguli à linea plani; nomine latitudinis intelligimus
distantiam anguli ab una aliqua linea normali ad lineam plani; dummodo
hæ normales eandem habeant positionem respectu basium, & respectu
vestigiorum & elevationum. Quemadmodum autem per concursum altitudinis
~FG~, & latitudinis ~HI~, ope duorum circinorum invenitur unus angulus in
una basi; ita inveniuntur cæteri tum in ea, tum in reliquis._
The Fifth Figure.
_Plans of Squares, with their Elevations._
Besides what has been already said of the fore-short’ning of Squares in
Perspective, it is convenient to observe, That the Foot of the first
Square is here set within the Line of the Plan, as much as the Space BA
optically contracted; because the Line BD has the Distance BA from the
Visual AO: And in like manner, the second Square is distant from the Line
of the Plan the Space EA; and so for the rest.
I would have you observe in all these Squares, That by the _Length_ I
always understand part of the visual Lines, and by the _Breadth_ those
parallel to the Ground-line; which in the first Square are drawn from
the Points in which the Lines BD, CD, tending to the Point of Distance,
intersect the Visual AO.
Under the Plans of these Squares are described three others just like
them, which are easily converted into three Bases, by erecting, at
pleasure, the two first Perpendiculars of equal Height, and thence
drawing two Visuals to the Point of Sight O, which also bound the rest,
as in the Figure. Observe also, That the Geometrical Height of every
thing is to be set perpendicularly from the Ground-line, or Line of the
Plan, as the Geometrical Length and Breadth are also placed on the same
Line.
The three other Bases below are form’d without the Help of Occult Lines,
by making use only of the Heights and Breadths of the Angles, taken
from the Perspective Plan and Upright. By _Height_ I understand the
Distance of each Angle, or Corner, from the Ground-Line; By _Breadth_,
the Distance of an Angle, or Corner, from any Line perpendicular to the
Ground-line; provided these Lines have always the same Place in respect
of the Bases, as they have in respect of the Perspective Plan and
Upright. And as, by the Help of two Compasses, the Height FG, and the
Breadth HI determine the Corner of the first Base; so, in like manner,
are found the Corners of the other Bases.
[Illustration: FIG. VI.]
FIGURA SEXTA.
Modus opticæ delineationis, absque lineis occultis.
_In hac figura sexta, vestigium geometricum ~B~ seorsim posui ab
elevatione geometrica ~A~, ut deinceps faciemus. Vestigium ~B~ opticè
contractum in ~E~ est ~NMRS~; elevatio contracta longitudinis vestigii
est ~FTSN~. Posito autem quòd altitudines ~FN~, ~1, 5~, ~2, 6~, sint
æquales; latitudines ~NM~, ~1, 2~, ~5, 6~, sint æquales; & rectæ ~NM~,
~5,6~, sint in linea ~X~ plani; rectæ ~FN~, ~1, 5~, sint in perpendiculo
~V~: anguli ~3~ & ~4~ basis ~C~ habent eandem elevationem seu distantiam
à linea ~X~ plani, quam habet angulus ~T~: anguli ~1~ & ~2~ habent
elevationem, quam angulus ~F~: anguli ~3~ & ~7~ habent eandem latitudinem
seu distantiam à perpendiculo ~V~, quam habet angulus ~R~: anguli ~2~ &
~6~ habent eandem latitudinem, quam habet angulus ~M~._
The Sixth Figure.
_The Manner of designing in Perspective, without occult Lines._
In this sixth Figure, I have design’d the Geometrical Plan B separately
from the Geometrical Elevation A, as I shall always do hereafter. The
Plan B optically contracted, or put in Perspective, in E, is NMRS; the
Elevation of its Length in Perspective is FTSN. Then supposing the
Heights FN, 1,5, 2,6, equal; and the Breadths NM, 1,2, 5,6, equal; the
Lines NM, 5,6, to be in the Line of the Plan X; and the Lines FN, 1,5, in
the Perpendicular V: the Angles 3 and 4 of the Base C have the very same
Elevation or Distance from the Line of the Plan X, as has the Angle T:
the Angles 1 and 2 have the same Elevation with the Angle F: the Angles 3
and 7 have the same Breadth or Distance from the Perpendicular V, as the
Angle R has: the Angles 2 and 6 have the same Breadth, as the Angle M has.
[Illustration: FIG. VII.]
FIGURA SEPTIMA.
Aliud exemplum vestigii geometrici, cum elevatione longitudinis.
_Si delineanda sit basis dissecta in quatuor partes, fiat vestigium ~A~
cum suis divisionibus longitudinis ~ED~ & latitudinis ~CD~. Easdem vero
divisiones latitudinis habebit in ~EF~ elevatio ~B~ quæ pertingit usque
ad ~X~. Porro ad contractionem opticam vestigii adhibebitur papyrus
complicata in latum & in longum, transferendo in lineam plani latitudinem
& longitudinem vestigii. Deinde nullo negotio fiet optica deformatio
elevationis, ut clarè positum est in figura. Quomodo autem ex vestigio &
ex elevatione longitudinis opticè imminutis eruatur basis nitida sine
lineis occultis, ex præcedentibus manifestum est. Optarem ut per assiduam
circini tractationem in hac methodo exercenda operam sedulò ponas; quum
ex ea pendeat omnis facilitas delineationum opticarum._
The Seventh Figure.
_Another Example of a Geometrical Plan and Upright, put in Perspective._
For drawing in Perspective a Pedestal, or Base, divided into four Parts,
make the Plan A with its Divisions of Length ED, and of Breadth CD;
and the same Divisions of Breadth EF, in the Elevation B, prolong’d
to X. Then make the Perspective-Plan, by transferring the Breadth and
Length into the Ground-line, by means of your Paper folded cross-wise.
From which Plan the Perspective-Upright is very easily made, as may
be plainly seen in the Figure. How the Base below, without occult
Lines, is made from the Perspective-Plan and Upright, is manifest from
what has been said before. I could wish you would be very diligent in
the Practice of this Method by the Compass; because the Dispatch of
Perspective-Delineations chiefly depends thereon.
[Illustration: FIG. 8.]
FIGURA OCTAVA.
Optica projectio stylobatæ.
_Si libitum fuerit delineare stylobatam, cum projecturis in summo &
imo, incipies ab elevatione geometrica ~A~, ducendo occultas ad id
necessarias, tum versus perpendicularem ~L~, tum deorsum pro vestigio
geometrico ~B~, cujus distantiæ transferentur in spatium ~G~. Si mensuræ
longitudinis distent spatio ~C~ à mensuris latitudinis, vestigium
deformatum videbitur distare à linea ~K~ plani, quantum est idem spatium
~C~. In construenda optica elevatione ~D~, visuales ex punctis lineæ ~L~
dabunt lineas latitudinis; lineas vero altitudinis accipies ex lineis
vestigii contracti, ut in figura. In formando stylobata nitido ~EF~,
locum anguli ~H~ dabit concursus latitudinis ex linea ~L~ usque ad ~M~, &
altitudinis ex linea ~K~ usque ad ~I~. Concursus tum ejusdem altitudinis,
tum latitudinis ex ~L~ usque ad ~O~, dabit angulum ~N~. Demum altitudinem
anguli ~P~ accipies ex ~K~ usque ad ~Q~; latitudinem ex ~L~ usque ad ~R~._
The Eighth Figure.
_The Projection of a Pedestal in Perspective._
If you would draw a Pedestal, with the Projecture of its Cap and Base,
you must begin with the Geometrical Elevation A, by drawing such occult
Lines as are necessary, as well sideways to the Perpendicular L, as
downwards for making the Geometrical Plan B, whose Distances must be
transferr’d, and carry’d into the Space G. If the Measures of the Length
be placed the Distance of the Space C, from those of the Breadth, the
Perspective-Plan will then appear removed within the Ground-line K, as
much as the said Space C is. In the Construction of the Perspective
Elevation D, the Visuals drawn from the Points of the Line L give the
Lines of the Breadth; and those of the Height are taken from the Lines
of the Perspective-Plan, as in the Figure. In delineating the clean or
finish’d Pedestal EF, the Intersection of the Breadth from L to M, with
the Height from K to I, gives the precise Place of the Corner H. The
Intersection of the same Height with the Breadth LO gives the Angle N.
Lastly, the Angle P is found by the Intersection of the Height KQ, with
that of the Breadth LR.
[Illustration: FIG. IX.]
FIGURA NONA.
Optica delineatio Architecturæ Jacobi Barozzii; & primum, de Stylobata
Ordinis Etrusci.
_Perspectiva nusquam clariùs emicat, quàm in Architectura. Iccirco tibi
ob oculos pono Architecturam Jacobi Barozzii, quem à patria nuncupant ~Il
Vignola~, reliquis fortasse usitatiorem; in eaque continetur elevatio
geometrica singulorum quinque Ordinum, qui vocantur, Etruscus, Doricus,
Ionicus, Corinthius, & Romanus, vel Compositus; delineando seorsim partes
cujuscunque Ordinis in figuris grandioribus. Elevationi geometricæ
suum vestigium nos addemus; ex vestigio autem & ex elevatione opticè
deformatis, eliciemus apparentias solidorum juxta regulam traditam.
Exempli gratia, si delineare velis stylobatam quadratum & pilam Ordinis
Etrusci, præter elevationem geometricam ~A~ delineare oportet vestigium
geometricum ~B~; ex ambobus autem opticè contractis formatur stylobata
nitidus ~D~, cum anta & pila existente ad latus, accipiendo altitudines
à linea plani, latitudines à linea perpendiculari ad ipsum planum. In
alia delineatione posuimus pilam ex adverso, ut eis omni modo delineandis
assuescas._
_Ad vitandam confusionem linearum, proderit ut figuræ fiant his nostris
multò grandiores: in quem finem singulis paginis apposita est scala
modulorum. Hoc nomine intelliguntur partes æquales, in quas dividuntur
lineæ latitudinis & altitudinis elevationum geometricarum; ac lineæ
latitudinis & longitudinis vestigiorum geometricorum. Si moduli sint
parvi, subdividuntur singuli in duodecim partes; ac prout fuerint
grandiores, subdividuntur in partes triginta, vel sexaginta, vel
centumviginti. ~Modulos Etruscum Doricúmque in partes duodecim; reliquos
autem in octodecim partiti sunt.~_
The Ninth Figure.
_The Architecture of ~Vignola~ in Perspective; and first, of his Pedestal
of the ~Tuscan~ Order._
Perspective never appears more graceful, than in Architecture; for
which Reason I present you with that of _James Barozzi_, from his
Country generally call’d _Vignola_; which perhaps is more in use than
any other; and contains the Geometrical Upright of each of the five
Orders, _viz._ the _Tuscan_, _Dorick_, _Ionick_, _Corinthian_, and the
_Roman_, or _Composite_; together with a separate Delineation of the
Parts of each Order, in larger Figures. To this Geometrical Elevation
we shall add the Plan, and, from both of them reduc’d into Perspective,
shall draw the Appearances of Solids, according to the Rule before laid
down. For Example: If you would draw the square _Tuscan_ Pedestal, and
its Pilaster, you must, from the Geometrical Elevation A, make the
Geometrical Plan B; and from both of them reduc’d in Perspective, draw
the finish’d Pedestal D, with that of its Pilaster on the Side, by
taking the Heights from the Ground-line, and the Breadths from a Line
perpendicular to the same. On the other Side we have placed the Pilaster
on the Back-part, that you may practise the Drawing them in any manner.
For avoiding the Confusion of Lines, I advise you to make the Figures
as much larger than ours as you can; for which purpose there is annex’d
a Scale of Modules to each Figure. By this Name we understand the equal
Parts, into which the Lines of the Breadth and Height of the Geometrical
Uprights, and of the Breadth and Length of the Geometrical Plans, are
divided. If the Modules are small, they are subdivided into twelve Parts;
and according as they are larger, into thirty, sixty, or an hundred and
twenty Parts. _I have divided the ~Tuscan~ and ~Dorick~ Module into
twelve Parts, and that of the other Orders into eighteen._
[Illustration: FIG. 10.]
FIGURA DECIMA.
Optica deformatio stylobatæ Dorici; ubi de modo vitandi confusionem, in
vestigiis delineandis.
_Elevatio geometrica ~B~ stylobatæ Dorici continet eandem symmetriam
partium quæ habetur apud Barozzium; ex eaque eruitur vestigium
geometricum ~A~ per lineas occultas, quæ descendant ex punctis
terminativis præcipuarum projecturarum. Earundem projecturarum distantiæ
transferendæ sunt in lineam elevationis, notando puncta quæ necessaria
sunt ad deformandam elevationem longitudinis stylobatæ._
_Si ob propinquitatem lineæ plani ad lineam horizontis, vestigium evadat
confusum, fiant in distantia congrua sub linea plani aliæ lineæ planorum
ipsi parallelæ, cum suis vestigiis. Quid autem emolumenti afferat
distantia major præ minori, ostendit vestigium ~E~ distinctiùs vestigio
~D~. Singula hæc vestigia fiunt notando in linea cujuslibet plani
mensuras latitudinis & longitudinis vestigii ~A~, & ducendo lineas ad
eadem puncta oculi ac distantiæ._
_Stylobatam nitidum descripsimus ex parte ~G~, tum ex necessitate, tum
ut videas, pro distantia ~FO~, usurpandam esse distantiam ~GO~ penitus
æqualem._
The Tenth Figure.
_A ~Dorick~ Pedestal in Perspective; with the Manner of avoiding
Confusion, in designing the Plans._
The Geometrical Elevation B has the same Members and Proportions, as the
_Dorick_ Pedestal of _Vignola_; and the Geometrical Plan A is form’d, by
letting fall occult Lines from the principal Projectures of the Upright.
Occult Lines are also to be continued to the Perpendicular F, from the
several Members requisite for elevating in Perspective the Length of the
Pedestal.
When, by reason of the too near Approach of the Ground-line to that of
the Horizon, the Plan becomes thereby confus’d; draw at a convenient
Distance underneath, other Ground-lines parallel to the first; together
with the Plans in Perspective. And of what Advantage the Removal of the
Ground-line is, is evident from the Plan E, which is much more distinct
than the Plan D. Each of these Plans is made, by marking upon its
respective Ground-line the Measures of the Breadth and Length of the Plan
A, and by drawing Lines to the same Points of Sight and Distance, which
were first assign’d.
We have placed the finish’d Pedestal on the Side G, partly for want of
Room, and partly to shew, that the Point of Distance G is there made use
of, GO being equal to FO.
[Illustration: FIG. XI.]
FIGURA Undecima.
Stylobatæ Ionici deformatio; ubi de vitanda confusione in elevationibus.
_Tum in figura præcedenti, tum rursus in hac, ostendimus quid agendum sit
ubi vestigia ~AA~ nimium obliquentur, unde oritur confusio; præcipuè
in lineis parallelis quæ exhibent latitudines. Non minor difficultas
interdum occurret in elevationibus longitudinis opticè deformandis; quòd
videlicet, ob nimiam earum obliquitatem, pervium non sit altitudines
singularum projecturarum probè discernere ac designare. Ad scopulos
istos declinandos, loco elevationis ~B~ adhibebitur elevatio ~C~, quæ
distinctior est, tum illâ, tum duabus intermediis ~D~ & ~E~, ob majorem
distantiam quam habet à puncto oculi._
_In delineando stylobata nitido, latitudines accipientur ex ultimo
vestigio, ponendo unam cuspidem circini in linea perpendiculari, quæ
proxima est literæ ~O~: altitudines accipientur ex elevatione ~C~,
ponendo unam cuspidem circini in linea plani, ut in præcedentibus
ostensum est._
The Eleventh Figure.
_The ~Ionick~ Pedestal in Perspective; with the Manner of avoiding
Confusion, in Elevations._
As in the foregoing Figure, so in this also is shewn what is to be done,
where the Plans AA lie so oblique, as to cause Confusion; especially in
the Parallel-lines which give the Breadths. The like Inconvenience often
happens in elevating the Lengths in Perspective; when by their too near
Approach to the Point of Sight, the Contour of the several Mouldings
can’t be distinctly delineated: For avoiding which, instead of B you may
make use of the Elevation C, which is not only more distinct than the
former, but better than either of the two intermediate ones D or E, by so
much as it is more remote from the Point of Sight.
In designing the finish’d Pedestal, the Breadths are taken from the
lowest Plan, by setting one Point of the Compasses in the perpendicular
Line OL: the Heights are taken from the Elevation C, by placing one Point
of the Compasses in the Ground-line, as has been shewn before.
[Illustration: FIG. XII.]
FIGURA Duodecima.
Deformatio stylobatæ Corinthii, cum duabus pilis.
_Ornatus gratiâ, stylobatæ Corinthio additæ sunt pilæ, quæ pone columnas
locari solent. Ut autem pilæ clariùs appareant, columna omissa est,
cujus deformandæ rationem nondum tradidimus. Mensuras omnes ex Barozzio
acceptas esse demonstrat ipsum schema, in quo elevatio geometrica
stylobatæ est ~A~; vestigium ejus geometricum est ~B~: pilæ ~CC~.
Vestigium opticè contractum est ~D~, elevatio longitudinis stylobatæ
opticè contracta est ~E~, ac methodo consuetâ ex iis eruetur stylobata
nitidus cum suis pilis._
The Twelfth Figure.
_The ~Corinthian~ Pedestal, with its Pilasters, in Perspective._
For Ornaments sake, we have added to this _Corinthian_ Pedestal the
Pilasters, which are usually placed behind Columns: And that they may be
the more perspicuous, have left out the Column, not having yet shewn the
Manner of putting it in Perspective. The Scheme shews the Measures are
taken from _Vignola_; in which the Geometrical Upright of the Pedestal is
A; the Geometrical Plan of the same is B; that of the Pilasters CC. The
Plan in Perspective is D, the Elevation in Perspective is E; from which
the finish’d Pedestal and Pilasters are drawn by the usual Method.
[Illustration: FIG. XIII.]
Figura Decimatertia.
Projectio stylobatæ, ordinis Compositi.
_Quum pagina non caperet integrum stylobatam tantæ molis, fingere
oportuit detractum illi esse aliquid de trunco; ac partem supremam
stylobatæ sustentari ab infima, non immediatè, sed per quatuor asseres;
eisque impositam fuisse adjumento funium suspensorum ex trochlea.
Elevatio geometrica stylobatæ est ~B~; vestigium geometricum est ~A~. Ex
his eruitur optica delineatio vestigii ~C~ & elevationis ~D~. Ac postea
formatur stylobata nitidus ~E~, accipiendo latitudines ex vestigio ~C~,
altitudines ex elevatione ~D~._
The Thirteenth Figure.
_The Projection of a Pedestal, of the Composite Order, in Perspective._
Wanting Room in this Page to describe so large a Pedestal entire, we
imagine it to have lost part of its Trunk, and the upper part to be set
on the lower; not immediately, but on four Cross-pieces that intervene;
and for placing it thereon, we suppose the Assistance of Ropes and a
Pulley. The Geometrical Elevation of the Pedestal is B; its Plan A; from
whence are found their Projections in Perspective D and C. Then taking
the Breadths from the Plan C, and the Height from the Elevation D, you
complete the finish’d Pedestal E.
[Illustration: FIG. XIV.]
Figura Decimaquarta.
Deformatio circulorum.
_Ut stylobatis imponere liceat columnas cum suis basibus & capitellis,
docendus est modus qui servandus est in projectione optica circulorum,
tum singularium, tum duplicium aut multiplicium circa idem centrum._
_Vestigium geometricum ~A~ constat quadrato in quatuor partes æquales
diviso, cui circulus inscribitur, additis diagonalibus: & ubi hæ secant
circulum, fiunt rectæ parallelæ ad singula latera ipsius quadrati.
Deinde quadratum cum omnibus divisionibus opticè imminuitur; ac tum per
quatuor puncta ubi tres lineæ rectæ se intersecant, tum per quatuor
extrema reliquarum duarum diametrorum circuli, ducetur cum venustate
circumferentia circuli ~B~. Si addere velimus alium circulum, vestigio
geometrico ~C~ inscribetur aliud quadratum; indeque habebitur optica
delineatio duplicis circuli ~D~. Inter hos duos quomodo liceat describere
tertium, per octo sectiones quadratorum, ostendunt figuræ ~E~ & ~F~. Uno
verbo, circuli describuntur per quadrata, adhibendo sectiones visualium
cum parallelis ad lineam plani; ac nullum est punctum in quadratis &
circulis ~A~, ~C~, ~E~, cui per sectiones illas nequeat inveniri punctum
correspondens in quadratis & circulis ~B~, ~D~, ~F~. Nihilominus ubi opus
habeas pluribus circulis, autor tibi sum ne multiplices quadrata, plus
confusionis allatura tibi quam adjumenti._
The Fourteenth Figure.
_Circles in Perspective._
That upon Pedestals you may be able to place Columns with their Bases and
Capitals, it is requisite you should know the Manner of putting Circles
into Perspective; whether single, double, or many concentrick.
The Geometrical Plan A consists of a Square with a Circle inscrib’d,
whose Diameters divide it into four equal Parts; and the Diagonals
being drawn where they intersect the Circle, continue Lines parallel
to each Side of the Square. The Square, with all its Divisions, being
put in Perspective; by the four extreme Points of the Diameters, and by
those of the Intersection of the Diagonals, you neatly trace by hand
the Circumference B. If you would add another Circle, you must inscribe
another Square, as in the Plan C; from whence you find in Perspective
the double Circle D. Between these two Circles, you may, by the eight
Intersections of the Squares, describe a third; as is evident by the
Figures E and F. In a word, all Circles are described by the Help of
Squares, tracing them by the Intersections of the visual Lines, with
those parallel to the Ground-line: Nor is there any Point in either the
Squares or Circles A, C, E, whose correspondent Point may not be readily
found by such Sections, in the respective Squares and Circles B, D, F.
Nevertheless, where your Work requires many Circles, I would advise you
to use as few Squares as possible; lest they perplex, rather than assist
you.
[Illustration: FIG. XV.]
Figura Decimaquinta.
Optica delineatio Columnæ.
_Descripturi frustum cylindricum ~I~ uniforme, fiet elevatio ~A~, &
vestigium geometricum ~B~, saltem quoad medietatem. Ex hoc opticè
deformato, ut vides in ~C~, ducendæ sunt parallelæ tum latitudinis ad
visualem ~D~, tum elevationis ad visualem ~E~; ex quibus describentur
circuli opticè contracti ~F~ & ~L~, accipiendo latitudines ex vestigio
~C~, altitudines ex perpendiculari ~M~; & juxta hanc methodum circuli
~F~ & ~L~ fiunt sine ope quadratorum. Demum ducendæ sunt perpendiculares
~G~ & ~H~, quæ tangant circulos ~F~ & ~L~ in punctis terminativis maximæ
latitudinis._
_Nullum est punctum in vestigio ~C~, cui per lineas latitudinis &
elevationis nequeat inveniri locus correspondens in circulo ~F~. Exempli
gratia; locus puncti ~7~ est punctum ~6~. Hunc autem locum habemus per
tres lineas, ~CD~, ~DE~, ~E7~._
_In delineandis duobus frustis cylindricis, cum summo & imo scapo, eandem
regulam servare oportebit._
The Fifteenth Figure.
_A Column in Perspective._
Being to describe Part of the Shaft of a Pillar without Projectures, make
the Elevation A, and the Geometrical Plan B, at least to the middle:
From this brought into Perspective, as you perceive in C, must be drawn
Parallels both of Breadth to the Visual D, and of Elevation to the Visual
E; from which are described the Circles in Perspective F and L, taking
the Breadths from the Plan C, and the Heights from the Perpendicular M:
And according to this Method the Circles F and L are made, without the
Help of Squares. Lastly, draw the Perpendiculars G and H, by the Points
which terminate the greatest Breadth of the Circles F and L.
There is not a Point in the Plan C, but what, by means of the Lines of
Breadth and Elevation, may be found in the Circle F. For Instance; the
Place of the Point 6 is 7, which is found by the three Lines CD, DE, E7.
In designing the two Pieces of a Pillar, with the Projecture of the
Fillet at Head and Foot, you must observe the very same Rule.
[Illustration: FIG. XVI.]
Figura Decimasexta.
Optica projectio basis Etruscæ.
_Ex elevatione geometrica ~A~ eruitur vestigium ~B~. Hoc autem deformato
in ~C~ & ~D~, ex circulis vestigii ~C~ habentur latitudines columnæ,
quadræ, ac tori triplicis basis: & eodem modo ex vestigio ~D~ habentur
latitudines quadræ ac tori ultimæ basis. Ex maximis latitudinibus
circulorum vestigii ~C~ ereximus perpendiculares ad partes quæ ipsis
respondent in basi; ut agnoscas quænam sint puncta maximæ latitudinis in
eisdem partibus. Hæc puncta (quæ in circulo maximo vestigii ~C~ sunt ~M~
& ~N~) invenientur tangendo circumferentiam uniuscujusque circuli regulâ
parallelâ ad lineam perpendicularem ~E~, nam si figura exactè delineata
fuerit, regula tanget singulos toros trium basium in punctis maximæ hinc
inde latitudinis._
_Magis laborandum erit in reperiendis altitudinibus quatuor basium.
Verum si sedulò inspiciatur deformatio elevationis ~F~, aliarumque
duarum, (quæ factæ sunt, notatis in linea perpendiculari ~E~ divisionibus
desumptis ex elevatione geometrica ~A~) constabit, nullum esse punctum
in circulis vestigii ~C~, cui nequeat inveniri punctum correspondens in
toro & quadra ipsius basis, ut ostendunt lineæ occultæ, quæ incipiunt ex
~M~ & ~N~. Earum quælibet ex vestigio ~C~ pervenit ad lineam visualem,
& continuatur cum linea altitudinis ex visuali ad elevationem ~F~, &
cum alia linea latitudinis ex elevatione ~F~ ad basim. Porrò ex figura
constat, superficiem superiorem quadræ subduci oculis à columna, &
aliquid ex parte postica tori quod cæteroqui conspiceretur, abscondi
à quadra. Proinde torus, qui ex punctis maximæ latitudinis retrorsum
flectitur, eousque delineandus est, quoad hinc inde occurrat quadræ ipsum
cooperienti. Præstaret autem singula membra ita exactè delineari, quasi
essent diaphana; ut partes oculis imperviæ, omnino cohæreant cum partibus
quæ ipsis conspicuæ sunt._
_Completâ delineatione, si figuram tuam ex perpendiculo puncti oculi
ex debita distantia contemplatus fueris, omnes defectus facilè deteges
& statim corriges. Præcipuam diligentiam pones in formando & emendando
toro, qui habet duas rotunditates; unam quatenus ambit columnam; alteram
quatenus caret angulis, ut ostendit elevatio geometrica in ~I~._
The Sixteenth Figure.
_The ~Tuscan~ Base in Perspective._
From the Geometrical Elevation A, is drawn the Plan B; which being put
into Perspective, as you see in C and D, from the Circles of the Plan
C you have the Breadths of the Column, and of the List, and _Torus_ of
the three Bases: And after the same manner, by the Plan D, you have the
Breadth of the List and _Torus_ of the last Base. From the greatest
Breadth of the Circles of the Plan C, we have erected Perpendiculars to
the Parts that answer them in the Base, to the end that you may see where
the Points fall, which terminate the greatest Breadth of those Parts.
These Points (which in the biggest Circle of the Plan C are M and N) are
found by touching the Extremity of the Circumference with a Line parallel
to the Perpendicular E: for if the Figure were exact, that Line would
touch every _Torus_ of the three Bases in the extreme Points of their
Breadth.
The Heights of the four Bases are something more difficult to be found.
Nevertheless, if you consider well the Elevation F, and the other two G
and H, (which are made by transporting the Divisions of the Elevation
A upon the Perpendicular E) it will plainly appear that there is no Point
in the Circles of the Plan C, to which there may not be a correspondent
Point found in the _Torus_ and List of the said Base; as the occult
Lines shew, that arise from M and N; each of which is a Continuation
of three Lines: The first of Breadth, from the Plan C to the Visual;
the second of Height, from the Visual to the Elevation F; the third of
Breadth, from the Elevation F to the Base. Now, tho’ it’s plain by the
Figure, that the Body of the Column prevents the Sight of good part of
the Fillet, and the same Fillet takes off from part of the _Torus_, which
would otherwise be visible; for which Reason the Back-part of the _Torus_
is continu’d only till it meet the same: Yet it’s certainly best to draw
every Member complete, as tho’ the Work were transparent; that the Parts
hidden from the Eye may the better agree with those that are expos’d to
it.
When your Draught is finish’d, if you view it at the due Distance, and
perpendicularly to the Point of Sight; you’ll readily discover and
rectify what’s amiss. Your chief Care will be employ’d in shaping the
_Torus_, difficult by reason of its Roundness both ways; namely, in the
Contour of its Moulding, as in the Elevation I; and in the Circuit it
makes about the Column.
[Illustration: FIG. XVII.]
Figura Decimaseptima.
Deformatio basis Doricæ.
_Ad vitandam satietatem quam pareret nimia uniformitas, unam ex basibus
invertimus. Utraque autem basis delineata est methodo quam tradidimus
figurâ præcedenti. Eademque methodus adeò manifestè patet ex lineis
occultis latitudinum & elevationum, ut superfluum futurum sit ipsam
repetere._
The Seventeenth Figure.
_The ~Dorick~ Base in Perspective._
That you may not be tir’d with practising one and the same thing, I have
here, for Variety-sake, inverted one of the Bases. Both of ’em are drawn
after the Manner explain’d in the foregoing Figure; which is so evident
from the occult Lines of the Plan and Elevation here given, that I think
it superfluous to say any more of it.
[Illustration: FIG. XVIII.]
Figura Decimaoctava.
Optica delineatio basis Ionicæ.
_Ex multitudine ac varietate figurarum hujus Operis, disces, mi Lector,
modum deformandi res demissas & sublimes, magnas & parvas. In hac figura,
linea cui bases duarum columnarum incumbunt, est conjunctim linea plani,
& linea horizontalis; linea cui bases trium columnarum incumbunt, est
altior linea horizontali. Quemadmodum autem, si linea plani sit inferior
linea horizontali, lineæ quæ tendunt ad punctum oculi & ad punctum
distantiæ, ascendunt sursum; ita si linea plani sit superior horizontali,
lineæ quæ veniunt ad punctum oculi & ad punctum distantiæ, tendunt
deorsum. Quòd si in eadem tabula sint plura plana, eorumque aliqua sint
altiora, alia verò demissiora linea horizontali, lineæ omnes planorum,
ac linea horizontalis, sunt invicem parallelæ; adeoque ex linea, quæ
omnes eas normaliter secet, statim dignosci potest, in qua proportione,
singula plana sint altiora vel profundiora linea horizontali. Velim
quoque observes, latitudinem columnæ mediæ, minorem esse latitudine
columnarum lateralium; & discrimen inter hujusmodi latitudines eò est
majus, quò punctum distantiæ fuerit vicinius puncto oculi. Quæ dicta sunt
de columnis, intelligere oportet de basibus, & de optica delineatione
ambarum. Nihilominus, si figura ex debito puncto inspiciatur, columnæ
pictæ habebunt eandem apparentiam, quam haberent columnæ solidæ, invicem
æquales._
The Eighteenth Figure.
_The ~Ionick~ Base in Perspective._
By the Multitude and Variety of Figures in this Work, the Reader will be
instructed in delineating things, however different in Size or Situation.
In this Figure, the Line on which the two Columns rest, is both the
Horizontal and the Ground-line; that on which the three Columns are
plac’d, is so much higher than the Horizontal Line. And as, where the
Ground-line is beneath the Horizontal, the Lines drawn to the Points
of Sight and Distance tend upwards; so, where the same is above the
Horizontal, the Lines to the Points of Sight and Distance tend downwards.
If in the same Picture there are different Grounds, some higher,
others lower than the Horizontal Line; yet are all those Ground-lines,
and the Horizontal, parallel one to another; and therefore, by a Line
cutting them all perpendicularly, you presently know in what proportion
each Plan or Ground is higher or lower than the Horizontal. I would
have you observe, That the Breadth of the middle Column is, by the
Perspective, render’d less than that of the Side-Columns; and that this
Difference is the greater, as the Point of Distance approaches nearer
to the Point of Sight. What has been said of the Columns, is also to
be understood of the Bases, and the Projections of all their Parts in
Perspective: Nevertheless, if the Picture be view’d from its due Place,
the Columns will have the same Effect, as if solid; and all appear equal
one to the other.
[Illustration: FIG. XIX.]
Figura Decimanona.
Optica imminutio basis Corinthiæ.
_Hæc basis juxta regulas traditas opticè contracta est. Porrò altitudo
superficiei ~A~ est eadem cum altitudine lineæ visualis ~CD~; latitudo
crucis ~A~ est eadem cum latitudine crucis secundi circuli vestigii ~B~,
incipiendo à minimo omnium. Duæ lineæ normaliter infixæ basi, ostendunt
maximam latitudinem quam habere debet columna supra imum scapum. Maxima
latitudo tori superioris & utriusque astragali, est eadem cum maxima
latitudine tertii circuli. Maxima latitudo tori inferioris est eadem cum
maxima latitudine ultimi circuli._
The Nineteenth Figure.
_The ~Corinthian~ Base in Perspective._
This Base is put in Perspective by the Rules before laid down. The
Height of the Superficies A is the same with that of the visual Line
CD; the Breadth of the Cross A is the same with that of the second
Circle of the Plan B, beginning with the least. The two Lines that stand
perpendicularly on the Surface of the Base, shew the greatest Breadth of
the Columns Shaft above the Fillet. The Extent of the upper _Torus_ and
the two Astragals, is the same with that of the third Circle; and the
Extent of the lower _Torus_ is the same with that of the outward Circle.
[Illustration: FIG. XX.]
FIGURA Vigesima.
Basis Acticurga opticè imminuta.
_Basis Acticurga Pictoribus præ reliquis familiaris est, quia cum
omnibus ferè Ordinibus egregiè consentit. Porrò ex punctis ~E~ & ~F~
maximæ utrinque latitudinis extimi circuli vestigii, habetur maxima
latitudo tori inferioris ~CD~. Ac cætera quæ spectant ad ipsum & ad torum
~AB~, petenda sunt ex dictis de basi Etrusca._
The Twentieth Figure.
_The ~Attick~ Base in Perspective._
The _Attick_ Base is more frequently made use of by Painters, than any
other; because it suits well with most of the Orders. The Points E and F,
the greatest Breadth of the outward Circle of the Perspective-Plan, give
the greatest Breadth of the lower _Torus_ CD. And whatever else relates
either to this or the upper _Torus_ AB, is to be sought in the same
Manner, as has been shewn in the _Tuscan_ Base.
[Illustration: FIG. XXI.]
Figura Vigesimaprima.
Optica imminutio capitelli Etrusci.
_Eâdem cum reliquis formâ, eâdemque methodo capitella delineanda sunt:
quum habeant ipsa quoque suum cimatium quadratum, & sint rotunda. Linea
plani solet in iis fieri altior lineâ horizontali: quia quum capitella
imponenda sint columnis homine altioribus, plerumque apparent sublimiora
nostris oculis._
The Twenty-first Figure.
_The ~Tuscan~ Capital in Perspective._
The Manner before deliver’d concerning Bases, is of the same Use in
delineating Capitals; forasmuch as these also have their square _Abacus_,
and their round Members. The Ground-line in Capitals is usually plac’d
above the Horizon; because when they are set upon Columns which exceed a
Man’s Height, they are generally represented above the Eye.
[Illustration: FIG. XXII.]
Figura Vigesimasecunda.
Optica projectio capitelli Dorici.
_Capitellum hoc pluribus membris constat, adeóque operosius est quàm
præcedens. Nihilominus accurata delineatio vestigii geometrici omnes
difficultates complanabit._
Twenty-second Figure.
_The Projection of a ~Dorick~ Capital, in Perspective._
This Capital consisting of more Members than the foregoing, will be more
troublesom to put in Perspective; but an accurate Delineation of the
Geometrical Plan will certainly remove many seeming Difficulties.
[Illustration: FIG. XXIII.]
Figura Vigesimatertia.
Deformatio capitelli Ionici.
_Capitellum Ionicum poscit duas elevationes geometricas distinctas,
alteram faciei, alteram lateris; ex iisque conflatur vestigium
geometricum ~A~, quod opticè contrahitur, translatis in ~B~ punctis
latitudinis ~C~, & in ~E~ punctis longitudinis ~D~ more consueto: ut ex
punctis ~B~ latitudinis, lineæ tendant ad punctum oculi; ex punctis verò
~E~ longitudinis, lineæ tendant ad punctum distantiæ._
_Ex vestigio capitelli opticè contracto eruenda est elevatio longitudinis
ut in figura. Ex utrisque verò juxta morem fiet capitellum nitidum,
acceptis latitudinibus ex vestigio, altitudinibus ex elevatione
longitudinis. Hæc quoque dabit maximam latitudinem singularum volutarum._
_Modum delineandi capitellum Ionicum, in quo helices volutarum
obliquentur, dabimus infra figurâ trigesimâ._
Twenty-third Figure.
_The ~Ionick~ Capital in Perspective._
The _Ionick_ Capital requires two distinct geometrical Elevations,
one of the Front, the other of the Side; from both which is found the
geometrical Plan A, which is put in Perspective by transferring into B
the Points of Breadth C, and into E the Points of Length D, after the
usual Manner; that from the Points of Breadth B, Lines may be drawn
towards the Point of Sight; and from the Points of Length E, towards the
Point of Distance.
From the Plan of the Capital in Perspective, is to be drawn the Upright
of the Length, as in the Figure; and from both, as usual, the finish’d
Capital is wrought, by taking the Breadths from the Plan, and the
Heights from the Elevation; this giving the utmost Height, and that the
utmost Breadth of each of the Volutes.
The Manner of describing the _Ionick_ Capital, whose Volutes lie
obliquely, we shall hereafter treat of in the Thirtieth Figure.
[Illustration: FIG. XXIV.]
Figura Vigesimaquarta.
Optica projectio capitelli Corinthii.
_Capitellum Corinthium absolvere non poteris, nisi elevatione geometrica
ejusque vestigio exactissimè delineatis juxta regulas Barozzii._
_Ad formandum ex vestigio ~B~ vestigium ~E~, rectis occultis fient
quadrata necessaria ad contractionem opticam quatuor vel trium saltem
circulorum; translatis in lineam ~D~ divisionibus lineæ ~C~, & aliis,
more consueto. Contrahentur deinde lineis occultis vestigia foliorum, &
absolventur cætera quæ posita sunt in vestigio_ E.
_Ut fiat optica elevatio longitudinis ~F~, in lineam perpendicularem
~H~ transferentur ex elevatione ~A~ omnes ejus divisiones. Complebitur
autem per lineas rectas, quæ ex punctis divisionum ducantur ad punctum
oculi, ac per rectas ex circulorum summitate ac profunditate, quæ rectæ
sint parallelæ ad lineam ~D~, ac perveniant ad visualem ~G~; indeque
descendant, ac sint parallelæ ad lineam perpendicularem_ H.
_Capitellum nitidum exordieris ab infimo circulo ~I~, ostendente ambitum
columnæ. Succedent folia ~1~, ~2~, quorum latitudines accipientur
ex vestigio ~E~ per circinum, positâ unâ ejus cuspide in linea ~H~;
altitudines verò accipientur ex elevatione ~F~, posita una cuspide
circini in linea ~D~. Idipsum dico tum de foliis ~3~, ~3~, ~4~, ~4~, tum
de folio ~5~, ac de aliis, & demum de cymatio. Descensus verò lineæ curvæ
ipsius cymatii incipiet ex acie ~L~._
Twenty-fourth Figure.
_The ~Corinthian~ Capital in Perspective._
There is no Completing the _Corinthian_ Capital, unless you most
accurately describe its Geometrical Elevation and Plan, according to the
Rules of _Vignola_.
Being to form the Plan E from the Plan B, you must, with occult Lines,
make the Squares necessary for bringing four, or at least three of the
Circles into Perspective; transferring into the Line D the Divisions
of the Line C, and the rest as usual. Then, with other occult Lines,
contract the Plans of the Leaves, and finish what’s farther requisite in
the Plan E.
To make the Optick Elevation of the Length F, you must transfer into the
Perpendicular H all the Divisions of the Elevation A; and complete the
same, by Lines drawn toward the Point of Sight, till they meet their
respective Perpendiculars; which proceeding from all parts of the Circles
parallel to the Line D, intersect the Visual G; from whence they descend,
Parallels to the Perpendicular H.
In working the clean Capital, you should begin with the lowest Circle I,
which denotes the Compass of the Column. Then make the Leaves 1, 2, by
taking their Breadths from the Plan E, with the Compasses, and keeping
one Point of them upon the Line H; and their Heights from the Elevation
F, keeping one Point on the Line D. The same must be done, as well by the
Leaves 3, 3, 4, 4, as by the Leaf 5, and the others; and last of all, by
the _Abacus_ also; the Sinking of the Horns whereof answers that of the
visual Line L.
[Illustration: FIG. XXV.]
Figura Vigesimaquinta.
Optica descriptio capitelli Compositi.
_Ex iis quæ diximus de capitello Corinthio, didiceris modum faciendi
capitellum Compositum. Velim autem tibi persuadeas, cum lectione harum
regularum quæ sunt magistri inanimes, circini usum perpetuò conjungi
oportere. Hic enim vivi magistri defectum unicè supplere potest._
The Twenty-fifth Figure.
_The ~Composite~ Capital in Perspective._
From what has been said of the _Corinthian_ Capital, may be learnt the
Manner of putting the _Composite_ also into Perspective. I wish I could
prevail with you, that to the Reading of the Rules, which in themselves
are but lifeless Masters, you would constantly add a diligent Practice of
the Figures by the Compasses; this being the only way to supply the Want
of a living Master.
[Illustration: FIG. XXVI.]
Figura Vigesimasexta.
Deformatio coronicis Etruscæ.
_Post capitella sequuntur coronices, quæ utpote quadratæ, minimam habent
arduitatem. Inter coronices verò, nulla est Etruscâ simplicior ac
facilior. Ex elevatione geometricâ, more solito, formatur vestigium
geometricum; ex eoque opticè contracto eruitur similis elevatio
longitudinis. Demùm ex elevatione & vestigio componitur coronix nitida.
Memineris autem duas esse lineas, quæ hinc inde terminant latitudinem
elevationis opticæ. Linea quæ altior est, dat altitudinem anterioris
faciei coronicis, alia quæ est depressior, dat altitudinem faciei
posterioris. Et ita erit in posterum._
Twenty-sixth Figure.
_The ~Tuscan~ Entablature in Perspective._
After Capitals we proceed to _Entablatures_, which because they are
square, are less difficult than the former. And of all Entablatures,
that of the _Tuscan_ Order is the most simple and easie to be put
in execution. From the Geometrical Upright is drawn, as usual, the
Geometrical Plan; from the Plan put in Perspective is describ’d the
Optick Elevation of the Length; and from both the latter is wrought the
clean Entablature requir’d. You may observe, here are two Lines that
terminate the Breadth of the Perspective on one side and the other. The
Line which proceeds from the higher Corner of the Visual, gives the
Height of the most advanc’d Part; that from the lower determines the
Height of the Back-part. And so for the future.
[Illustration: FIG. XXVII.]
Figura Vigesimaseptima.
Optica delineatio coronicis Doricæ.
_In faciendâ coronice Doricâ, quæ majorem operam poscit, ob denticulos
& triglyphos; communis regula servanda est. Si autem libeat coronicem
nitidam describere in papyro separatâ ab ejus præparationibus, id
profectò licet, tum in hoc, tum in quocunque alio schemate._
Twenty-seventh Figure.
_The ~Dorick~ Entablature in Perspective._
In making the _Dorick_ Entablature, which has something more Work in it
than the former, on account of its Dentels and Triglyphs; the common Rule
is to be observ’d. And if you would delineate the finish’d Entablature in
a Paper distinct from that of its Preparations, you are at liberty so to
do, either in this or any other Figure.
[Illustration: FIG. XXVIII.]
Figura Vigesimaoctava.
Præparatio figuræ sequentis.
_In figurâ vigesimaoctavâ, quæ continet vestigium & elevationes
geometricas figuræ vigesimænonæ, oportuit latus ~C~ delineare seorsim à
facie ~B~; quia facies exhibet latitudinem ædificii, latus verò exhibet
longitudinem; atque una non est alteri æqualis. In vestigio geometrico
solidus paries est ~A~: circuli referunt summum scapum columnarum. Cætera
dant projecturas coronicis, cum suis mutulis._
Twenty-eighth Figure,
_Preparatory to the following Figure._
In this Twenty-eighth Figure, which contains the Plan and Geometrical
Elevations of the Twenty-ninth Figure, it was requisite to delineate the
Side C separately from the Front B; because the Front, which signifies
the Breadth of the Building, and the Side, which shews its Length, are
not equal one to the other. In the Geometrical Plan the solid Wall is A:
the Circles express the Nakeds of the Pillars Shafts at top. The rest is
the Projecture of the Cornice, with its Mutules.
[Illustration: FIG. XXIX.]
Figura Vigesimanona.
Optica projectio ædificii Dorici.
_Habes in hac figura vigesimanona, opticam delineationem vestigii, &
unius ex elevationibus figuræ vigesimæoctavæ; nimirum, elevationis
longitudinis; ex quibus eruitur imago nitida ædificii Ordinis Dorici, cum
summitatibus & capitellis trium columnarum; ejusque epistylium, zophorus,
& corona._
BO _est linea horizontis; ~AC~ est linea plani; in quam, ex lineis
~D~ & ~C~ figuræ vigesimæoctavæ, transferuntur puncta latitudinis &
longitudinis duarum elevationum; prolongando versus ~C~ ipsam lineam
plani, ut oportet. Operaberis autem, ut diximus figurâ vigesimatertia;
nimirum, in puncto ~V~ desinet latitudo vestigii, incipiet longitudo;
& ex punctis latitudinis lineæ tendent ad punctum oculi; ex punctis
longitudinis lineæ occultæ tendent ad punctum distantiæ. Ubi verò hæ
lineæ secant visualem ~VO~, fient parallelæ ad lineam ~AC~, cum cæteris
quæ necessaria sunt ad complendam delineationem opticam vestigii._
_Elevatio ~C~ figuræ vigesimæoctavæ opticè contrahetur more consueto,
translatis in lineam ~AB~ divisionibus lineæ ~E~ vel ~F~, ex quibus
fient visuales ad punctum oculi; ac demissis ex linea visuali ~AO~
perpendicularibus ad lineam ~AC~, ita ut lineæ parallelæ ad lineam plani
~AC~ continuentur cum aliis lineis parallelis ad lineam ~AB~._
_Hic quoque locum habet observatio illa, cujus meminimus figura
vigesimasexta, de lineis quæ deorsum excurrunt, & hinc inde terminant
membra elevationis opticæ. Ex iis autem desumuntur projecturæ omnes
coronicis & capitellorum._
Twenty-ninth Figure.
_A Projection of the ~Dorick~ Order in Perspective._
In this Twenty-ninth Figure, you have in Perspective the Plan, and one
of the Uprights of the Twenty-eighth Figure; namely, that of the Length;
from whence is drawn this finish’d Piece of the _Dorick_ Order, which has
the upper Part and Caps of three Pillars, with their Architrave, Freeze,
and Cornice.
BO is the Horizontal-line; AC that of the Plan; into which, from the
Lines D and C of the Twenty-eighth Figure, are transferr’d the Points
of Breadth and Length of the two Elevations; first prolonging the Line
itself, as much as is needful, through C. The Work is then perform’d,
as was shewn in the Twenty-third Figure; namely, the Divisions of the
Breadth of the Plan end in the Point V, at which those of Length begin.
From the first, Lines are drawn to the Point of Sight; and from the
latter, occult Lines are directed to the Point of Distance: And where
these cut the Visual VO, Lines are drawn parallel to AC; with those that
are farther necessary for completing the Plan in Perspective.
The Elevation C of the Twenty-eighth Figure is put in Perspective, as
usual, by transferring the Divisions of the Line E, or F, into that of AB
in this Plate; from whence drawing Visuals to the Point of Sight, they
are intersected by Perpendiculars let fall from those Divisions of AO
made by the Parallels to the Ground-line AC, and again continu’d parallel
to the Perpendicular AB.
The Observation, mention’d in the Twenty-sixth Figure, is also pertinent
in this place; That the Lines, which, in the Perspective-Elevation, tend
downward, give the Advance and Recess of the several Members of the
Work; and from them are taken all the Projectures of the Entablature and
Capitals.
[Illustration: FIG. XXX.]
FIGURA Trigesima.
Optica projectio ædificii Ionici; ubi de modo jungendi fictum cum vero.
_Si tibi Pictor quum sis, occasione apparatûs quadraginta horarum, vel
sepulcri Domini, mutare ad tempus libeat formam architecturæ alicujus
Ecclesiæ jungendo fictum cum vero, ut mihi sæpius contigit Mediolani ac
Romæ, cum ingenti spectatorum delectatione & admiratione; paucis ostendam
tibi modum quem servare debeas in operando._
_Sectio coronicis veræ, quæ, ut suppono, videri debet continua esse
cum coronice picta in telario, est ~A~; elevatio geometrica coronicis,
& reliquorum quæ delineanda sunt, est ~B~; vestigium geometricum est
~C~. Porrò, tum vestigium tum elevatio longitudinis opticè contrahentur
more consueto, ut vides in ~C~ & ~B~: ex iisque formabitur in telario
coronix nitida cum columna & anta; ipsumque telarium depictum, normaliter
coagmentandum erit veræ coronici._
_Ut fiat ea pars longitudinis, quæ coronicem pictam continuare videatur
cum vera, & erui non potest ex elevatione deformata; oportet sectionem
~A~ transferre in ~D~, ducendo visuales ex punctis terminativis membrorum
sectionis ~D~, usque dum occurrant lineis latitudinis eorundem membrorum.
Quod si colores in telarium scitè inducantur, angulus in ~E~, quamvis
merè depictus, videbitur verus; & ex adverso, anguli quos telarium ipsum
depictum facit cum diversis adeò crepidinibus coronicis veræ, nusquam
apparebunt, præterquàm in quadra simæ dumtaxat; & unio architecturæ veræ
cum ficta dignosci non poterit._
The Thirtieth Figure.
_An ~Ionick~ Work in Perspective; with the Manner of reconciling the
fictitious to the solid Architecture._
If, being a Painter, you were requir’d, against the Solemnity of the
Holy-Week, to alter for a while the Architecture of some Altar-piece, by
joining Painting to the real Work; as I have often done, both at _Rome_
and _Milan_, to the great Satisfaction and Surprize of the Beholders: I
shall briefly shew the Method to be observ’d in performing the same.
The Dissection of the solid Cornice, which I here suppose shall appear
continu’d in that painted on the Canvass, is A; the Geometrical Elevation
of the Cornice, and other Parts to be drawn, is B; the Geometrical Plan
is C. The Plan and Elevation of the Length are put in Perspective after
the usual manner, in C and B; from those the finish’d Cornice, with the
Pillar and Pilaster, are delineated on the Canvass; and the Picture is
then conjoin’d, at right Angles, to the true Cornice.
For adjusting the Members so, that the painted Cornice may seem to be the
real one continu’d, (which can’t be done by the Perspective Upright) you
must transfer the Section A to D; and from the terminating Points of the
several Members thereof, draw visual Lines, till they meet those of their
respective Members in the Perspective. And if the Colours are laid by a
skilful Hand, the Angle at E, tho’ painted only, will appear as real;
and on the contrary, the Angles which the Members of the painted Cornice
make with the different Projectures of those of the true, will never be
discern’d, unless in the very uppermost Fillet; but the Conjunction of
the real with the painted Architecture, will be altogether imperceptible.
[Illustration: FIG. XXXI.]
Figura Trigesimaprima.
Optica projectio coronicis Corinthiæ, cum capitello & summitate columnæ.
_In hoc schemate linea plani est ~CIE~, horizontis est ~DFO~; punctum
oculi est ~O~, distantiæ est ~D~. Elevatio geometrica capitelli Corinthii
cum sua coronice est ~A~, quorum divisiones cernuntur in perpendiculari
~CD~. Vestigium geometricum ~B~ habet longitudinem æqualem latitudini:
opticè autem contrahitur methodo consueta. Nimirum, translatis
divisionibus latitudinis & longitudinis in lineam plani ~CIE~; ex punctis
latitudinis fiunt visuales ad punctum oculi; ex punctis verò longitudinis
fiunt occultæ ad punctum distantiæ: hoc modo habes quicquid necessarium
est ad contractionem opticam vestigii. Nam lineæ longitudinum sunt partes
visualium, ut patet in ~GN~, ~HL~: lineæ latitudinum, parallelæ ad lineam
plani fiunt ex punctis in quibus lineæ tendentes ad punctum distantiæ
secant visualem ~HO~, ut vides in ~NL~. Porro, si tantundem prolongaretur
horizontalis ~DO~, ita ut haberet duo puncta distantiæ remota æqualiter
ab ~O~, medietas diagonalium, quæ sunt in quadrato majori ~GNLH~ opticè
deformato, & in quadratis ejus minoribus, tendent ad unum punctum
distantiæ; altera medietas ad aliud punctum distantiæ._
_Elevatio longitudinis opticè contrahitur ductis parallelis ad ~CE~,
quæ ubi pervenerint ad visualem ~IO~, continuentur cum aliis parallelis
ad ~IK~. Præterea, translatis in lineam ~IK~ divisionibus lineæ
perpendicularis ~CD~, ex punctis divisionum fiunt visuales ad punctum
oculi, ac ducuntur singula membra ipsius elevationis, cujus latitudines
sunt partes visualium, altitudines verò sunt partes linearum parallelarum
ad ~IK~. Demùm ex vestigio & ex elevatione longitudinis, formatur coronix
nitida cum capitello. Ut autem faciliùs delineentur mutuli, primùm fient
quadratâ formâ, ut in ~M~; deinde congruus flexus in singulos inducetur._
The Thirty-first Figure.
_The Optick Projection of a ~Corinthian~ Cornice, with the Capital and
PART of the Column._
In this Figure the Line of the Plan is CIE, that of the Horizon is
DFO; the Point of Sight is O, the Point of Distance D; the Geometrical
Elevation of the _Corinthian_ Capital, with its Entablature, is A; whose
Divisions are seen in the Perpendicular CD. The Length and Breadth of the
Geometrical Plan B are equal, and the Plan is put into Perspective after
the usual Method; to wit, by transferring the Divisions of Breadth and
Length into the Line CIE; from the Points of Breadth drawing Visuals to
the Point of Sight; and from those of Length occult Lines to the Point
of Distance: by which Intersections you have all that’s necessary for
putting the Plan into Perspective. For the Lines of Length are Parts of
visual Rays, as is manifest by GN, HL; and the Lines of Breadth are made
Parallels to the Ground-line, from the Intersections before-mention’d,
as is seen in NL. Moreover, if the Horizontal-line DO were so prolong’d,
as to receive another Point of Distance equidistant from O; half the
diagonal Lines of the great Square GNLH, and of the lesser Squares
contain’d therein, would tend to one Point of Distance, and the other
half to the other.
The Elevation of the Length is put in Perspective, by continuing the
Parallels to CE, till they cut the Visual IO; and from thence dropping
Lines parallel to IK: Then transferring into IK the Divisions of the
Perpendicular CD, from them make visual Lines to the Point of Sight, and
draw the several Members of the Upright; whose Breadths are Parts of
Visuals, and their Heights Parts of Perpendiculars, or Lines parallel
to IK. Lastly, from the Plan and Elevation of the Length, you delineate
the finish’d Cornice and Capital: But that you may more easily draw the
Modillions, first make them in a square Form, as in M; and that will very
much assist you to give the Scroll of each a more agreeable Turn.
[Illustration: FIG. XXXII.]
Figura Trigesimasecunda.
Delineatio geometrica coronicis, Ordinis Compositi.
_Ut hoc schema grandius ac distinctius esset, ejus medietatem dumtaxat
suscepi delineandam. ~PN~ est vestigium geometricum. ~M~ est solidus
paries. ~OO~ spatia columnarum. In ~H~ sunt crepidines coronicis.
Elevatio geometrica latitudinis ædificii constat epistylio ~T~, zophoro
~L~, & coronâ ~V~, supra quam eminet fastigium ~S~._
_Jam ut inveniatur centrum arcuum, distantiæ ~AV~ fiat æqualis distantia
~AC~. Positaque una cuspide circini in ~C~, alia extendatur usque ad ~V~:
ita fient arcus, quorum ultimus est ~BD~, omnesque sunt concentrici.
Elevatio ~F~ ostendit longitudinem ædificii ex parte ~GI~; elevatio ~E~
ostendit longitudinem ipsius ex parte ~DR~._
Thirty-second Figure.
_The Geometrical Design of a Cornice, of the ~Composite~ Order._
That this Figure might be larger and more distinct, I have here describ’d
only the Half of it. PN is the Geometrical Plan. M is the solid Wall. OO
are the Places of the Columns. H shews the Projectures of the Cornice.
The Geometrical Elevation of the Breadth of the Frontispiece, consists of
the Architrave T, the Freeze L, and the Cornice V, over which is rais’d
the Pedament S.
For finding the Center of the arch’d Lines of the Pedament, make the
Distance AC equal to that of AV; and placing one Point of the Compasses
in C, extend the other to V, and describe the Arch. The other Arches, of
which BD is the utmost, have all the same Center. The Elevation F shews
the Length of the Work on the Side GI. The Upright E shews the Length of
the same on the Front DR.
[Illustration: FIG. XXXIII.]
Figura Trigesimatertia.
Deformatio coronicis Compositæ.
_Figura hæc trigesimatertia minus ardua tibi videbitur, si ex ea
delineandam primùm suscipias medietatem quæ respondet vestigio ~PN~ &
elevationi ~BR~ figuræ trigesimæsecundæ; rejecto in ultimum fastigio,
postquàm cætera compleveris. Linea ~BV~ est horizontalis. Punctum oculi
est ~V~, punctum distantiæ remotum est ab ~V~ spatio ~BV~, additis
modulis quatuordecim cum dimidio. Linea plani est ~AR~, in quam ex ~Q~
versus ~A~ transfertur latitudo ~P~; ex ~Q~ versus ~R~ transfertur
longitudo ~N~, cum omnibus earum divisionibus; ut ex punctis latitudinis
fiant visuales ad punctum oculi; & ex punctis longitudinis fiant
occultæ ad punctum distantiæ. Ex his habes quicquid necessarium est ad
projectionem opticam vestigii, ut ostendimus figurâ trigesimaprimâ.
Eademque methodo, quam ibi servavimus, contrahes elevationem ~P~
longitudinis coronicis: ac tum ex illa, tum ex vestigio, eruetur coronix
nitida more consueto._
_Ut delineetur fastigium, transferendæ sunt in lineam ~AB~ divisiones
ipsius ex elevatione ~F~ figuræ trigesimæsecundæ, ac ducendæ visuales
ad punctum oculi, additis lineis terminativis uniuscujusque membri,
quæ accipientur ex vestigio ~Q~ opticè deformato. Centrum ~O~ arcuum
fastigii nitidi, remotum est à summitate coronicis, medietate distantiæ,
quam habent ungues quadræ cui fastigium ipsum incumbit. Ac proinde, si
accipias ex elevatione ~P~ diversas altitudines membrorum fastigii;
latitudines verò accipias ex vestigio ~Q~; opus tuum feliciter absolves._
The Thirty-third Figure.
_A ~Composite~ Cornice in Perspective._
This Thirty-third Figure will be found the less difficult, if you
first attempt that Half which answers to PN in the Plan, and BR in the
Upright of the Thirty-second Figure; leaving the Pedament, till all
the rest be finish’d. The Line BV is the Horizontal. V is the Point of
Sight; the Point of Distance is fourteen Modules and a half without
the Point B, more than the Interval BV. The Line of the Plan is AR, in
which from Q toward A you have the Divisions of Breadth of the foregoing
Plan P; and from Q to R those of the Length thereof N: From the former,
Visuals are drawn to the Point of Sight; and from the latter, occult
Lines to the Point of Distance. And from these you have all that’s
necessary for putting the Plan in Perspective; as was shewn in the
Thirty-first Figure. By the Method there observ’d, you may also describe
the Perspective-Elevation of the Length P; and from this, and the Plan,
delineate the finish’d Cornice after the usual Manner.
For making the Pedament, the Divisions of the Elevation F in the
Thirty-second Figure, must be transferr’d into the Line AB, and Visuals
drawn from them to the Point of Sight; giving to each Member its proper
Out-line and Contour, as may be taken from the Perspective-Plan Q. The
Center O of the Arches in the finish’d Pedament, is plac’d below the
upper Member of the Cornice, as much as half the Extent of the upper
Fillet from whence the Pedament springs. And by taking the several
Heights of the Members thereof, from the Elevation P; and the Breadths
from the Plan Q; you will successfully finish and complete your Work.
[Illustration: FIG. XXXIV.]
Figura Trigesimaquarta.
Præparatio ad figuram trigesimamquintam.
_Si placuerit conferre figuram trigesimamtertiam cum præsenti figura
trigesimaquarta, dignosces vestigium & elevationem coronicis Compositæ
alio modo hic deformari, mutando scilicet longitudinem in latitudinem, &
latitudinem in longitudinem. Propterea hæc figura tantum spatii occupat,
ut eam seorsim à coronice nitida delineare oportuerit._
_Divisiones latitudinis in vestigio incipiunt ex ~V~ versus ~R~, & sunt
eædem cum divisionibus rectæ ~IG~ figuræ trigesimæsecundæ. Divisiones
longitudinis incipiunt ex ~V~ versus ~S~, & sunt eædem cum divisionibus
rectæ ~IP~ duplicatis. Ex divisionibus latitudinis fiunt visuales ad
punctum oculi; ex divisionibus longitudinis fiunt rectæ ad punctum
distantiæ; cum reliquis quæ necessaria sunt ad complendum vestigium
~AVDC~._
_Elevatio longitudinis coronicis & fastigii, opticè contrahitur per
lineas parallelas ad lineam plani ~AS~; quæ ubi pervenerint ad visualem
~AC~, continuentur cum aliis parallelis ad perpendiculum ~P~, ut diximus
figurâ trigesimaprimâ. In idem perpendiculum ~P~ transferuntur ex figurâ
trigesimasecundâ divisiones rectæ ~DR~; & insuper altitudines, quas
puncta ~KXZ~ habent supra rectam ~VA~; fientque visuales ad punctum
oculi: sectiones autem visualium cum parallelis ad perpendiculum ~P~,
dabunt sex puncta simæ fastigii, respondentia punctis ~KXZ~ duplicatis,
figuræ trigesimæsecundæ; earumque ductu formandus est supremus arcus.
Eodem artificio fient reliqui omnes._
_Faciliùs delineabitur coronix, cujus maximam partem occupant lineæ
visuales ad punctum oculi: porrò, membra omnia, exceptâ simâ, communia
sunt coronæ & fastigio. Adeoque puncta similia in lineis terminativis
membrorum singulorum, ex quibus desumuntur crepidines & ungues figuræ
nitidæ, sunt parallela ad perpendiculum ~P~._
The Thirty-fourth Figure,
_Preparatory to the Thirty-fifth._
If you please to compare the Thirty-third Figure with this Thirty-fourth
Figure, you will perceive the Plan and Elevation of this _Composite_
Cornice to be delineated differently from that; to wit, by making the
Length of that the Breadth of this, and the Breadth of that the Length of
this: On which account, this Figure takes up so much Room, that there was
a necessity of drawing the finish’d Cornice on a separate Paper.
The Divisions of Breadth in the Plan begin from V toward R; and are the
same with those of the Line IG in the Thirty-second Figure. The Divisions
of Length are set from V toward S; and are the same with those of the
Line IP in the Thirty-second Figure; which being the Half, is here
doubl’d. From the Divisions of Breadth, Lines are drawn to the Point of
Sight; and from those of the Length, Lines to the Point of Distance; with
the farther Requisites for completing the Plan AVDC in Perspective.
The Upright of the Length of the Cornice and Pedament, is made by
producing Parallels to the Ground-line AS; till they intersect the Visual
AC; and thence continuing Lines parallel to the Perpendicular P, as was
directed in the Thirty-first Figure. Into the same Perpendicular P are
transferr’d the Divisions of the Line DR in the Thirty-second Figure;
and also the Heights which the Points KXZ have above VA in the same
Figure. From all which, Visuals are drawn to the Point of Sight; which
being intersected by the Perpendiculars, give six Points on the _Cima_ of
the Pedament, which answer to the said Points KXZ of the Thirty-second
Figure, doubl’d: By these the outward Arch is form’d. And by the same
Rule, you find Points for all the others.
You will more easily draw the Cornice, the greatest Part of it consisting
of visual Lines to the Point of Sight: Moreover, all the Members, except
the upper _Cima_, are common both to the Cornice of the Entablature,
and to the Pedament; so that the corresponding Points, in the Out-lines
of their several Members, from whence the Breaks and Contours of the
finish’d Piece are taken, are found in the same Parallels to the
Perpendicular P.
[Illustration: FIG. XXXV.]
Figura Trigesimaquinta.
Deformatio coronicis Compositæ, ad latus inspectæ.
_Artificium nitidæ coronicis, ex vestigio & elevatione figuræ
trigesimæquartæ eruendæ, non differt ab eo quod sæpè traditum est. Itaque
supposito, quòd linea plani & horizontis, ac puncta oculi ac distantiæ,
habeant in hoc schemate situm omnino eundem, quem habent in præcedenti;
ope duorum circinorum, invenientur distantiæ, quas anguli necessarii ad
integram delineationem coronicis, habent à linea plani, & à linea normali
ad ipsam lineam plani. Nam ducendo lineas visuales, aliasque lineas
parallelas ad ipsum perpendiculum, cum terminis & flexibus qui conveniunt
singulis membris, complebitur delineatio._
_In fastigio visuales sunt penitus occultæ: puncta autem similia ~H~
& ~L~, ex quibus fastigium incipit introrsum flecti, incidunt in unam
eandemque visualem. Idipsum dico de aliis punctis similibus. Nam
lineæ rectæ omnes, quæ in figura trigesimatertia sunt parallelæ ad
lineam plani, in figuris trigesimaquarta & trigesimaquinta sunt partes
linearum visualium._
The Thirty-fifth Figure.
_A Side-View of the ~Composite~ Cornice, in Perspective._
The Manner of drawing this finish’d Cornice, from the preceding Plan and
Elevation, is the same with that so often shewn you. Admitting therefore,
that the Lines of the Plan and Horizon, and the Points of Sight and
Distance, have the very same Position in this, that they had in the
preceding Scheme; all the Angles necessary for delineating the entire
Cornice, are readily found by the help of two pair of Compasses; taking
their Distances one way from the Ground-line; and the other way from a
Line perpendicular to the same: Then drawing the visual and perpendicular
Lines, and keeping the Place and Contour of the several Mouldings, you
complete your Design.
In the Pedament the visual Lines are wholly occult; and the Points H
and L, where the Pedament begins to break back, being of like Height,
are found in one and the same Visual: And the same may be said of all
Points that are of equal Height from the Plan; for all the right Lines,
which in the Thirty-third Figure are Parallels to the Ground-line, in the
Thirty-fourth and Thirty-fifth Figures are Parts of the visual Lines.
[Illustration: FIG. XXXVI.]
FIGURA Trigesimasexta.
Præparatio ad figuram trigesimamseptimam.
_In vestigio geometrico ~C~, & in ejus elevatione ~AB~, præcipuas tantùm
lineas adnotavi, ne figuram confunderem, & ut studiosorum industriæ
aliquid relinquerem. Linea plani ~EG~ habet divisiones latitudinis ~P~,
& longitudinis ~Q~, vestigii geometrici ~C~. Ex punctis latitudinis
ducentur more solito visuales ad ~O~ punctum oculi; ex punctis
longitudinis fient occultæ ad punctum distantiæ, quod extra lineam
~AB~ protenditur modulis quatuordecim: & ubi occultæ ex divisionibus
longitudinis secant visualem ~FO~ fiunt parallelæ ad lineam plani ~EF~,
adhibitis sectionibus talium parallelarum cum visualibus, ad complendam
deformationem vestigii._
_Eædem lineæ quæ in vestigio deformato sunt parallelæ ad ~EF~,
prolongantur usque ad visualem ~EO~, & continuantur cum aliis parallelis
ad perpendiculum ~DE~. Fiunt quoque visuales ad punctum oculi ex
divisionibus elevationis ~AB~ translatis in perpendiculum ~DE~;
adhibitis sectionibus talium parallelarum cum visualibus, ad complendam
deformationem longitudinis elevationis._
The Six and thirtieth Figure,
_Preparatory to the Thirty-seventh._
In the Geometrical Plan C, and in the Elevation thereof AB, I have only
mark’d the principal Lines, as well for avoiding Confusion in the
Figure, as that something might be left to the Industry of the Studious.
The Line of the Plan EG has the Divisions of Breadth P, and of Length
Q, of the Geometrical Plan C. From the Points of Breadth are drawn, as
usual, Visuals to the Point of Sight O; From the Points of Length occult
Lines are produc’d to the Point of Distance, which lies fourteen Modules
without the Line AB: And where the occult Lines from the Divisions of
Length cut the Visual FO, Parallels are made to the Ground-Line EF; and
from the Intersections of those Parallels with the Visuals, you complete
the Delineation of the Plan in Perspective.
The Lines which in the Plan are parallel to EF, being prolong’d to the
Visual EO, are then continu’d parallel to the Perpendicular DE. And from
the Divisions of AB, produc’d to DE, visual Lines are drawn to the Point
of Sight; which intersecting the Perpendiculars aforesaid, you from
thence find the Length of the Elevation in Perspective.
[Illustration: FIG. XXXVII.]
FIGURA Trigesimaseptima.
Deformatio columnæ Etruscæ.
_Ex præparatione quam exhibuimus figurâ trigesimasextâ, eruitur columna
hæc nitida Ordinis Etrusci, opticè imminuta per latitudines & altitudines
partium singularum; quæ accipiuntur ope duorum circinorum, ut sæpiùs
dictum est._
The Thirty-seventh Figure.
_A ~Tuscan~ Column in Perspective._
From the Preparation exhibited in the Thirty-sixth Figure, is drawn this
complete Piece of the _Tuscan_ Order, brought into Perspective by means
of the Breadths and Heights of the several Parts, exactly taken off with
the Compasses, as has been often said.
[Illustration: FIG. XXXVIII.]
FIGURA Trigesimaoctava.
Præparatio ad figuram trigesimamnonam.
_Hæc figura est simillima figuræ trigesimæsextæ. In vestigio ~P~ limes
prominentiæ coronicis est ~R~; coronæ verò in stylobatâ est ~T~.
soliditas stylobatæ est ~V~. ambitus columnæ in imo est ~X~, in summo
~Z~._
The Thirty-eighth Figure.
_Preparatory to the Thirty-ninth._
This Figure is very much the same with the Thirty-sixth. In the Plan
P, the utmost Projecture of the Cornice is R; that of the Cap of the
Pedestal is T; the Trunk of the Pedestal is V; the naked Shaft of the
Column at bottom is X, at top is Z.
[Illustration: FIG. XXXIX.]
FIGURA Trigesimanona.
Deformatio ædificii Dorici.
_Habes hoc loco ædificium Doricum, addito statuæ unius ornamento. Velim
autem, ut si figuram aliquam ex his desumptam, delineandam assumas,
aliquid mutes saltem in loco punctorum oculi aut distantiæ. Hoc modo
majores in hac arte progressus facies; & si alicubi cælator aberraverit,
ex lapsu illius nullum senties detrimentum._
The Nine and thirtieth Figure.
_A Piece of ~Dorick~ Architecture in Perspective._
In this Plate you have a _Dorick_ Composition, with the additional
Ornament of a single Statue; but I would advise, when you undertake to
work after any of these Designs, you would at least place the Points
of Sight and Distance somewhat differing from those here given; which
Practice will both greatly further your Progress in this Art, and prevent
any Inconvenience, that may arise from a Mistake of the Engraver.
[Illustration: FIG. XL.]
FIGURA QUADRAGESIMA.
Vestigium geometricum ædificii Ordinis Dorici.
_Vt studiosorum, qui sedulò se exercuerint in praxibus hucusque traditis,
& ad majora inhient, utilitati serviam, delineandam suscepi medietatem
arcûs cum tribus columnis, ac totidem statuarum loculamentis. Ad vitandam
autem confusionem, ea dumtaxat membra in vestigio adumbrantur, quæ
recensuimus figurâ trigesimaoctavâ, & ostendunt characteres ~A~, ~B~,
~C~, ~D~, ~E~._
The FORTIETH FIGURE.
_The Geometrical Plan of a Design, of the ~Dorick~ Order._
For the Benefit of the Studious, who, having reduc’d to Practice the
Rules hitherto laid down, aim at yet greater Things; I have here
undertaken to delineate half an Arch adorn’d with three Columns, and as
many Niches for Statues. But to avoid Confusion, I have given full Lines
to those Members only, which were mention’d in the Thirty-eighth Figure,
and which are here denoted by the Characters A, B, C, D, E.
[Illustration: FIG. XLI.]
FIGURA Quadragesimaprima.
Elevatio geometrica ædificii Dorici.
_Ex vestigio geometrico eruitur hæc elevatio geometrica longitudinis
ædificii nostri. Et iccircò figura ista quadragesimaprima, cujus
mensuræ omnes desumptæ sunt ex Barozzio, congruit longitudini figuræ
quadragesimæ._
The Forty-first FIGURE.
_The Geometrical Elevation of the foregoing Design._
This Upright is drawn from the foregoing Geometrical Plan; and therefore
all the Parts of this Design, whose Measures are taken from _Vignola_,
exactly answer those of the Fortieth Figure.
[Illustration: FIG. XLII.]
FIGURA Quadragesimasecunda.
Modus vitandi confusionem, in contractione vestigiorum, & elevationum.
_Contractiones vestigii figuræ quadragesimæ, & elevationis figuræ
quadragesimæprimæ, ob nimiam obliquitatem quam habent, valde confusæ
sunt. Medebimur tamen incommodo isti, uti fecimus figuris decimâ &
undecimâ. Et ostendit chartula, exhibens in parvo tum figuram hanc
quadragesimamsecundam, tum quatuor sequentes._
The Forty-second FIGURE.
_The Manner of avoiding Confusion, in reducing Plans and Elevations into
Perspective._
The Reducing into Perspective the Plan of the Fortieth Figure, and
the Upright of the Forty-first Figure, would become very confus’d,
through the great Obliquity of the Rays: We have therefore remedy’d
the Inconveniences of both, by the Methods explain’d in the Tenth and
Eleventh Figures. And this Plate contains in little, what is more at
large describ’d in Parts, as well in this, as the four subsequent Figures.
[Illustration: FIG. XLIII.]
FIGURA Quadragesimatertia.
Contractio vestigii figuræ quadragesimæ.
_Linea plani multò remotior est à lineâ horizontali in hoc schemate, quàm
in præcedenti. Ideo istud vestigium vacat omni confusione. Cætera patent
ex iis quae sæpiùs dicta sunt, & ex figuræ hujus inspectione. Oportet
autem, rectas parallelas ad lineam plani, prolongari usque ad visualem
~TO~, (quæ cadit extra paginam) ut adminiculo parallelarum, fiat elevatio
longitudinis nostri ædificii, de quâ dicemus figurâ quadragesimaquartâ._
The Forty-third FIGURE.
_The Plan of the Fortieth Figure in Perspective._
By placing the Ground-line in this, much more remote from the Horizontal,
than it is in the foregoing Figure, all Confusion is here avoided. The
rest is evident from what has been often said on this Head, and a bare
Inspection of the Figure. Parallels to the Ground-line must nevertheless
be continu’d to the Visual TO, which falls without this Page; that from
them may be rais’d the Elevation of the Length of this Design, which we
shall handle in the next Figure.
[Illustration: FIG. XLIV.]
FIGURA Quadragesimaquarta.
Contractio elevationis figuræ quadragesimæprimæ.
_Rectæ parallelæ ad lineam plani figuræ quadragesimætertiæ, ubi
pervenerint ad visualem ~TO~, continuandæ sunt, more solito, cum
parallelis ad lineam perpendicularem. In hanc autem transferre oportet
omnes divisiones, quas ex Barozzio habet elevatio hujus ordinis; ac
ducere visuales. Quomodo autem, adminiculo visualium & parallelarum,
compleatur elevatio, constat ex figura, & clarius ex chartula figuræ
quadragesimæsecundæ. Numeri ~1~, ~2~, ~3~, ~4~, geminati, ostendunt
centra & altitudines semicirculorum seu arcuum figuræ quadragesimæquintæ;
videlicet, numerus inferior designat centrum, superior verò designat
altitudinem semicirculi._
The Forty-fourth FIGURE.
_The Elevation of the Forty-first Figure in Perspective._
When the Parallels to the Ground-line in the Forty-third Figure, are
prolong’d to the Visual TO, they are then, as usual, to be continu’d
Parallels to the Perpendicular: On which Perpendicular, those Divisions
given by _Vignola_, for the Proportions of this Order, are to be
transferr’d; and Visuals drawn from them to the Point of Sight. How by
these Visuals and Parallels the Elevation is rais’d in Perspective, is
manifest in part from this Figure, but more clearly from the Forty-second
Figure. The Numbers 1, 2, 3, 4, which you here see doubl’d, give the
Centers and Heights of Semicircles of the Arches in the Forty-fifth
Figure; the lower Numbers denoting the Centers, and the upper Numbers the
Heights of the Semicircles of the same.
[Illustration: FIG. XLV.]
FIGURA Quadragesimaquinta.
Dimidium ædificii Dorici opticè deformati.
_Huic figuræ delineandæ plures præiverunt, ejusdemque latitudines mutuati
sumus ex figura quadragesimatertia, altitudines ex quadragesimaquarta.
Superest autem, ut lumina & umbræ scitè inducantur in singulas partes
ædificii._
The Forty-fifth FIGURE.
_One Half of the ~Dorick~ Design in Perspective._
The foregoing Figures being preparatory to this, the Breadths are taken
from the Forty-third, and the Heights from the Forty-fourth Figure. It
only remains, that the Lights and Shades be skilfully dispos’d to each
Part of the Work.
[Illustration: FIG. XLVI.]
FIGURA Quadragesimasexta.
Alterum dimidium ejusdem ædificii.
_Supersedere poteram delineatione alterius medietatis ædificii nostri.
Verùm operæ non peperci, ut ostenderem diversitatem luminum & umbrarum,
quæ conveniunt partibus cæteroqui omnino similibus._
The Forty-sixth FIGURE.
_The other Half of the same Design._
I might very well have omitted this Half of the Design, but that I spar’d
no Pains, to shew the Diversity of the Lights and Shadows, that must be
given to those Parts of the Work, which in other Respects are alike.
[Illustration: FIG. XLVII.]
FIGURA Quadragesimaseptima.
Vestigia ædificii Ionici.
_Vestigium geometricum ~A~ ædificii Ionici, sub se habet suam
deformationem ~B~. Hæc autem ut evadat distinctior, lineam plani, quæ in
sequentibus figuris habebit distantiam ~PE~ ab horizontali ~OE~, deorsum
protraximus in ~CD~, ut etiam fecimus figurâ quadragesimasecundâ &
quadragesimatertiâ. Linea visualis ~OM~ eundem habet usum, quem visualis
~OT~ figuræ quadragesimætertiæ; videlicet, ut in ea terminentur parallelæ
ad lineam plani ex membris vestigii ~B~, eademque continuentur cum aliis
parallelis ad rectam ~EC~, pro deformandâ elevatione quam apponemus
figurâ quadragesimanonâ._
The Forty-seventh FIGURE.
_The Plan of an ~Ionick~ Building._
The Geometrical Plan of this _Ionick_ Work is A, underneath is its
Perspective B; to render which more distinct, the Ground-line that in
the following Figures has only the Distance PE from the Horizontal
EO, is here remov’d downward to CD, as was done in the Forty-second
and Forty-third Figures foregoing. The visual Line OM is of the same
use as that of OT in the Forty-third Figure; namely, to terminate the
Lines which are drawn from the Members of the Plan B parallel to the
Ground-line; from whence they are again continu’d parallel to the
Perpendicular EC, for making in Perspective the Elevation inserted in the
Forty-ninth Figure.
[Illustration: FIG. XLVIII.]
FIGURA Quadragesimaoctava.
Elevatio geometrica ædificii Ionici.
_Ex hac elevatione quæ clarè ostendit membra totius ædificii secundum
longitudinem dissecti, desumuntur altitudines ac terminationes membrorum
singulorum. Peritiores tamen hac figurâ delineandâ supersedere
solent, quia terminationes haberi possunt ex vestigio ~A~ figuræ
quadragesimæseptimæ, altitudines verò ponendæ iterum sunt figurâ
sequenti._
The Forty-eighth FIGURE.
_The Geometrical Upright of the foregoing ~Ionick~ Design._
From this Figure (which distinctly shews the Composition of the whole
Work, in respect of its Length) are taken the Heights and Terminations
of the several Members thereof. But those that are skill’d in this Art,
usually omit the delineating these Elevations; because the Terminations
may be taken from the Plan A in the Forty-seventh Figure; and the Heights
must be repeated in the following Figure.
[Illustration: FIG. XLIX.]
FIGURA Quadragesimanona.
Deformatio elevationis ædificii Ionici.
_Hæc figura continens deformationem præcedentis elevationis, perficitur
methodo illa, quam ostendimus figurâ quadragesimasecundâ; nimirum, ex
vestigio ~B~ figuræ quadragesimæseptimæ, ducere oportet parallelas ad
lineam plani ~CD~, quæ ubi pervenerint ad visualem ~OM~, continuandæ
sunt cum aliis parallelis ad lineam ~EC~. Easdem parallelas in hanc
figuram translatas secant visuales ex linea recta ~AB~, in qua positæ
sunt altitudines ædificii Ionici, desumpta vel ex figura præcedenti, vel
ex Barozzio. Nullum autem est punctum in membris hujus elevationis, quod
non inveniatur per sectiones visualium ex linea ~AB~, cum parallelis ad
eandem lineam._
The Forty-ninth FIGURE.
_The Elevation of the ~Ionick~ Design in Perspective._
This Plate containing the Perspective of the foregoing Upright, is
drawn by the Method laid down in the Forty-second Figure; to wit, from
the Plan B of the Forty-seventh Figure, Parallels to the Ground-line
CD are prolong’d to the Visual OM; and thence are continu’d Parallels
to the Perpendicular EC. These being transferr’d into this Figure, are
intersected by the visual Lines that proceed from AB, which contains the
Heights of this _Ionick_ Composition, agreeable to the foregoing Figure,
and the Rules deliver’d by _Vignola_. Now there is no Point in any Member
of this Upright, but may be found by the Intersection which the visual
Line from AB makes with its respective Perpendicular.
[Illustration: FIG. L.]
FIGURA Quinquagesima.
Architectura Ionica.
_Ex vestigio figuræ quadragesimæseptimæ, & ex elevatione figuræ
quadragesimænonæ, eruitur hoc ædificium Ionicum, quod esse poterit
vel principium alicujus turris campanariæ, aut basis cujuspiam arcûs
triumphalis. Vereor ut cælator suam diligentiam in hoc schemate
satis probaverit. Ejus tamen errata facilè ipse deteges, & omni studio
cavebis._
The Fiftieth FIGURE.
_A Design of ~Ionick~ Architecture._
From the Plan of the Forty-seventh Figure, and from the Upright of the
Forty-ninth Figure, is drawn this _Ionick_ Piece; which might well serve
for the lower Order of a Turret, or for part of a Triumphal-Arch. I fear
the Engraver has not been so exact in this Scheme, as he ought; but you
will readily discover his Mistakes, and carefully beware of them.
[Illustration: FIG. LI.]
FIGURA Quinquagesimaprima.
Ordo Corinthius.
_Complectitur hæc pagina molem contractam Ordinis Corinthii, cum suis
præparationibus. Vestigium ~A~ exhibet parietem pone columnas cavum
instar canalis. Idem vestigium opticè deformatur in ~D~: omissâque
elevatione geometricâ, per ejus altitudines notatas in lineâ ~BC~
projicitur elevatio; ac methodo consuetâ, ex vestigio & elevatione
componitur ædificium, addito statuæ unius ornamento._
The Fifty-first FIGURE.
_A ~Corinthian~ Design in Perspective._
This Plate contains the Perspective of a _Corinthian_ Work, with its
Preparations. The Geometrical Plan A shews the Wall wrought hollow
behind the Columns. The said Plan in Perspective is D: and leaving
out the Geometrical Elevation, the Perspective thereof is describ’d,
by transferring the Heights of the former into the Line BC. From the
Perspective-Plan and Upright the Design is finish’d after the usual
Manner; to which is added the Ornament of a single Statue.
[Illustration: FIG. LII.]
Figura Quinquagesimasecunda.
Delineatio columnæ spiralis, Ordinis Compositi.
_Posita elevatione geometrica columnæ rectæ, ac divisione illius in
vigintiquatuor partes æquales, columna spiralis absolvitur per partes
circumferentiæ circulorum, quorum diametri sunt æquales diversis
latitudinibus columnæ rectæ, ut ostendit figura in ~A~. Ad projectionem
opticam elevationis, notandæ sunt quatuor occultæ rectæ, quæ ex terminis
convexitatis & concavitatis infimarum spirarum ejusdem elevationis
~A~, descendunt ac desinunt in duos circulos vestigii geometrici ~B~.
Vestigium ipsum opticè imminutum habetur in ~C~: eædem autem sunt
maximæ hinc inde latitudines, tum in circulo majori, tum in convexitate
infimarum columnæ spirarum; eædem sunt maximæ latitudines, tum in circulo
minori, tum in concavitate ipsarum spirarum; ut dignosces applicando
regulam spiris simul & circulis. Ex quatuor punctis maximæ latitudinis
duorum circulorum, incipiunt quatuor lineæ parallelæ ad lineam plani,
quæ ubi pervenerint ad visualem ~ED~, continuandæ sunt cum parallelis ad
perpendiculum ~DF~. In eandem lineam ~DF~, ex elevatione ~A~ transferre
oportet vigintiquatuor partes æquales altitudinis columnæ, ac ducere
visuales ad ~O~ punctum oculi. Per sectionem autem visualium cum
prædictis quatuor parallelis ad lineam ~DF~, ducuntur lineæ undulatæ
~MN~, ~PQ~, ex quibus eruuntur lineæ utrinque terminativæ columnæ
spiralis nitidæ. Ex linea verò ~GH~ habetur facies anterior stylobatæ,
columnæ & coronicis; ex linea ~IL~ habetur facies eorum posterior._
The Fifty-second FIGURE.
_The Description of a wreath’d Column, of the Composite Order._
Having made the Geometrical Elevation of a streight Column, and divided
the Height of its Shaft into Four and twenty equal Parts; the Wreathing
is describ’d by Parts of the Circumference of Circles, whose Diameters
are equal to the several Breadths, or Diameters, of the streight Column;
as is shewn in the Figure A. For putting the Upright into Perspective,
four streight occult Lines are of use, which descend from the Extent
of the Swellings and Sinkings of the lower Wreaths of the Column A;
and terminate in two Circles of the Geometrical Plan B. The said Plan
laid down in Perspective is C. The utmost Extent of the greater Circle
determines that of the Convex Parts of the lower Wreaths: The greatest
Breadth of the lesser Circle gives that of the hollow Parts of the said
Wreaths; as may be perceiv’d, by applying a Ruler from the Wreaths to
the Circles of the Plan. From the four Points of greatest Breadth in
those Circles, four Lines parallel to the Ground-line are continu’d to
the Visual ED, and thence again continu’d parallel to the Perpendicular
DF. From the Elevation A, the Four and twenty equal Parts of the Columns
Height are transferr’d into the Line DF, and Visuals drawn from each to
the Point of Sight O. By the Intersections of those Visuals with the
four Perpendiculars aforesaid, are drawn the wav’d Lines MN, PQ; from
which, both the Out-lines of the finish’d Column are describ’d. But the
Fore-part of the Pedestal, Column, and Cornice, is taken from the Line
GH; the Back-part of the same from the Line IL.
[Illustration: FIG. LIII. A.]
Fig. Quinquages. tertia A.
Ordines Architecturæ, desumpti ex Palladio & Scamozzio.
_De Ordinibus Architecturæ, præter Barozzium, egregiè scripserunt
Palladius & Scamozzius; ac singuli, jure merito, suos habent asseclas &
patronos. Ut ergò, etiam juxta laudatissimorum Autorum placita, opticas
projectiones facere possis, omnes Ordines in hac paginâ exhibere volui,
ut in eorum Libris inveniuntur._
The Fifty-third Figure A.
_The Orders of Architecture, taken from ~Palladio~ and ~Scamozzi~._
Besides _Vignola_, _Palladio_ and _Scamozzi_ have also written
excellently well of the Orders of Architecture; and each of ’em have
deservedly their Followers and Admirers. That you might therefore be
enabl’d to make Designs in Perspective, after the Proportions of the most
celebrated Masters, I have in this Plate given you the Measures of all
the Orders, as deliver’d by them in their Books.
[Illustration: FIG. LIII. B.]
Fig. Quinquages. tertia B.
Modus triplex delineandi columnas spirales.
_Columnæ figuræ superioris carent ea concinnitate, qua præditæ sunt
columnæ spirales æneæ celeberrimi Equitis Bernini ad sepulcrum S. Petri
in Vaticano. Itaque methodum triplicem exhibeo ad minuenda spatia totius
altitudinis columnæ._
1. _Recta ~OA~ sit æqualis altitudini ~AB~ columnæ. Fiat autem recta
~OB~, & arcus ~AP~ ex centro ~O~, divisus in partes duodecim æquales,
ducendo rectas, quæ per puncta divisionum desinant in columnam rectam;
ac demum fiant parallelæ ad basim: Spatia inter has parallelas dabunt
aperturam circini pro triangulis æquilateris & pro spiris, ut ostendit
columna ~1~._
2. _Translatâ in ~C~ tertiâ parte altitudinis columnæ ab ejus imo scapo,
habeat circinus aperturam ~CD~; ac posito uno ejus crure prius in ~D~,
postea in ~C~, fiant duo parvi arcus ad ~E~: sectio illorum arcuum erit
centrum arcûs ~DC~, quem oportet dividere in duodecim partes æquales,
& ex punctis divisionum ducere parallelas ad basim. Tum spatiis inter
parallelas divisis in quatuor partes æquales, tres ex illis partibus
dabunt longitudinem crurum pro triangulis isoscelibus; vertices autem
triangulorum erunt centra singularum spirarum, ut ostendit columna ~2~._
3. _Ductâ ex medio summitatis ~G~ rectâ ~GF~, spatium ~HF~ transferatur
in ~I~, & fiat recta ~IL~ parallela ad basim ~HF~; spatium ~IL~
transferatur in ~N~, ac fiat ~NM~, & sic deinceps. In parvis columnis
triangula sine sensibili errore duci possunt per diagonales: in columnis
tamen grandioribus, alterutrum ex modis antea explicatis adhibere necesse
est._
The Fifty-third Figure B.
_Three different Ways of delineating wreath’d Columns._
The wreath’d Columns describ’d in the Fifty-second Figure, being divided
into Twenty-four equal Parts, want very much of that Elegancy of Contour,
which is visible in those brass Pillars, made by the famous Cavalier
_Bernino_, for S. _Peter_’s Sepulcher in the _Vatican_. Wherefore I here
lay before you three several Ways of diminishing the Spaces through the
whole Height of the Column.
1. Make the right Line OA equal to AB the Height of the Column; then draw
the Line OB, and on the Center O describe at pleasure the Arch AP, which
divide into twelve equal Parts, and by the Divisions draw streight Lines
from the Center O to the Line of the Column; and lastly continue the same
Parallels to the Base. The Spaces between these Parallels, shall be the
Sides of equilateral Triangles, wherewith you are to describe the Wreath
of the Column, as is seen in Column 1.
2. Having set the third Part of the Columns Height, from the Bottom of
the Shaft to the Point C; with the Interval CD, from the Centers D and
C, describe the Parts of Arches intersecting at E. On the Center E,
with the same Interval, describe the Arch DC, which divide into twelve
equal Parts; and from the Points of those Divisions, draw Parallels
to the Base. Then dividing each Space between the Parallels into four
equal Parts; three of those Parts shall be the Sides of the _Isosceles_
Triangle; whose _Vertex_ is the Center whereon to describe each Wreath of
Column 2.
3. Having drawn from the midst of the Columns top G, the Line GF, make HI
equal to HF, and draw IL parallel to the Base HF: Again, make IN equal to
IL, and draw NM also parallel, and so on. In small Pillars, the Centers
of the Diagonals of these Spaces may, without sensible Errour, serve for
describing the Wreaths; but in greater Columns, either of the other two
Methods is rather to be chosen.
[Illustration: FIG. LIV.]
FIGURA Quinquagesimaquarta.
Vestigia ædificii Ordinis Corinthii.
_Descripturi ædificium Corinthium octangulare, ponimus hic vestigia unius
ex quatuor partibus pilarum, quibus imponetur fornix in modum tholi, ut
constabit in figurâ quinquagesimaoctava. Ad faciliorem descriptionem,
in parte inferiori paginæ posui vestigium geometricum stylobatæ,
in superiori vestigium geometricum coronicis, cum latitudinibus &
longitudinibus membrorum singulorum; ut eas transferendo in lineam
plani more consueto, utrumque vestigium opticè deformetur. Ad vitandam
confusionem, prius notare oportebit puncta quæ spectant ad membra
propinquiora solido parieti, deinde alia._
The Fifty-fourth FIGURE.
_The Plan of a Design of the ~Corinthian~ Order._
Being to describe an Octangular _Corinthian_ Work, I have here inserted
the Plan of one Quarter of the Composition; which is vaulted in Form of a
_Cupola_, as is seen in the Fifty-eighth Figure. To render the Plan less
confus’d, I have, in the lower part of the Plate, given the Geometrical
Plan of the Pedestal; and in the upper part, that of the Cornice; with
the Breadths and Lengths of each Member: so that by transferring the same
into the Ground-line, after the usual Manner; you delineate each Plan
in Perspective. For avoiding Confusion, ’twill be requisite first, to
transfer the Points of those Members that are next the Solidity of the
Wall; and then proceed to the others.
[Illustration: FIG. LV.]
FIGURA Quinquagesimaquinta.
Elevatio ædificii Ordinis Corinthii.
_Elevatio geometrica ædificii octangularis congruit cum duobus ejus
vestigiis figuræ antecedentis. Quia verò elevatio parietis abscondit
secundam ex quatuor columnis, eademque in ædificio deformato conspicua
futura est; iccircò eam lineis occultis designare oportuit._
The Fifty-fifth FIGURE.
_The Geometrical Elevation of a ~Corinthian~ Work._
The Geometrical Elevation of this Octangular Design, is wholly
correspondent to the two Plans of the foregoing Figure: But because the
Wall in this Upright takes off the Sight from the second of the four
Columns, which is notwithstanding visible in the finish’d Perspective
that follows; ’tis requisite to delineate the same with occult Lines, as
in the Figure.
[Illustration: FIG. LVI.]
FIGURA Quinquagesimasexta.
Deformatio vestigiorum & elevationis ædificii Corinthii.
_In hac figurâ, lineam plani coincidere volui cum linea horizontis.
Itaque videri non posset vestigium inferius, nisi ut alias deorsum
protraxi lineam plani, hic è converso sursum promovissem lineam
horizontis, quam constitui mediam inter lineas plani utriusque vestigii,
ut ambæ projectiones essent æquè distinctæ. In elevatione, columna
secunda, quam, ut dixi, paries abscondit, lineis occultis designanda est._
The Fifty-sixth FIGURE.
_The Perspective Plans and Upright of the ~Corinthian~ Design foregoing._
In this Figure, I have made the Ground-line coincident with that of
the Horizon, in which case the lower Plan can’t be seen, unless the
Ground-line be sunk lower, as before intimated; or contrariwise, the
Point of Sight rais’d higher, as I have here done, keeping it in the
midst between the Ground-lines of the two Plans, that the Perspective
of both might be equally distinct. In the Elevation, the second Column,
which I mention’d to be hidden by the Wall, should be design’d with
occult Lines.
[Illustration: FIG. LVII.]
FIGURA Quinquagesimaseptima.
Adumbratio figuræ sequentis.
_Figuram hanc seorsim delineavi, ut videas quomodo facienda sit operis
totius adumbratio, accipiendo altitudines membrorum singulorum ex
elevatione; latitudines & longitudines ex vestigiis. Quæ omnia ex
diagrammatis inspectione clarissimè apparent._
The Fifty-seventh FIGURE.
_The rough Draught of the following Figure._
I have drawn this Figure apart, that you may see the Manner of describing
the Out-line of the whole Work, by taking the Heights of the several
Members from the Elevation, and their Breadths and Lengths from the
Plans; all which is very plain, upon Inspection of the Figure.
[Illustration: FIG. LVIII.]
FIGURA Quinquagesimaoctava.
Ædificium Ordinis Corinthii octangulare.
_Hucusque descripsimus pilas anticas sinistras ædificii Corinthii. En hoc
loco medietatem dexteram totius Operis. Integrum verò ædificium habebis
figurâ sexagesimâ._
The Fifty-eighth FIGURE.
_Part of an Octangular Work of the ~Corinthian~ Order._
Hitherto the nearest left-hand Quarter of this _Corinthian_ Design has
been describ’d. In this Plate you have the right-hand Half of the whole
Work; and in the Sixtieth Figure, the entire Perspective compleat.
[Illustration: FIG. LIX.]
FIGURA Quinquagesimanona.
Vestigia tabernaculi octangularis.
_Projectiones rerum octangularium sunt quadratis difficiliores: ideò
in eis explicandis diligentiæ non peperci. Moles cujus vestigia
vides in ~A~ & ~B~, convenit in multis cum eâ quam ereximus figurâ
quinquagesimaoctavâ. Visualis ~CD~ recipit sectiones perpendicularium,
quæ deserviunt pro elevatione figuræ sequentis, ut sæpius dictum est. Si
facies interior delineanda sit seorsim à facie anteriori, illam perficies
ope linearum ~CE~, istam ope linearum ~FD~._
The Fifty-ninth FIGURE.
_The Plans of an Octangular Tabernacle._
Octangular Figures being more difficult to be put in Perspective,
than the Square; I shall use my best Endeavours to render the Method as
plain as possible. The Composition whose Plans you see in A and B, has
much Affinity with that describ’d in the Fifty-eighth Figure. The Visual
CD receives the Sections, from which Perpendiculars are rais’d for the
Elevation and Profile of the following Figure, as has been often said. If
you would delineate the Back-part separate from the Fore-part, you may do
the former by means of the Line CE, and the latter by that of FD.
[Illustration: FIG. LX.]
FIGURA SEXAGESIMA.
Tabernaculum octangulare.
_Hoc tabernaculo aliquoties usus fui pro expositione quadraginta horarum.
Si colores scitè inducti fuerint in duos ordines telariorum, resectis
omnibus quæ ad molem ipsam non pertinent, spectatoribus imponet, & solida
videbitur. Oportebit autem exemplar externæ faciei eruere ex parte ~DF~
vestigii & elevationis; exemplar interioris faciei eruere ex parte ~EC~,
servando in omnibus regulas quas hucusque tradidimus._
The SIXTIETH FIGURE.
_An Octangular Tabernacle in Perspective._
I have sometimes made use of this Tabernacle for the Exposition of the
_Forty Hours_. If the Colours are laid by a skilful Hand, on two Ranges
of Cloth, and the Frame cut away according to the Out-line of the Work,
they will wonderfully deceive the Eye, and appear as solid; but then the
outer Range must be drawn after the Plan and Elevation of the Part DF in
the foregoing Figure; and the inner Range after that of EC; in all things
observing the Rules hitherto deliver’d.
[Illustration: FIG. LXI.]
FIGURA Sexagesimaprima.
Modus erigendi machinas, quæ constant pluribus ordinibus telariorum.
_Ex figuræ inspectione addisces modum erigendi machinas quæ constant
pluribus ordinibus telariorum. Tabernaculum hoc nostrum indiget duobus
tantum ordinibus; nam telaria propinquiora oculo exprimunt faciem
externam, remotiora exhibent faciem internam. Ne autem lateant stipites
quibus telaria sustinentur, medietatem telariorum adumbrare omisimus.
Recta ~LS~ est linea plani, recta ~DG~ est linea horizontalis; ac
punctum distantiæ quod cadit extra paginam in recta ~CG~ prolongatâ,
debet esse remotum à puncto ~C~, quantum in superiori parte figuræ
quinquagesimænonæ, punctum distantiæ est remotum à puncto oculi. Eadem
horizontalis ~DG~ secatur normaliter in ~C~ à recta ~EF~, quæ est sectio
externæ faciei tabernaculi, & ex ~C~ incipiunt divisiones in partes
æquales pro reticulatione anterioris faciei telariorum, ut dicemus figurâ
sexagesimasecunda. Recta ~IL~ quæ est sectio internæ faciei tabernaculi,
distat ad libitum à recta ~EF~ cui est parallela. Porrò, per divisiones
rectæ ~EF~ (ut vides in ~M~, ~N~, ~O~) ex puncto distantiæ ducendæ sunt
visuales ad rectam ~IL~ pro reticulatione aliorum telariorum: distantia
enim ~DC~ facit ut augere oporteat ea quæ in telariis pinguntur, alioquin
justo minora viderentur. Atque hinc dignosces, cur arcus qui in telariis
anterioribus pertingeret solum ad ~B~, in posterioribus elevetur usque ad
~H~._
_Figura sequenti proponemus modum delineandi faciem internam telariorum,
adhibita reticulatione externæ faciei: ad intelligentiam verò illius
methodi, fiat in hac figurâ recta ~HP~ parallela ad ~DC~, ac recta ~BC~
dividatur in totidem partes æquales, in quot partes divisa fuerit recta
~PC~._
The Sixty-first FIGURE.
_The Manner of erecting Machines, that consist of several Ranges of
Frames._
By casting your Eye on the Figure, you’ll readily apprehend the Manner
of erecting the several Ranges of Frames. This Tabernacle last describ’d
needs only two of them; the Frame next the Eye represents the outer Face,
and the hinder Frame the inner Face thereof. I have here describ’d but
the Half-Breadth of the said Frames, that you might have a Sight of the
Poles and Braces which support them. The Line LS is the Line of the Plan,
or Ground-line; the Line DG is that of the Horizon; and the Point of
Distance, which falls without the Page CG prolong’d, is as far from the
Point C, as the Point of Distance is from the Point of Sight in the upper
Part of the Fifty-ninth Figure. The Horizontal DG is cut perpendicularly
in C by the Line EF, which is the Section of the outer Face of the
Tabernacle; and from the Point C begin the equal Divisions for the
Net-work of the foremost Frame, as is shewn in the Sixty-second Figure.
The Line IL, which is the Section of the inner Face of the Tabernacle,
may at pleasure be set nearer or farther from the Line EF, to which it is
parallel. By the Divisions of the Line EF (as M, N, O) Lines are drawn
from the Point of Distance to the Perpendicular IL, for the Net-work of
that Frame; for the Distance DC obliges the Parts of D to be painted
larger, otherwise they will appear less than they really ought. And from
hence you may discern, why the Arch, which in the foremost Frame would
reach only to B, does in the hindmost rise up to H.
In the following Figure is shewn the Manner of delineating the inner
Frame, from the Net-work of the outer Face; for the better understanding
of which, make the Line HP in this Figure parallel to DC, and let the
Line BC be divided into as many equal Parts, as the Line PC was.
[Illustration: FIG. LXII.]
FIGURA Sexagesimasecunda.
De reticulandis telariis, quæ repræsentent ædificia solida.
_Duo exemplaria tabernaculi quæ seorsim delineanda sunt, conjunctim
habes in ~A~. Utrisque deservit eadem reticulatio, quam suis numeris
insignivimus. Postquam ergo designaveris amplitudinem totius ædificii,
cum proportione ad ipsam reticulabis pavimentum ~B~ aulæ cujuspiam quod
capiat rem totam, ascriptis eisdem numeris quos habet exemplar: ejusque
retis ope, ducentur in pavimento lineæ terminativæ totidem membrorum,
quot futura sunt telaria exprimentia faciem externam tabernaculi. Ubi
hæc parata fuerint, singula disponentur exactè suis locis in ipsomet
pavimento; ac funiculis colore nigro imbutis, repetetur in telariis eadem
reticulatio, additis ad libitum pluribus visualibus; quarum adjumento
dum seorsim pinguntur telaria, duci queant rectæ tendentes ad punctum
oculi seu perspectivæ. Alia quoque reticulatio super pavimento necessaria
est pro internâ facie tabernaculi: ac duæ reticulationes pavimenti eam
inter se proportionem habebunt, quam habent divisiones rectarum ~IL~,
~EF~, figuræ sexagesimæprimæ. Hujus retis ductu fient lineæ terminativæ
telariorum cum reliquis, ut jam indicavimus._
_Juxta hanc methodum nequeunt duci lineæ terminativæ interioris faciei,
nisi fiat in pavimento aliud rete deleto priori, quod esset valdè
laboriosum. Postquam ergo ex vestigio figuræ quinquagesimænonæ eruta
sint duo exemplaria, in exemplar faciei externæ transferatur recta ~PC~
figuræ sexagesimæprimæ, in exemplar faciei internæ transferatur recta
~BC~. Si autem recta ~PC~ divisa fuerit in quindecim partes æquales,
dividetur ~BC~ in quindecim partes æquales, atque ope harum divisionum
reticulare oportebit utrumque exemplar. Porrò licet quadrata in reti
exemplaris faciei externæ sint majora quadratis exemplaris internæ
faciei, nihilominus idem rete pavimenti deserviet pro ducendis lineis
terminativis utriusque faciei. Quæ dicta sunt de duobus exemplaribus,
valent de aliis quotcunque. Exempli gratiâ; si construere placeat quinque
ordines telariorum, fient quinque exemplaria in papyro. Si in omnibus
exemplaribus usurpetur eadem reticulatio, in pavimento facere oportet
quinque diversas reticulationes. Si autem in exemplaribus fiant
quinque diversæ reticulationes, in pavimento sufficit una reticulatio._
_Curandum est ut singula retis quadrata in telariis sint exacta, omnesque
illorum anguli sint recti. Modus expeditissimus faciendi angulos rectos
est hujusmodi. Posito uno crure circini in puncto ~F~ lineæ rectæ ~EF~,
alioque crure posito ubilibet in ~O~, fiet circulus ~GFI~, & ex puncto
~G~ diameter ~GI~. Si recta ~HF~ transeat per puncta ~I~ & ~F~, est
normalis ad ~EF~._
The Sixty-second FIGURE.
_Of making the Net-work on Frames, for representing the Architecture as
solid._
You have jointly in A, the two Designs of a Tabernacle, which are to
be drawn separately; the same Net-work serving for both, which is also
mark’d with Numbers. When you have therefore resolv’d on the Size of
your Work, on the Pavement of some Room capacious enough make a Net-work
answerable, and affix thereto the Numbers, as in your Copy: By the Help
of which, you may on the Pavement describe the Out-line of all those
Members that are requisite to the outer Frame of the Tabernacle. This
being done, let the Frame be laid exactly in its place on the said
Pavement, and with a black Line strike thereon the same Net-work; adding
as many visual Lines as you please, which will be of Use for drawing
Lines to the Point of Sight, when you come to paint the Frames asunder.
Another Net-work on the Pavement is also necessary for the inner Face
of the Tabernacle, which should bear such Proportion to this, as the
Divisions of the Line IL do to those of EF in the Sixty-first Figure; and
by this means the Out-lines of the inner Frame, _&c._ may be drawn, as
has been shewn already.
Thus the Out-line of the inner Face can’t be describ’d, without rubbing
out the first Net-work, and making a second on the Pavement; which would
be very troublesom. Wherefore, from the Plan of the Fifty-ninth Figure,
take the two Designs, and transfer the Line PC of the Sixty-first Figure
on the outer Face, and the Line BC on the inner Face. Then if PC were
divided into fifteen equal Parts, BC shall be divided in the same manner,
and by these Divisions make the Net-work on each Design. And although
the Squares of the outer Face be larger than those of the inner one, the
same Net-work may nevertheless serve for giving the Out-line of both.
What has been said of these two Designs, may be understood of many. For
Instance; if five Ranges of Frames were requir’d, five Designs must be
made in Paper. If in all the Designs the same Net-work be us’d, then five
several Net-works must be made on the Pavement; but if the Designs have
five different, then one Net-work on the Pavement will suffice.
You must be very careful that all the Squares of the Net-work be exactly
divided, and at right Angles. The ready way of making a right Angle is
thus: Placing one Foot of the Compasses in the Point F of the Line EF,
and the other at pleasure in O, describe the Circle GFI; and from the
Point G draw the Diameter GI. The Line FH drawn by the Points FI, shall
be perpendicular to FE.
[Illustration: FIG. LXIII.]
FIGURA Sexagesimatertia.
Vestigia ædificii quadrati.
_Vestigium geometricum ~A~ hujus ædificii habet in ~B~ suam
deformationem. Discrimen inter pilas ~C~ & ~D~ oritur ex eo, quòd in ~C~
posita sint vestigia stylobatarum, in ~D~ autem posita sint vestigia
coronicum._
The Sixty-third FIGURE.
_The Plan of a square Design._
The Geometrical Plan of this Design A, is brought into Perspective in B.
The Difference between the Parts C and D arises from hence, that the Plan
of the Pedestals is plac’d in C, and that of the Cornice in D.
[Illustration: FIG. LXIV.]
FIGURA Sexagesimaquarta.
Ædificium quadratum.
_Ex deformatione vestigii & elevationis, methodo consuetâ eruitur imago
totius ædificii, quæ potest esse exemplar aræ maximæ alicujus Ecclesiæ.
Hanc machinam, non sine communi approbatione, aliquoties adhibui, in
apparatu quadraginta horarum; locum in medio vacuum occupantibus Angelis
cum nubibus, additâ figurarum aliquot copiâ in parte inferiori. Modus
faciendi in telariis remotioribus ab oculo partem tholi rotundi quam hic
vides, deducitur ex iis quæ tradidimus in projectione circulorum._
The Sixty-fourth FIGURE.
_A square Design in Perspective._
From the Plan and Upright in Perspective, this finish’d Piece of the
whole Work is delineated after the usual Manner, and may serve for
the Design of a great Altar in a Church. I have sometimes, for the
Solemnity of the _Forty Hours_, expos’d this painted on a Machine, with
an universal Satisfaction; Angels with Clouds possessing the higher part
of the Hemisphere within, and Groups of Figures the lower part. The
Manner of designing on the inner Frame, that part of the said _Cupola_
which you here see, is deduc’d from what has been before said of putting
Circles into Perspective.
[Illustration: FIG. LXV.]
FIGURA Sexagesimaquinta.
Vestigium ædificii rotundi opticè imminutum.
_Qui sedulam operam in circulis deformandis non posuerint, eosque minimo
negotio ex usu describere nequiverint, frustra conabuntur projicere
vestigia ædificiorum rotundorum. Ad vitandam confusionem, proderit in
vestigio notare primùm lineas occultas membrorum præcipuorum; iisque
translatis in elevationem, addere sensim reliquas. Hac industriâ ego
ipse in hoc schemate usus sum. Quum autem experimento didicerim summam
arduitatem harum descriptionum, aliam regulam adhibere jamdiu cœpi, quam,
ut suprà diximus, in aliud Opus reservamus._
The Sixty-fifth FIGURE.
_The Plan of a Circular Work in Perspective._
They that have not diligently apply’d themselves to the putting Circles
into Perspective, and, by a constant Practice, render’d the Work familiar
to them, will in vain attempt that of the Plans of round Buildings. To
prevent Confusion, you’ll do well, first to mark the occult Lines of the
principal Members; and after those are transferr’d into the Upright, then
proceed to the rest, as I myself did in this Figure. But having found
by Experience, the great Difficulty of describing these round things, I
have long since made use of another Method, which, as I said before, is
reserv’d for another Volume.
[Illustration: FIG. LXVI.]
FIGURA Sexagesimasexta.
Projectio ædificii rotundi.
_Mirifice oculis imponunt imagines rerum rotundarum, si omnibus resectis
quæ ad eas non pertinent, exactè delineatæ ac depictæ fuerint. Hanc
figuram ex vestigio eruere oportebit methodo consuetâ, eamque in
Templo S. Ignatii Collegii Romani construxi pro feriâ V & VI Hebdomadæ
sanctioris. Intra arcum, super altari, locus erat urnæ sepulcrali, cum
Venerabili Sacramento. Sub altari visebatur simulacrum Christi Domini è
Cruce depositi: in medio columnarum, imago Beatæ Virginis dolentis; super
balaustiis Angeli lugentes, cum instrumentis cruciatuum Salvatoris._
The Sixty-sixth FIGURE.
_A Circular Design in Perspective._
The Appearance of round things, if well design’d, masterly painted, and
the Frame cut away to the Out-line of the Work, do wonderfully deceive
the Eye. This Figure is drawn from the Plan, as usual; and was put in
execution by me, in the Church of S. _Ignatius_ of the _Roman_ College,
for the _Thursday_ and _Friday_ of the Holy Week. Within the Arch, on the
Altar, was plac’d a sepulchral Urn containing the Holy Sacrament. Beneath
the Altar was laid a Figure of our Saviour Christ taken down from the
Cross. In the midst of the Tambour, was a Picture of the Blessed Virgin
in extreme Sorrow; and on the Ballustrade, Angels mourning, bearing the
Instruments of the Passion.
[Illustration: FIG. LXVII.]
FIGURA Sexagesimaseptima.
Vestigium geometricum, ac prima præparatio ad figuram septuagesimamprimam.
_Egregiam adeò speciem præsetulit, atque oculis adeò imposuit machina
quam construxi anno 1685, pro supplicatione quadraginta horarum, in
Templo Urbis Farnesiano, ut decreverim satisfacere Studiosis, publici
juris faciendo non modò imaginem totius ædificii, sed etiam illius
vestigia & elevationes: quæ omnia eâ diligentiâ delineavimus, veluti
Opus ipsum non pennicillo colorandum, sed lapidibus extruendum fuisset.
Spatia nigrantia soliditatem designant parietum & columnarum. Cæteræ
lineæ sunt crepidines stylobatarum & coronicum. Initium delineationis
fiet ab iis membris, ex quibus oriuntur lineæ occultæ positæ in ~A~, (quæ
autem dicuntur de hac medietate, intelligi debent de aliâ) ne multitudo
linearum confusionem pariat. In ~B~ lineæ curvæ occultæ sunt vestigium
tholi qui complet summitatem ædificii. Vestigium ~C~ exhibet ambulacrum
interius. Omisimus autem vestigium theatri, quia paginæ angustia illud
non capit._
The Sixty-seventh FIGURE.
_The Geometrical Plan, and first Preparation to the Seventy-first Figure._
The Machine which I erected in the Year 1685, in the Church _Farneze_,
or _Jesuits_ Church at _Rome_, for the Devotions of the _Forty Hours_;
had so admirable an Effect, and so pleasantly deceiv’d the Eye, that
I resolv’d to gratify the Studious, not only with a general View, but
with the Plan and Elevation thereof; all which was perform’d with such
Exactness, that the Work itself seem’d rather to consist of solid Stones,
than to be wrought by the Painter’s Hand. The hatch’d Part denotes
the Solidity of the Walls and Columns. The other shews the Breaks and
Projectures of the Pedestals and Cornices. Lest many Lines should cause
Confusion, begin with those Members, which produce the occult Lines on
the Side A; understanding the same also of the other half. In B the
occult curv’d Lines are the Plan of the _Cupola_ which crowns this
Structure. The Plan C is that of the inner Vestibule, but that of the
Theater is here omitted, through Want of Room in the Page.
[Illustration: FIG. LXVIII.]
FIGURA Sexagesimaoctava.
Elevatio geometrica vestigii præcedentis, & secunda præparatio ad figuram
septuagesimamprimam.
_In hoc schemate habes elevationem ædificii sectam in longum, quam figurâ
septuagesimâ opticè projiciemus: eisdemque membris constare videbis
elevationem deformatam, quibus constat elevatio geometrica. Hinc disces
ad excogitandas hujusmodi machinas, eandem Architecturæ scientiam in
Pictore necessariam esse, quæ ad construenda solida ædificia exigitur
in Architecto._
The Sixty-eighth FIGURE.
_The Geometrical Elevation of the foregoing Plan, and second Preparation
to the Seventy-first Figure._
In this Figure you have the Elevation of the aforesaid Structure
dissected lengthwise; the Perspective thereof is describ’d in the
Seventieth Figure; and you may observe that both of them consist of the
same Members: whence you may perceive, that for designing things of this
kind, the Painter ought to have no less Skill in Architecture, than is
requir’d for the Execution of solid Works.
[Illustration: FIG. LXIX.]
FIGURA Sexagesimanona.
Deformatio vestigii figuræ sexagesimæseptimæ, & præparatio tertia ad
figuram septuagesimamprimam.
_Artificium projectionis vestigii hujus, explicatum à nobis est figurâ
quadragesimasecundâ. Nimirum, ut parallelæ sint invicem distantiores,
lineam plani deorsum protraximus, ut ex intuitu figuræ statim cognosces._
The Sixty-ninth FIGURE.
_The Plan of the Sixty-seventh Figure in Perspective, and third
Preparation to the Seventy-first Figure._
The Artifice us’d in projecting the Perspective of this Plan, has been
already shewn in the Forty-second Figure; namely, that for giving the
greater Distance between the Parallels, the Ground-line is drawn much
lower than its true Place; as is manifest on Inspection of the Figure.
[Illustration: FIG. LXX.]
FIGURA SEPTUAGESIMA.
Deformatio elevationis figuræ sexagesimæoctavæ, & præparatio quarta ad
figuram septuagesimamprimam.
_Quæ dicta sunt de projectione vestigii nostri ædificii, habent locum
in elevatione. Nimirum, ut parallelæ invicem notabiliter distarent, usi
sumus industriâ quam declaravimus figurâ quadragesimasecundâ._
The Seventieth FIGURE.
_The Perspective of the Elevation of the Sixty-eighth Figure, and the
fourth Preparation to the Seventy-first Figure._
What has been said of the Perspective-Plan of this Structure, is also
here practis’d in the Elevation; namely, that the Parallels might be
sufficiently distinct, the Perpendiculars are drawn more remote from the
Point of Sight, as was shewn in the Forty-second Figure.
[Illustration: FIG. LXXI.]
FIGURA Septuagesimaprima.
Theatrum repræsentans Nuptias Canæ Galilææ, constructum Romæ, anno 1685.
in expositione Ven. Sacramenti in Templo Farnesiano Societatis JESU.
_Ex antecedentibus præparationibus eruimus projectionem nobilis hujus
Architecturæ, quæ oculos implebat tum ad lucem solis diurnam, tum
præcipuè ad lumen candelarum; ex quibus multæ palam erant expositæ,
aliæ omnino latebant, ut illuminarent sex diversos ordines telariorum
quibus tota machina constabat, non computando in hoc numero telaria,
quæ in medio arcûs maximi exprimebant nubes refertas Angelis adorantibus
Venerabile Sacramentum. Nubes istas omisimus, ne absconderentur
partes interiorum ædificiorum. In disponendis autem ordinibus
telariorum, servatus est modus quem declaravi figurâ sexagesimaprima
& sexagesimasecunda; ac præterea in eligenda eorum distantia curatum
fuit, ut candelæ in parte postica telariorum collocatæ, illuminarent
faciem telariorum interiorum. Porrò quot membra præcipua in duabus
faciebus majoribus, totidem distincta telaria numerabantur, quorum
proinde connexiones discerni vix poterant; eorumque aliquot paria ferreis
hamulis copulata erant, ut explicari ac replicari possent, ad faciliorem
tractationem diuturnioremque conservationem._
_Qui hucusque sequuti me fuerint, nihil dubito quin suum iter felicissimè
sint prosequuturi; atque Opera his nostris majora melioraque inventuri._
The Seventy-first FIGURE.
_A Theater representing the Marriage of ~Cana~ in ~Galilee~, erected in
the ~Jesuits~ Church at ~Rome~, in the Year ~1685~; for the Solemnity of
exposing the Holy Sacrament._
From the foregoing Preparations, is drawn the Perspective of this noble
Piece of Architecture; which struck the Eye when seen by Day-light, but
was more especially surprizing by Candle-light; many of the Candles being
expos’d to Sight, and others altogether hidden, to illuminate the six
different Ranges of Scenes, of which the whole Work consisted, without
reckoning that in the midst of the great Arch, representing Clouds fill’d
with Angels adoring the blessed Sacrament. Those Clouds are here omitted,
that the inner Parts of the Work might be the better seen. In disposing
the several Ranges of Scenes, the same Method was observ’d, which was
deliver’d in the Sixty-first and Sixty-second Figures; and great Care was
also taken in their Distances, that the Candles plac’d on the Back of one
of them might illuminate the Face of the other behind it. Moreover, each
Scene consisted of as many parts, as there were principal Members in the
two greater Façades; so that the Joints were scarcely discernible: and
some Pairs of them being coupl’d with Hinges, folded and unfolded, for
the more easy managing and preserving them.
I doubt not but those who have follow’d me thus far, will be encourag’d
so to prosecute their Studies, as to be able to design even greater and
more noble Works, than these of mine.
[Illustration: FIG. LXXII.]
FIGURA Septuagesimasecunda.
De theatris scenicis.
_Theatris quæ jam delineavimus affinia sunt theatra scenica: in his tamen
non adeò facilè reperitur punctum oculi seu perspectivæ. Præterea, quia
ex obliquitate canalium intra quos moventur scenæ, oritur ut lineæ rectæ
quæ videri debent parallelæ ad lineam plani, non debeant esse parallelæ
sed obliquæ, harum delineatio difficultate non caret. Incommodum istud
vitari posset adhibendo canales parallelos ad poscenium, ut alicubi
fieri solet, præsertim in Germaniâ. Nihilominus usus Italicus affert
hoc adjumentum, ut illi quibus incumbit suggerere actoribus, vel scenas
movere, aliisque similibus præesse, facilius lateant & liberius fungantur
munere suo._
_Ut brevem summam habeas eorum quæ deinde latius declaraturi sumus,
hanc figuram contemplare. ~1~, ~2~, ~3~, ~4~, est vestigium aulæ quæ
habet in longitudine centumviginti palmos Romanos, in latitudine
sexaginta palmos; ut ostendit scala ~S~ triginta palmorum. Medietatem
loci occupat theatrum, medietatem obtinent podia & loca spectatorum.
~O~ punctum in quo uniuntur lineæ visuales, ~D~ locus pro apparentiis
rerum magis ac magis distantium. ~BC~ locus poscenii. ~HH~ sunt canales
obliqui, quorum latitudo est dupla latitudinis scenarum. ~FG~ frons
& facies theatri. ~AO~ ejus profunditas aut longitudo. ~E~ locus pro
psaltibus, tibicinibus, & fistulatoribus. ~K~ spatium pro spectatoribus.
~I~ vestigium podiorum. ~L~ scalæ podiorum. ~N~ ipsorum elevatio. ~M~
declivitas tabulati, cum sectione & elevatione theatri, & scenis ex
latere inspectis, quæ cum suis canalibus congruunt, ut demonstrant lineæ
occultæ. ~OO~ linea normalis ad lineam horizontalem. ~P~ & ~Q~ elevatio
scenarum coram inspectarum, quæ introrsum flectuntur; & in latitudine
congruunt cum canalibus vestigii ~B~, in altitudine cum sectionibus
elevationis ~M~; ut constat ex lineis occultis. In eâdem elevatione ~M~
pars altitudinis tribuenda est scenis, pars laquearibus ~R~, per quæ
jungitur unumquodque par telariorum. ~VV~ lineæ ad explorandum an detur
vacuum inter scenas & laquearia, vel inter scenas, vel inter laquearia.
In quibusdam autem scenis, loco laquearium pinguntur nubes & aer._
The Seventy-second FIGURE.
_Of Scenes for the Stage._
Scenes for the Stage have very much Affinity with those lately describ’d,
but the Point of Sight is not so easily found in these; and from the
Obliquity of the Grooves in which the Scenes run, it comes to pass, that
the right Lines which ought to appear parallel to the Line of the Plan,
must not be drawn parallel thereto, but oblique; which is a Work of some
Difficulty. This indeed may be avoided, by fixing the Grooves parallel
to the Poscene; as is usual in some Places, especially in _Germany_.
Nevertheless, the _Italian_ Manner has this Advantage; That those who
are employ’d to prompt the Actors, and shift the Scenes, _&c._ are less
expos’d to Sight, in the Performance of their Business.
In this Figure I have given you an Abridgment of those things, which
shall hereafter be more enlarg’d on. The Numbers 1, 2, 3, 4, denote the
Area of a Hall an hundred and twenty _Roman_ Palms in Length, and sixty
in Breadth; as is manifest from the Scale of thirty Palms mark’d S. Half
this Space is taken up by the Stage, the other half by the Spectators. O
is the Point in which the visual Lines concenter. D is the Place of those
things that are to appear most remote. BC is the Place of the Poscene.
HH are the oblique Grooves, whose Lengths are double the Breadth of
the Scenes. FG is the Front of the Stage. AO is its Depth or Length.
E is the Place for the Musick. K is the Room for Spectators. I is the
Plan of the Galleries. L the Stairs to the same. N is the Elevation of
the Galleries. M shews the Declivity of the Floor, with the Section
and Elevation of the Stage and Scenes view’d on the Side; answering
their respective Grooves, as the occult Lines demonstrate. OO is a Line
perpendicular to that of the Horizon. P and Q are the Elevation of the
Scenes view’d in Front, turning inwards, in Breadth agreeing with the
Length of the Grooves of the Plan B; and in Height answering that of the
Sections of the Elevation M; as is evident from the occult Lines. In this
Profile M, part of the Height belongs to the Scenes, and part to their
Soffites, or Ceilings, R; where each Pair of these Frames are join’d. VV
are the Lines by which is espy’d what Vacancy there is either between
the Scenes and their Ceilings, between the Scenes themselves, or between
their respective Ceilings; though in some Scenes the Place of these last
is supply’d by painting therein the Air with Clouds, _&c._
[Illustration: Fig. lxxiii.]
FIGURA Septuagesimatertia.
Aliud vestigium theatri, ubi de modo inveniendi ejus punctum.
_Si pingendæ sint scenæ theatri alicujus antea constructi, delineare
oportebit vestigium geometricum ex ipso erutum, (ad formam vestigii quod
cernis in hac paginâ) ut inveniatur longitudo theatri, seu distantia quam
ejus punctum habet à puncto ~A~: id autem nullo negotio fiet, accipiendo
distantias ~BC~ inter primos canales, & ~DE~ inter ultimos, ac ducendo
visuales ~MO, NO~: nam theatrum habebit longitudinem ~AO~, ac punctum
perspectivæ in vestigio theatri erit ~O~. Præterea scire oportebit
longitudinem & latitudinem canalium, eorumque numerum, distantias, &
flexus; ac præcipuè curandum est, ut licet sint obliqui ad lineam ~MN~,
sint invicem paralleli in unoquoque latere, ac singuli tangant lineas
~MO, NO~. Jam si rectæ ~AO~ fiat æqualis recta ~FA~, in ~F~ erit punctum
distantiæ: adeoque si theatrum juxta methodum à nobis tradendam depictum
fuerit, spectatori qui consistat in ~F~ apparebit veluti tabula picta
juxta leges perspectivæ, posita in ~A~._
The Seventy-third FIGURE.
_Another Plan of a Theater, with the Method of finding the Point of Sight
therein._
If it be requir’d to paint the Scenes of some Theater already built, the
Geometrical Plan thereof must first be carefully drawn, (as you see, for
Example, in this Plate) that the Length of the Theater may be found; or
the Distance of its Point from that of A; which is easily done, by taking
the Interval BC of the first Grooves, and DE of the latter; and drawing
the Visuals MO, NO: for AO is the Length of the Theater, and the Point
of Sight, or Perspective, therein, is O. Moreover the Length and Breadth
of the Grooves must be known, as also their Numbers, Distance, and
Obliquity; and especial Care must be taken, that though they be oblique
to the Line MN, that on each Side they be Parallels between themselves,
and that they all touch the Lines MO, NO. If you then make AO equal to
FA, the Point of Distance will be F; and if the Theater be painted
according to the Rules hereafter given, it will appear to him that views
it from F, as a regular Piece of Perspective plac’d in A.
[Illustration: FIG. LXXIV.]
Figura Septuages. quarta.
Sectio Scenarum Theatri.
_Præter vestigium Theatri delineanda est sectio scenarum. Itaque si
acceptis mensuris altitudinis, quam punctum ~A~ unde incipit tabulatum,
ac punctum ~D~ poscenii, habent supra planum horizontale ~FV~, fiant ex
perpendiculo ~NV~ tum recta ~ADO~ ex qua innotescit declivitas tabulati,
tum recta ~NO~, quæ sit parallela ad ~FV~ & æqualis rectæ ~AO~ figuræ
septuagesimætertiæ; punctum theatri in elevatione est ~O~; in poscenio
verò punctum theatri est ~Q~. Si maxima scenarum altitudo sit ~EB~, recta
~OE~ dat altitudinem omnium reliquarum. Vera tamen altitudo cujuslibet
scenæ est illa quam habet linea major, ex minori autem dignoscitur
quantum obliquitas cujusque scenæ apparenter minuat altitudinem extremæ
illius lineæ. Porro excessus quo linea major superat minorem tum in summo
tum in imo, diligenter notandus est, hinc enim pendet intelligentia
figuræ septuagesimæquintæ. Punctum ~M~ quod est remotum ab ~N~ quantum in
figura septuagesimatertia punctum ~F~ est remotum ab ~A~, designat locum
unde Theatrum spectari oporteat, ut ibidem notavimus._
_In construendo tabulato solet servari hæc regula, ut altitudo puncti ~O~
sit æqualis altitudini oculi, & elevatio ex ~A~ usque ad ~D~ sit nona
circiter vel decima pars ipsius longitudinis ~AD~. Expediret autem ad
scenas facilius movendas, pavimentum ~F~ esse profundius pavimento ~G~,
ut erecto corpore sub tabulato ambulari possit._
Seventy-fourth Figure.
_The Section or Profile of Scenes for Theaters._
Besides the Plan of the Theater, the Section of the Scenes is also to
be delineated, for finding the Point of the Theater in the Elevation.
Wherefore, setting the Measures of the Heights which the Point A, where
the Floor of the Stage begins, and the Point D of the Poscene, have above
the Level of the Horizontal FV; from the Perpendicular NV draw the right
Line ADO, which gives the Declivity of the Stage; then make NO parallel
to FV, and equal to AO of the Seventy-third Figure: The Point of the
Theater in Elevation is O; the Point of the same on the Poscene is Q. If
EB be the greatest Height of the first Scene, the Line OE determines the
Height of all the others. The longest of the two Lines gives the true
Height of each Scene; and the shorter discovers how much of that Height
the Sight loses on the Out-line, by the oblique Position of the Scenes.
Moreover, the Excess of the longer Line above the shorter, as well at
top as at bottom, is to be well observ’d; for on this depends the right
Understanding of the Seventy-fifth Figure. The Point M, which is as far
distant from N, as that of F is from A in the Seventy-third Figure,
denotes the Place from whence the Stage ought to be view’d; as is there
mention’d.
In laying the Floor of the Stage, this Rule is commonly observ’d, That
the Height of the Point O be made equal to the Height of the Eye, and
that the Rise of the Floor from A to D, be about a Ninth or Tenth Part of
the Length AD. ’Tis also requisite, for the better shifting the Scenes,
that the Pavement F be sunk lower than that of G, that a Man may walk
upright under the Floor thereof.
[Illustration: FIG. LXXV.]
FIGURA Septuagesimaquinta.
Elevatio scenarum coram inspectarum: ubi docetur artificium ut scenæ
obliquæ appareant rectæ.
_Scenæ quas vides in ~S~, habent suam latitudinem à vestigio figuræ
septuagesimætertiæ, altitudinem ab elevatione figuræ septuagesimæquartæ,
ac censentur erectæ & canalibus insertæ, quæ omnia repræsentantur etiam
figurâ septuagesimasecunda in ~P~ & ~Q~. Velim observes quantum elevetur
tabulatum in principio ~A~, in poscenio ~D~, & in puncto theatri ~O~.
Similiter notare oportet elevationem singularum scenarum, quæ propter
obliquitatem canalium flectuntur introrsum: iccirco lineæ ~BL~, ~KI~,
partis ~C~, non videntur parallelæ ad lineam plani, ut reipsa sunt; ac
visualis ~LF~ non tendit ad punctum oculi ~O~, sed ad punctum ~F~. Si
autem excessus apparens, quem recta ~BK~ habet in summo & imo supra
rectam ~LI~ transferatur in partem ~E~ scenarum, (iidem excessus desumi
etiam possunt ex figura septuagesimaquarta) ac ducantur rectæ ~LG~, ~IH~,
habebuntur lineæ apparenter parallelæ ad lineam plani. Si fiat recta
~LO~, quæ cum ~LG~ faciat angulum ~GLO~ æqualem angulo ~BLF~, eadem ~LO~
tendet exactissimè ad punctum ~O~ oculi, eâque utendum erit ut visuali._
_In ~P~ supponimus scenas ~M~ & ~N~ jacere super pavimento unas super
aliis, ac duas lineas ~RT~ habere distantiam eandem cum duabus ~LI~, &
ita in reliquis scenis. Ubi notandum est, lineas ~RS~, ~TV~, easdem esse
cum lineis ~LG~, ~IH~, scenarum ~E~: nihilominus lineas ~RS~, ~TV~, non
esse parallelas, quum tamen ~LG~, ~IH~, videantur parallelæ. Proinde, si
fiat recta ~RL~, & anguli ~SRL~, ~GLO~, sint æquales, rectâ ~RL~ utendum
erit tanquam visuali, in ~L~ erit punctum accidentale oculi pro pingendis
scenis ~N~, ac lineæ ~RS~, ~TV~, habebuntur ut parallelæ: id autem quod
superest in telario ultra tales lineas, pro nihilo computabitur, ibique
pingetur aer aut aliquid aliud. Punctum accidentale oculi pro pingendis
scenis ~M~ erit in ~I~._
The Seventy-fifth FIGURE.
_The Elevation of Scenes in Front, and how the oblique Scenes are made
to appear direct._
The Scenes in S have their Breadth from the Plan of the Seventy-third
Figure, and their Height from the Elevation of the Seventy-fourth
Figure; and are suppos’d to stand perpendicularly in their Grooves; all
which is also represented in P and Q of the Seventy-second Figure. I
would have you observe, how much the Floor rises, from its Edge A, to
the Poscene D, and to the Point of the Theater O. You should also note
the Elevation of each Scene, which, by reason of the Obliquity of the
Grooves, turn inward: Wherefore the Lines BL, KI, of the Part C, do not
seem Parallels to the Ground-line, as they really are; and the Visual LF
tends not to the Point of Sight O, but to the Point F. But if the seeming
Excess, which the Line BK has at top and at bottom, above the Line LI, be
transferr’d on the Side of the Scenes E, (which Excess may also be taken
from the Seventy-fourth Figure) and you draw the Lines LG, IH; these
Lines will appear Parallels to the Line of the Plan. Then drawing the
Line LO, so as to make the Angle GLO equal to the Angle BLF, the said LO
shall tend directly to the Point of Sight O; and serve for a visual Line.
In P, I suppose the Scenes M and N to lie one upon another on the Floor,
and the two Lines RT to have the same Distance as the Lines LI; and so
of the others. Where you are to take Notice, that the Lines RS, TV, are
the same with the Lines LG, IH, of the Scenes E: and that the Lines RS,
TV, are not Parallels; altho’ LG, IH, seem to be so. Therefore, if you
draw the Line RL, so that the Angles SRL, and GLO, be equal; the Line RL
shall serve as a Visual, and L shall be the accidental Point of Sight,
for painting the Scenes of the Side N; and the Lines RS, TV, shall be
us’d as Parallels. What remains on the Frame, beyond those Lines, is to
be reckon’d as nothing; but you may paint there Air, or what you please.
The accidental Point of Sight for painting the Scenes of the Side M, is I.
[Illustration: FIG. LXXVI.]
FIGURA Septuagesimasexta.
Modus delineandi exemplar scenarum.
_Iterum delineavimus scenas erectas super tabulato; in ~B~ nudas, in
~A~ depictas, additis projecturis coronicum & aliorum ornamentorum.
Deformatio scenarum ~A~ eruitur methodo consuetâ ex vestigio ~C~, in quo
videbis lineam plani deorsum protractam. Vestigium autem geometricum est
in ~D~._
The Seventy-sixth FIGURE.
_The Manner of delineating the Designs of Scenes._
In this Plate you have another Design of Scenes erected on the Floor; the
naked Scenes are B; the painted ones A; with the additional Projectures
of Cornices and other Ornaments. The Draught of the Scenes A is produc’d
from the Plan C, after the usual Manner; in which you may observe the
Ground-line to be lower than its true place, for the greater Distinction
of the Parallels. The Geometrical Plan is D.
[Illustration: FIG. LXXVII.]
FIGURA Septuagesimaseptima.
Modus reticulandi & pingendi scenas theatri.
_Postquam in pavimento exactissimè disposueris tum poscenium, tum
ex ordine scenas reliquas, unam alteri incumbentem, ut figurâ
septuagesimaquintâ declaravimus, fiet linea horizontalis, in qua notanda
sunt tria puncta perspectivæ, unum in ~O~ usui futurum in pingendo
poscenio, ac duo reliqua hinc inde, singula videlicet pro scenis partis
oppositæ. Jam supponendo quòd in parvo exemplari ~A~ primæ scenæ facta
fuerit reticulatio per quadrata perfecta; proportionalis divisio
fiet tum in recta ~HI~ primæ scenæ ~B~, tum in recta ~CD~. Postea ex
puncto ~E~, per singula puncta divisionum rectæ ~HI~, fient visuales,
adhibendo funiculum colore nigro imbutum; earumque ope, ut figura
ostendit, reticulare oportebit scenam ~B~, tum remotâ ea scenam illi
subjectam, & eodem modo aliam & aliam; ac demum per divisiones quas
in recta ~LM~ faciunt visuales ex puncto ~E~, absolvetur reticulatio
poscenii, cujus quadrata esse debent perfecta, secus quadrata scenarum.
In parte inferiori paginæ, duæ scenæ ~G~ & ~F~ ostendunt ornamenta quæ in
scenis depingi possunt. Velim autem observes, tum lineas transversas
coronicum, quæ non sunt invicem parallelæ, tum visuales, quæ tendunt
ad puncta opposita. Nam ejusmodi lineæ continent duas peculiares
difficultates projectionum theatralium; easque ut superes, exactè
servandæ sunt regulæ quas declaravimus._
The Seventy-seventh FIGURE.
_The Manner of making the Net-work or Squares, and painting the Scenes of
Theaters._
After you have with great Exactness dispos’d the Poscene on the Pavement,
and the others in order one upon another, as was mention’d in the
Seventy-fifth Figure; draw the horizontal Line, and mark therein three
Points of Sight: That in O, for the Use of the Poscene; and the Points
on the Sides, for the Service of the opposite Scenes respectively. Then,
supposing that the Net-work of the small Draught of the first Scene A,
consists of perfect Squares; transport the same Divisions both on the
Lines HI and CD of the first Scene B; and with a black Line strike the
Visuals from the Point E, by the Points of the Divisions of HI; and
by the Help of those Visuals make the Net-work of the Scene B, as is
done in the Figure. When that’s done, lay it aside; and do the next in
the same manner; and so of the others. Lastly, by the Divisions, which
the Visuals from the Point E make on the Perpendicular LM, finish the
Net-work on the Poscene, which consists of perfect Squares, though that
of the Scenes does not. The two Scenes of the lower part of the Plate, G
and F, shew what Diversity of Ornament the Painter may introduce. I would
have you also take particular Notice, both of the transverse Lines of the
Cornice, which are not Parallels to each other; and of the Visuals which
are directed to their opposite Points: because in these two Particulars
lies the greatest Difficulty of describing Theatrical Designs; for the
surmounting which, it’s absolutely necessary, that you carefully regard
the Rules hitherto deliver’d.
[Illustration: FIG. LXXVIII.]
FIGURA Septuagesimaoctava.
De projectionibus horizontalibus.
_Quemadmodum facilior est deformatio columnarum jacentium, quàm
columnarum erectarum; (nam lineæ quæ in istis sunt perpendiculares,
in illis sunt visuales, ac nullus circulus amittit suam formam) ita
projectiones horizontales, quas in laquearibus delineare necesse est,
contra quàm Pictores imaginantur, expeditiores & faciliores sunt
verticalibus, quas hucusque tractavimus. Nam ut stylobatæ & columnæ
appareant erectæ, pingendæ sunt veluti jacentes._
_Deformationes horizontales auspicamur à mutulis, quia columnæ ac
stylobatæ identidem iis imponuntur, ut magis in prospectu sint. Ob
diversitatem verò quam habet latus mutuli à sua facie, utriusque
delineationem geometricam seorsim in hac figura exhibemus._
The Seventy-eighth FIGURE.
_Of horizontal Perspective._
As it is easier to describe in Perspective Columns lying on the ground,
than those that are erect, (the Lines in these last being Perpendiculars,
which in the former are Visuals, wherein no Circle loses its Form) so
the horizontal Projections of Perspective, proper for Ceilings, contrary
to the Judgment Painters usually make, are perform’d with more Ease
and Expedition, than the vertical, which we have hitherto treated of;
forasmuch as the Pedestals and Columns that must appear erect, are
painted as if lying on the ground.
I have usher’d in these horizontal Designs with those of Corbels,
because, for setting the Pedestals and Columns more in View, they
generally seem to be supported by them. And the Side of this Corbel being
different from its Face, I have here inserted a Geometrical Description
of each distinct.
[Illustration: FIG. LXXIX.]
FIGURA Septuagesimanona.
Projectiones vestigii & elevationis mutuli.
_Facies mutuli quam delineavimus figurâ septuagesimaoctavâ, gerit
hic munus vestigii; latus verò gerit munus elevationis; ut ostendunt
lineæ occultæ, quæ ex divisionibus faciei tendunt ad punctum oculi,
ex divisionibus lateris tendunt ad punctum distantiæ (puncta oculi
ac distantiæ in hac & sequentibus figuris cadunt extra paginam.) Per
sectiones harum linearum ducuntur lineæ quæ terminant singulas partes
vestigii deformati; hujusque adjumento ducitur elevatio lateris, ac
methodo consuetâ latitudines & longitudines mutuli solidi eruuntur ex
vestigio, altitudines ex elevatione. Hic & deinceps nomina longitudinis
& altitudinis usurpamus, veluti planum cujuslibet perspectivæ esset
verticale; in quâ suppositione, ~IL~ esset latitudo mutuli, ~SR~
altitudo, ~RL~ longitudo: quum ~SR~ reverà sit longitudo, ~RL~ altitudo.
Ad faciliorem descriptionem hujus figuræ observandum est, rectis ~IL,
LM, GH,~ hujus paginæ inesse divisiones rectarum ~DC, FE, AB,~ figuræ
septuagesimæoctavæ._
The Seventy-ninth FIGURE.
_The Plan and Elevation of a Corbel in Perspective._
The Face of the Corbel describ’d in the Seventy-eighth Figure, in this
does the Office of a Plan; and the Side serves here for the Elevation;
as is plain from the occult Lines, which from the Divisions of the Face
tend to the Point of Sight, and from those of the Side tend to the Point
of Distance; both which Points, in this and the succeeding Figure, fall
without the Plate. From the Intersections of these Lines are drawn
others, that determine each Part of the Perspective-Plan; by means of
which, the Elevation of the Side being also form’d, the Breadths and
Lengths of the solid Corbel are taken, as usual, from the Plan, and the
Heights from the Elevation. Here and henceforward, the Terms of Length
and Height are made use of, as though the Plan of each Perspective were
vertical; according to which Supposition, IL is the Breadth of the
Corbel, SR the Height, and RL the Length; whereas in reality SR is the
Length, and RL the Height. For the more ready Description of this Figure
you will do well to observe, that the Lines IL, LM, GH, of this Plate,
bear the same Divisions as DC, FE, AB, of the Seventy-eighth Figure.
[Illustration: FIG. LXXX.]
FIGURA OCTOGESIMA.
Horizontalis projectio mutuli inumbrati.
_In hac figurâ suas umbras mutulo addidimus: eumque si in altum supra
oculum elevaveris, & ex distantiâ quam ipsi dedimus suspexeris; miraberis
profectò, in alium longè concinniorem subitò mutatum fuisse._
The EIGHTIETH FIGURE.
_The Horizontal Projection of a shaded Corbel._
In this Figure you have the Corbel finish’d with its proper Shades;
which, if plac’d above the Eye, and beheld from the Distance here
assign’d it; you’ll be strangely surpriz’d at the sudden and most
agreeable Alteration you’ll find therein.
[Illustration: FIG. LXXXI.]
Figura Octogesimaprima.
Stylobatæ Corinthii horizontaliter contracti.
_In deformandis hisce stylobatis, usi sumus projectione vestigii &
elevationis, quam exhibet figura duodecima; ut figuram illam cum istâ
conferenti manifestissimè constabit. Porrò stylobatas pingi solere
incumbentes mutulis, diximus figurâ septuagesimaoctavâ._
The Eighty-first Figure.
_~Corinthian~ Pedestals in an Horizontal Perspective._
In delineating these Pedestals, I have made use of the Plan and Upright
put into Perspective in the Twelfth Figure; as will evidently appear,
by comparing that Figure with this. I have already mention’d, in the
Seventy-eighth Figure, that in painting these Pedestals, they are
generally suppos’d to be upheld by Corbels.
[Illustration: FIG. LXXXII.]
Figura Octoges. secunda.
Columna Corinthia horizontaliter deformata.
_Vestigium & elevatio stylobatæ, quem delineavimus figurâ duodecimâ,
suppeditat mensuras pilarum hoc loco deformandarum, ut ex iis eruatur
contractio columnæ. Huic autem soli suas umbras addidimus, ut clariùs
appareat modus & artificium totius operationis. Ex his vides, quadrata &
circulos in perspectivâ horizontali omninò retinere suam figuram, eamque
dumtaxat restringi paulatim & coarctari: quicquid in contrarium & verbis
& pennicillo docuerint Pictores nonnulli._
Eighty-second FIGURE.
_A ~Corinthian~ Column in Horizontal Perspective._
The Plan and Elevation of the Pedestal delineated in the Twelfth Figure,
gives also the Measures for reducing these Pilasters into Perspective;
from which the Contraction of the Column is taken. I have shadow’d
only this last, that the Manner of the whole Work might be the more
conspicuous. By this you see the Squares and Circles in Horizontal
Perspective always retain their Figures, without any Alteration, save
that of being gradually diminish’d and made less; notwithstanding what
some Painters have taught and practis’d to the contrary.
[Illustration: FIG. LXXXIII.]
Figura Octogesimatertia.
Capitella Corinthia horizontaliter contracta.
_Habes in hac paginâ deformationes vestigii & elevationis capitelli
Corinthii, quas desumpsimus ex delineationibus geometricis, transferendo
mensuras earum in lineas plani ~AB~, & elevationis ~AC~, ita ut facillimè
dignosci possit unde nascantur singulæ partes capitellorum nitidorum.
Nihil dubito quin deformationes horizontales sis experturus faciliores
verticalibus quas dedimus figurâ vigesimaquartâ. Nam in horizontalibus
gyrus foliorum circulis clauditur, quorum centra mutuantur latitudines
à suis vestigiis in punctis ~1~, ~2~, ~3~, ~4~; altitudines verò à
capitellis elevationis in punctis ~5~, ~6~, ~7~, ~8~._
Eighty-third FIGURE.
_A ~Corinthian~ Capital horizontally contracted in Perspective._
You have in this Plate the Perspective both of the Plan and Elevation of
the _Corinthian_ Capital, drawn from the Geometrical Descriptions, by
transferring their Measures into the Ground-line AB, and into that of the
Elevation AC; so that you may readily discover from whence every part of
the finish’d Capital is produc’d. I don’t doubt but you’ll experience
these horizontal Perspectives to be much less difficult than the vertical
propos’d in the Twenty-fourth Figure. For in these the Circuit of the
Leaves is determin’d by perfect Circles, whose Centers take their
Breadths from the Plan at the Points 1, 2, 3, 4; and their Heights from
the Capitals of the Elevation, at the Points 5, 6, 7, 8.
[Illustration: FIG. LXXXIV.]
Figura Octogesimaquarta.
Coronix Corinthia.
_Si faciendæ sint coronices quæ habeant angulos, elevatio geometrica
~A~ repræsentabit unum latus, alterum sectio ~B~. Curandum est autem,
ut crepidines partium, quas fingere volumus incumbere columnis, non
obsint concinnæ distributioni mutulorum. Ad contractionem elevationis
~A~ & sectionis ~B~, in lineam plani ~EF~ & elevationis ~EG~ transferre
oportet puncta diversarum latitudinum, quas habent in elevatione A ungues
epistylii, zophori, & coronæ, ducendo ex iis lineas ad punctum oculi;
in partem verò ~FH~ lineæ ~FE~ transferre oportet puncta longitudinis,
ducendo lineas ad punctum distantiæ. Hac industriâ perficies utramque
deformationem, quarum una geret munus vestigii, altera elevationis.
Utrobique autem designabis lineas terminativas partium coronicis, ac
sectionum ~C~ & ~D~._
Eighty-fourth FIGURE.
_A ~Corinthian~ Cornice._
If you are to describe Cornices having Angles, admit the Elevation A to
represent one Side, and the Section B the other. But Care is to be taken,
that the Breaks of those Parts which are suppos’d to be set directly over
the Columns, do not obstruct the regular Distribution of the Modillions.
For contracting into Perspective the Elevation A, and the Section B, you
must transfer into the Ground-line EF, and into that of the Elevation
EG, the Points of the several Breadths made by the Projectures of the
Architrave, Freeze, and Cornice of the Elevation A; and from them draw
Lines to the Point of Sight: Then on the Part FH of the Line FE, you
must note the Points of Length, and draw Lines from them to the Point of
Distance. By this Practice you complete these two Contractions, one of
which does the Office of a Plan, the other that of an Elevation. It’s
also requisite, that you draw the Out-line of the Members of the Cornice
on each side the Angle, & the Sections C and D.
[Illustration: FIG. LXXXV.]
Figura Octogesimaquinta.
Coronix Corinthia horizontaliter contracta.
_Soliditas coronicis cum omnibus projecturis eruta est ex vestigio &
elevatione figuræ octogesimæquartæ. Hic autem finem imponimus partibus
rerum, ad integra ædificia gradum facturi._
The Eighty-fifth Figure.
_A ~Corinthian~ Cornice in Horizontal Perspective._
The Solidity of this Cornice, with all its Projectures, is deduc’d from
the Plan and Elevation of the foregoing Figure. With this therefore I
shall conclude the Description of Parts of things, and proceed to that of
entire Structures.
[Illustration: FIG. LXXXVI.]
Figura Octogesimasexta.
Horizontalis projectio columnæ.
_Postquam sigillatim descripsimus mutulum, stylobatam, columnam &
coronicem, omnia ista conjungere placuit: ita clariùs apparebit quomodo
disponere oporteat delineationes geometricas, ut ex iis eruantur
projectiones horizontales._
_Linea plani est ~CD~, perpendicularis ~CI~. In ~A~ est elevatio
geometrica longitudinis columnæ, (supponimus columnam delineari veluti
jacentem humi.) In ~B~ ejus vestigium geometricum, cum divisionibus
latitudinis in lineâ ~ER~. Puncta longitudinis transferentur in lineam
plani ~CG~, puncta altitudinis ~EC~ transferentur in ~CF~, ducendo rectas
ex divisionibus ~CG~ ad punctum distantiæ, ex divisionibus ~CF~ ad
punctum oculi. Per sectiones verò visualis ~CO~ erigentur perpendicula, &
complebitur elevatio ~H~, ex quâ eruetur columna nitida ~L~._
_Si super vestigio ~M~ formare placeat aliam columnam, ejus latitudines
accipiendæ sunt ex columna ~B~; ac sectio projicienda est in ~N~, ut
ex hac tamquam ex elevatione eruatur columna ~P~. Si aliam columnam in
angulo addere libitum fuerit, ope sectionum ~HN~ facilè illam complebis._
The Eighty-sixth Figure.
_A Column in horizontal Perspective._
After the separate Description of a Corbel, Pedestal, Column, and
Cornice; I have here conjoin’d them all, that you might the better
perceive how to dispose Geometrical Elevations for the Business of
horizontal Perspective.
The Line of the Plan is CD, the Perpendicular CI; the Geometrical
Elevation of the Length of the Column, suppos’d to be lying on the
Ground, is A. The Geometrical Plan thereof is B, with the Divisions
of its Breadth on the Line ER. The Points of Length being transferr’d
on the Line of the Plan CG, and the Points of Height EC into CF; from
the Divisions of CG Lines are drawn to the Point of Distance; and from
those of CF to the Point of Sight. From the Sections of the Visual CO,
Perpendiculars are erected, and the Elevation H completed, from whence is
taken the finish’d Column L.
If upon the Plan M you would delineate another Column, the Breadths
thereof must be taken from the Column B, and another Profile design’d
in N, which serves as an Elevation for making the Column P. If another
Column were requir’d in the Angle, the Profiles HN assist you in the
ready Performance thereof.
[Illustration: Fig. lxxxvii.]
FIGURA Octogesimaseptima.
Præparatio necessaria ad sequentem figuram, & ad projectiones
horizontales in laquearibus vel testudinibus.
_Exhibet hæc figura in ~AA~ unum ex quatuor parietibus aulæ, cujus
altitudinem veram ~IH~ velis attollere apparenter usque in ~L~, pingendo
in laqueari, vel in testudine, seriem balaustiorum. In ~B~ est vestigium
geometricum quartæ partis laquearis. In ~C~ habetur elevatio medietatis
latitudinis. In ~D~ est sectio coronicis & mutulorum. In ~E~ posita
est elevatio medietatis longitudinis. In ~F~ est punctum oculi, in ~G~
punctum distantiæ: adeóque tota distantia est ~GF~._
The Eighty-seventh FIGURE.
_The Preparation necessary to the following Figure, and to all other
horizontal Perspectives, whether on flat or vaulted Ceilings._
The Figure AA represents one of the four Walls of a Hall, whose true
Height IH you would have appear rais’d to L, by painting a Ballustrade in
the Ceiling thereof. B is the Geometrical Plan of the fourth part of the
said Ceiling; C is the Elevation of half the Breadth; D is the Section
of the Cornice and Corbels; E is the Elevation of half the Length. In F
is the Point of Sight, in G the Point of Distance; so that the Distance
itself is FG.
[Illustration: FIG. LXXXVIII.]
Figura Octogesimaoctava.
Horizontalis projectio balaustiorum figuræ octogesimæseptimæ, cum brevi
distantia.
_Claritatis gratiâ totum laquear divisum est in quatuor partes. Prima
continet contractionem vestigii & elevationis, quæ perficiuntur methodo
consueta. Nam linea ~AOV~ est horizontalis, ~BC~ est linea plani. Punctum
oculi est ~O~, distantiæ ~E~. Secunda pars continet sectionem ~L~, quæ
dat projecturas mutulorum aliarumque partium, desumendas ex sectione ~D~
figuræ octogesimæseptimæ, deformando eam in angulis ~B~ & ~C~. Tertia
pars complectitur delineationem integram sine umbris: ultima pars eandem
complectitur cum umbris._
_Ob punctum distantiæ parum remotum à puncto oculi, nimiam amplitudinem
ac deformem apparentiam habere videtur hæc delineatio. Nihilominus, si ex
distantia ~EO~ figuram suspexeris, omnis deformitas evanescet._
_Ut fucus imperitis fiat, industrii Pictoris interest parare sibi
geminum exemplar suorum Operum, in quibus distantia sit nimis brevis;
unum videlicet palam ostendendum, in quo punctum distantiæ sit remotum à
puncto oculi, quantum necesse est ad vitandam omnem deformitatem. Alterum
verò, in ipsomet Opere clam usurpandum._
_Si pingendæ sint testudines, oportet prius facere in eis reticulationem
peculiarem; quæ quia difficilis est, & paucis explicari nequit, in aliud
Opus reservatur._
Eighty-eighth Figure.
_The horizontal Projection of the Ballustrade of the Eighty-seventh
Figure, view’d at a small Distance._
For the better Illustration of this Figure, I have divided the whole
Ceiling into Four Parts. The first contains the Plan and Elevation in
Perspective, after the usual manner; AOV being the horizontal Line, BC
that of the Plan; the Point of Sight O, and that of Distance E. The
second Part contains the Section L, which gives the Projectures of the
Corbels and other Parts taken from the Section D of the Eighty-seventh
Figure, by drawing it in the Angles B and C. The third Part comprehends
the Delineation of the Perspective without Shadows. The fourth Part
contains the same wholly shadow’d and finish’d.
Through the near Approach of the Point of Distance to the Point of Sight,
you may perhaps imagine this Draught will appear too wide, and so have an
ill Effect: But when once you view it from its due Distance EO, you will
find all such Doubts vanish and come to nothing.
When you have to deal with Persons unskill’d in these things, and are to
paint for so small a Distance; your best way is to make two Draughts; one
for publick Shew, in which you may place the Point of Distance so far
from the Point of Sight, as is necessary for preventing Deformity; and
the other you may privately make use of in performing your Work.
If you are to paint arch’d or vaulted Ceilings, a particular kind of
Net or Lattice-work must first be made therein; the Performance whereof
being difficult, and not capable of being explain’d in few words, I have
reserv’d it for another Volume.
[Illustration: FIG. LXXXIX.]
Figura Octogesimanona.
Horizontalis projectio architecturæ in laqueari quadrato.
_Si laquear sit quadratum, & valde distans ab oculo, architecturam huic
similem in eo depingere licebit. ~A~ est elevatio geometrica; eadem verò
deformata in ~B~ & ~C~, gerit munus vestigii & elevationis. Medietas
unius ex quatuor partibus, usui esse potest in toto opere, aut premendo
chartam, aut eâ perforatâ, immittendo per foramina carbonem minutissimè
contusum._
Eighty-ninth FIGURE.
_An horizontal Projection of Architecture in a square Ceiling._
If the Ceiling be square, and very remote from the Eye, you may paint
in it some such Piece of Architecture as this. A is the geometrical
Elevation; the same reduc’d into Perspective in B and C does the Office
of a Plan and Elevation. The Half of one of the four Parts may suffice
for the Draught of the whole Work, either by tracing over the Lines of
the Paper, or by pricking small Holes therein, and pouncing them through
with Charcole finely powder’d.
[Illustration: FIG. XC.]
FIGURA Nonagesima.
Horizontalis projectio tholi.
_Initium hujus rei fiet à vestigio geometrico, in quo duæ series
circulorum designant columnas; aliæ lineæ designant stylobatas,
ac projecturas & ungues basium & coronicum. Linea plani est ~AB~,
horizontalis ~CD~, perpendicularis ~AD~. Punctum oculi est ~O~, distantiæ
~D~; adeóque figura hæc debet habere supra oculum altitudinem ~DO~.
Punctum oculi positum fuit extra ipsum tholum, ut qui eum aspiciunt,
minus defatigentur, ac plus appareat de architectura & de artificio;
secus verò contingeret si punctum oculi esset in medio. Itaque puncta
lineæ ~EF~ transferentur in partem ~AG~ lineæ ~AD~. Centrum ~I~ vestigii
transferetur in ~H~ & ex omnibus his punctis fient visuales ad ~O~.
Deinde altitudine tholi, ac divisionibus partium singularum tum ipsius,
tum laternæ, translatis in lineam ~AB~, ex punctis divisionum fient rectæ
ad punctum distantiæ ~D~. Ubi autem hæ secant visualem ~AO~, erigentur
perpendicula, quorum sectiones cum visuali ~HO~ dabunt centra pro
singulis circulis. Inter visuales ~AG~ ducere oportet lineas terminativas
columnarum & coronicum; quemadmodum fieret, si ex vestigio eruta fuisset
elevatio geometrica. His positis, aggredieris delineationem opticam
ipsius tholi, translatis in perpendicularem ~EO~ centris ope parallelarum
~HI~, ~LN~; ac semidiametro ~LM~ fiet circulus ~NP~ pro simâ coronicis:
semidiametro ~ST~ fiet circulus ~QR~, & sic de reliquis. Quomodo autem
per rectas ex angulis vestigii ad punctum oculi, habeantur ungues
coronicis, ostendunt numeri ~1~, ~2~, ~3~, ~4~; lineæ verò laterales
unguium tendunt ad centra suorum circulorum, ut videre est in ~N 3, 4~.
In vestigio, ne nimium occupetur, mutulos omisimus._
_Ex his patet necessitas faciendi vestigium geometricum totius tholi, ac
non sufficere vestigium unius columnæ; quum singulæ peculiares exigant
deformationes. Quum autem Opus ipsum delineandum ac pingendum fuerit,
ipsum desumere non poteris ex parvo exemplari, ope reticulationis;
Quinimo suis locis ducere oportebit lineas visuales, & invenire centra
omnium circulorum. Figendo autem funiculum in singulis centris, ipsius
adjumento facillimè absolves omnes circumferentias._
The Ninetieth Figure.
_A Cupola in horizontal Perspective._
In the Execution of this Work, you are to begin with the Geometrical
Plan; in which the two Ranges of Circles denote the Columns, the other
Lines shew the Pedestals, with the Projectures and Breaks of the Bases
and Cornices. The Line of the Plan is AB, that of the Horizon CD, the
perpendicular Line is AD. The Point of Sight is O, that of Distance D;
wherefore this Figure ought to be plac’d as much above the Eye, as the
Height DO. I have set the Point of Sight something without the Cupola,
that the Eye might be less weary’d in viewing the Work, and embrace more
of the Architecture, than it could have done, had the Point of Sight been
in the midst. The Points of the Line EF are transferr’d into AG, part of
the Line AD. The Center of the Plan I is continu’d to H, and from all
these Points visual Lines are drawn to O. Then placing the Heights of
every part both of the Cupola and Lantern on the Line AB, from the Points
of those Divisions draw Lines to the Point of Distance D; and where they
cut the Visual AO, erect Perpendiculars intersecting the Line HO; which
Points are the Centers of the several Circles. On the Visuals, between
AG, must be describ’d the Out-lines of the Columns and Cornices, in like
manner as when a Geometrical Upright is rais’d from a Plan. This done,
you proceed to the Delineation of the Cupola itself in Perspective,
by transferring into the Perpendicular EO the several Centers of HO,
by Parallels to HI, as LN, _&c._ On the Center, with the Interval LM,
describe the Circle NP, for the Nose of the Cornice; and with the
Semidiameter ST describe the Circle QR, and so of the rest. The Numbers
1, 2, 3, 4, shew how the Breaks of the Cornice are determin’d by Lines
from the Angles of the Geometrical Plan tending to the Point of Sight,
till they intersect the Circle: The Returns of which Breaks are made by
Lines tending to the Centers of their respective Circles; as is plain
from N 3, and N 4. In this Plan I have omitted the Corbels, lest I should
too much encumber the Work.
Hence appears the Necessity of making the Geometrical Plan of the whole
Cupola, the Plan of a single Column not being sufficient; by reason each
requires its particular Delineation. And when the Work itself is to be
drawn for painting, you can’t well take it from a small Draught by way of
Net-work or Squares, but the visual Lines should be drawn in their proper
places, and the several Centers found; in which, by fixing Strings, you
may readily describe the Circumferences of all the Circles.
[Illustration: FIG. XCI.]
Figura Nonagesimaprima.
Tholus figuræ nonagesimæ, cum luminibus & umbris.
_Tholus quem vides in hac paginâ, pollicetur sibi vitam diuturniorem
illo, quem super telario plano insignis amplitudinis, depinxi anno 1685.
in Templo S. Ignatii Collegii Romani. Proinde si casus aliquis illum
absumat, non deerunt qui ex isto eundem in melius reficiant. Mirati
fuerunt Architecti nonnulli, quòd columnas anteriores mutulis imposuerim,
id enim in solidis ædificiis ipsi non facerent. Verùm eos metu omni
liberavit amicissimus mihi Pictor, ac pro me spopondit, damnum omne se
statim reparaturum, si fatiscentibus mutulis, columnas in præceps ruere
contingat._
The Ninety-first Figure.
_The Cupola of the Ninetieth Figure, with its Lights and Shades._
The Cupola in this Plate will in all Likelihood be of longer Duration,
than that which I painted on a very large Table, for the flat Ceiling
of the Church of S. _Ignatius_ of the _Roman_ College, _anno_ 1685. For
if that suffer by any Accident, with the help of this its place may be
supply’d by a better. Some Architects dislik’d my setting the advanc’d
Columns upon Corbels, as being a thing not practis’d in solid Structures;
but a certain Painter, a Friend of mine, remov’d all their Scruples,
by answering for me, That if at any time the Corbels should be so much
surcharg’d with the Weight of the Columns, as to endanger their Fall, he
was ready to repair the Damage at his own Cost.
[Illustration: FIG. XCII.]
Figura Nonages. secunda.
Tholus octangularis.
_Ex circulo fiet octagonum, accipiendo medietatem quadrantis circuli,
ut habeantur singula latera octagoni. In eisdem lateribus distribuetur
vestigium geometricum totius architecturæ, cum projecturis omnium
membrorum, juxta modum quem servavimus in limbo circulari figuræ
nonagesimæ. Utiliter etiam fieret elevatio geometrica totius Operis;
quamvis ob spatii angustias ego eam omiserim. Deinde positâ una cuspide
circini in centro circuli, extendetur alia cuspis ad altitudinem
singularum projecturarum inter spatium ~A~ & ~B~, ut hic vides: atque
ope parallelarum, omnia transferentur in lineam ~CD~, ut fiat optica
deformatio, quam poscit sectio elevationis, cum aliis præparationibus,
ut in figura præcedenti. Nam hic quoque ope circulorum invenire oportet
puncta extrema in prominentiis membrorum singulorum architecturæ: ut
conjungendo puncta per lineas rectas, quæ forment facies octagoni,
compleatur totum Opus._
Ninety-second Figure.
_An Octangular Cupola._
From the Circle describe the Octagon, by taking half the Quadrant of the
former for each Side of the latter. On these Sides the Geometrical Plan
of the whole Architecture is to be dispos’d, with the Projectures of
all the Members thereof, in the same manner as was done in the circular
Border of the Ninetieth Figure. It will also be expedient, to make the
Geometrical Elevation of the whole Work, tho’ thro’ Want of Room I have
here omitted it. Then placing one Point of the Compasses in the Center
of the Circle, extend the other to the Height of the several Projectures
between A and B, as you see in the Figure; and by help of the Parallels
transfer them all into the Line CD, for putting the Profile of the
Upright into Perspective, and drawing the other Requisites, as in the
foregoing Figure. For here also, by means of the Circles, are found
the extreme Points of the Projectures of the several Members of the
Architecture; and by conjoining these Points with strait Lines agreeable
to the Shape of the Octagon, the whole Work is completed.
[Illustration: FIG. XCIII.]
FIGURA Nonagesimatertia.
Vestigium templi Ludovisiani S. Ignatii almæ urbis.
_Constitueram huic Libro finem imponere figurâ nonagesimasecunda;
nihilominus ut satisfaciam precibus amicorum, cupientium addiscere modum
reticulationis opticæ, quæ adhibetur in superficiebus irregularibus,
ejusque memini figurâ octogesima octava, publici juris facere decrevi
ejus construendæ methodum. Ipsiusmet retis ope delineavi non solùm
ædificium mox repræsentandum, sed etiam figuras omnes testudinis templi
Ludovisiani, in qua pingenda nunc occupor. Eademque reticulatione, quæ
erit ultima figura hujus Libri, dabimus Operi nostro suum complementum;
quum nulla sit superficies, in qua suas delineationes juxta Perspectivæ
regulas, earum rerum Studiosi absolvere nequeant._
_Exhibet hæc figura vestigium totius templi. Quamvis enim non indigeam
nisi testudine inter januam maximam & tholum; proderit nihilominus
Architecturæ Studiosis, universi Operis elegantiam ac symmetriam per
otium contemplari._
The Ninety-third FIGURE.
_The Geometrical Plan of the Church of S. ~Ignatius~ at ~Rome~._
I had once determin’d to end this Book with the Ninety-second Figure; but
at the Request of some Friends, who were desirous to learn the Making
of Perspective Net-work for irregular Surfaces, as was hinted in the
Eighty-eighth Figure; I resolv’d to publish the Manner of performing
the same. By the Help of this Net-work, I delineated not only the
Architecture now to be treated of; but also each Figure in the Vault of
the Church of S. _Ignatius_, which I am at present employ’d in painting.
The Method is laid down in the last Figure of this Book, and entirely
completes the same; there being no Superficies, how irregular soever, but
the Studious may thereon describe, by these Rules, whatever Perspective
he has occasion for.
This Figure contains the Plan of the whole Church; for though my present
Design requir’d no more than the Vault of the Nave, between the great
Door and the Cupola; I thought it might be nevertheless acceptable to
the Curious in Architecture, to have a View of the whole Design, so
celebrated for the Elegancy and Proportion of its Parts.
[Illustration: FIG. XCIV.]
Figura Nonages. quarta.
Orthographia templi Ludovisiani.
_Vt magis tibi gratificer, orthographiam seu elevationem templi
Ludovisiani in longum dissecti delineavi, cum omnibus mensuris quæ
vestigio sunt communes; addito tholo juxta ideam Autoris. Ejus autem
nondum constructi loco, positum est in ~A~ & ~B~ telarium cum tholo
depicto, de quo supra in figuris nonagesimâ & nonagesimaprimâ._
Ninety-fourth FIGURE.
_The Orthography, or Geometrical Elevation of the Inside of S.
~Ignatius~’s Church._
For your greater Satisfaction, I have here given the Geometrical Upright
of the Church dissected lengthwise, with all its Measures agreeable to
those of the Plan; as also the Cupola design’d by the Author: Which not
being yet built, instead thereof is plac’d between A and B, the painted
Cupola before describ’d in the Ninetieth and Ninety-first Figures.
[Illustration: FIG. XCV.]
Figura Nonages. quinta.
Aliæ præparationes ad figuras nonagesimamoctavam & nonagesimamnonam.
_Ex hac figura in quatuor partes divisa, disces ex uno intuitu methodum
qua sum auspicatus opticam delineationem templi Ludovisiani. Prima pars
exhibet latus dextrum testudinis inter januam templi ac tholum. Secunda
pars continet vestigium ejusdem testudinis, arcubus ac lunulis distinctæ.
Tertia pars continet latus dextrum testudinis usque ad summitatem
fenestrarum, unde incipit Architectura quam pingimus in fornice. Quarta
pars est vestigium geometricum fornicis, cum prominentia quam habent
arcus in summitate jam dicta fenestrarum. Fingimus autem eandem esse
soliditatem, tum ædificii depicti, tum navis templi; solæ enim columnæ,
quæ respondent pilis templi, prominent extra ædificium._
The Ninety-fifth Figure.
_Other Preparations to the Ninety-eighth and Ninety-ninth Figures._
By this Figure divided into four Parts, you will at first Sight perceive
the Method I observ’d in beginning the Perspective Design of this Church
of S. _Ignatius_. The first Part shews the right-hand Side of the Vault
between the Door and the Cupola. The second contains the Plan of the same
Vault, with its Arches and Lunettes. The third Part represents the same
right-hand Side, to the top of the Windows; where begins the Architecture
painted in the Vault. The fourth Part contains the Geometrical Plan of
that part of the Vault which is painted; with the Lunettes made by the
Arches above the Heads of the aforesaid Windows. The Disposition of the
painted Architecture above, is the same with that of the Nave of the
Church; save that, answerable to the Pilasters below, I have suppos’d
Columns projecting over the Work.
[Illustration: FIG. XCVI.]
Figura Nonagesimasexta.
Aliæ præparationes ad figuras nonagesimamoctavam & nonagesimamnonam.
_Prima pars figuræ hujus trifariam divisæ, repræsentat elevationem
geometricam lateris templi supra coronicem, & ædificii in testudine
pingendi. Secunda pars complectitur arcum testudinis maximum, &
elevationem geometricam faciei ejusdem ædificii. Tertia pars exhibet
vestigium totius ædificii pingendi in testudine, cujus amplitudo
eadem est cum amplitudine navis, ut antea dicebamus. Porrò vestigium
geometricum non minus necessarium est ad pingendum ædificium, quàm ad
ipsum ex materiâ solidâ extruendum, ut alibi monuimus._
The Ninety-sixth Figure.
_Other Preparations to the Ninety-eighth and Ninety-ninth Figures._
In this Figure, which consists of three parts, the first represents the
Geometrical Elevation of the Right-side of the Nave above the Cornice,
and of the Design painted in the Vault. The second contains the great
Arch of the Vault, and the Geometrical Elevation of the Front of the
said Design. The third part shews the Plan of the whole Work painted on
the Vault, the Extent and Disposition of which is the same with that of
the Nave, as beforemention’d. The Geometrical Plan, as I have formerly
hinted, is no less necessary for the painting a Design in Perspective,
than it is for raising a Structure with solid Materials.
[Illustration: FIG. XCVII.]
Figura Nonages. septima.
Alia præparatio ad figuras nonagesimamoctavam & nonagesimamnonam.
_Ut optica projectio vestigii & elevationis quartæ partis totius Operis
distinctior evaderet, mensuras partium singularum quadruplicavi,
eandemque methodum in hac delineatione tenui, quæ figuris
octogesimasextâ, octogesimaseptimâ, octogesimaoctavâ, & octogesimanonâ,
explicata fuit. Punctum oculi positum est in medio navis Ecclesiæ;
punctum distantiæ est in lineâ ex quâ incipit arcus testudinis._
Ninety-seventh Figure.
_Another Preparation to the Ninety-eighth and Ninety-ninth Figures._
That the Perspective of the fourth part of the Plan and Elevation of
this Work might be more distinct, I have in this Figure made the Measures
of each part four times as big as in the former; and have kept the
same Method in this Delineation, as was deliver’d in the Eighty-sixth,
Eighty-seventh, Eighty-eighth, and Eighty-ninth Figures foregoing. I have
set the Point of Sight in the midst of the Nave of the Church; and the
Point of Distance is in the Line from which the Arch of the Vault springs.
[Illustration: FIG. XCVIII.]
Figura Nonages. octava.
Quadrans Architecturæ horizontalis in fornice, cum luminibus & umbris.
_Habes in hac paginâ quadrantem totius Operis, modo consueto erutum ex
præcedenti: nimirùm, cuspide circini ex angulis vestigii accipiuntur
lineæ perpendiculares; ex angulis verò elevationis desumuntur lineæ
parallelæ, ac lineæ visuales ad punctum oculi._
Ninety-eighth Figure.
_A fourth Part of the Architectonical Design, painted on the Vault of S.
~Ignatius~’s Church; with its Lights and Shadows._
In this Figure you have a Quarter of the whole Work, drawn from the
foregoing Figure, after the usual Manner; namely, by taking with the
Compasses the perpendicular Lines from the Angles of the Plan; and the
parallel Lines from those of the Elevation, as also the visual Lines to
the Point of Sight.
[Illustration: FIG. XCIX.]
Figura Nonagesimanona.
Alter quadrans totius Operis.
_Ob diversitatem duorum quadrantum, tum in longitudine, tum in luminibus
& umbris, seorsim apponendum utrumque censui; ut in eis delineandis omnem
difficultatem tibi adimerem._
The Ninety-ninth Figure.
_Another Quarter of the whole Design._
By reason of the Difference of the two Quarters, as well in Length, as in
their Lights and Shadows, I resolv’d to describe them separately, that
you might find no Difficulty in designing the whole Work.
[Illustration: FIG. C.]
FIGURA Centesima.
Modus reticulationis faciendæ in testudinibus.
_Opera quæ fiunt in planis, contenta sunt duplici reticulatione, ut notum
est. Nam una earum fit in exemplari, altera fit in superficie in quâ
ipsum Opus pingendum est. At verò testudines exigunt tres reticulationes.
Prima fit in exemplari, quod supponimus delineatum esse juxta regulas
Perspectivæ horizontalis. Secunda reticulatio constat ex funiculis, &
est pensilis; cujus formam geometricam habes in ~M~. Locum ubi figendi
sunt clavi qui sustineant funiculos, exhibent rectæ ~AB~, ~EF~: optica
verò deformatio retis est in ~N~. Punctum oculi est ~O~, distantiæ est
~LO~. Itaque si imagineris, tempore nocturno, lumen candelæ aut lucernæ
existere in ~O~, atque à reti ex funiculis projici lineas umbrosas in
testudinem, eædemque lineæ pennicillo colorentur, habebitur tertia
reticulatio ad pingendam testudinem necessaria._
_Dixi ~si imagineris~, quia in testudinem obductam tabulato, ac remotam
à reti, & multò magis à lumine, vel projici nequeunt umbræ, vel
nequeunt esse vividæ ac distinctæ, ut oportet. Itaque ubi nimia fuerit
distantia, figes in ~O~ extremitatem fili; eóque usque ad testudinem
extenso, utéris veluti radio ac lumine candelæ, ad notandum umbræ
locum. Proderit etiam, ut super tabulato motum fili obsecundes lumine
alicujus candelæ, quod ipsi filo proximè admoveas. Atque his aliisque
adminiculis, tuâque industriâ, colores induces super lineis umbrosis, ac
tertiam reticulationem absolves. Posset etiam rete ex filis figi in parvâ
distantiâ à coronice, puta in ~GH~, unde incipit basis ædificii: tunc
autem umbræ in fornice sunt magis distinctæ ac visibiles._
_Diligentissimè curabis, ne mensuræ exemplaris discrepent ullatenus à
mensuris testudinis: ut rete incidens in angulos, arcus, aut lunulas
testudinis, exactè respondeat reti exemplaris. Demum si in vitia quæ
emendari nequeant, incidere nolis; scito, regulas omnes Perspectivæ
horizontalis, æquè in hominibus aut animalibus, ac in columnis aut
coronicibus pingendis, omnino servari oportere._
The Hundredth Figure.
_The Method of drawing the Net or Lattice-Work on Vaults._
For Works on a flat Superficies, two Net-works are sufficient; as has
been already intimated: One drawn on the Copy; the other on the Table to
be painted. But for arch’d Surfaces, or Vaults, three are requir’d: One
made on the Copy, which I suppose drawn according to Rules of horizontal
Perspective. The second consists of a Frame of small Cords or Threads,
to be hung up; the Geometrical Form of which is M. The Lines AB, EF,
shew the Place where this Frame is to be fix’d, in the same manner as
the Perspective N. The Point of Sight is O; of Distance, LO. Therefore,
if you imagine a Lamp or Candle fix’d in the Night-time at the Point O;
the Shadows of the Thread, thrown thereby on the Vault, being trac’d by a
Pencil, make the third Net-work requir’d for painting the same.
I say, _if you imagine_ a Lamp thus fix’d; because either the Scaffold
to the Vault, or the great Distance of the Vault from the Net-work, or
the greater of both from the Light, may prevent the Shadows from being
thrown at all, or at least, may render them so faint, as not to be
distinct enough for the purpose. Therefore, where this happens, instead
of the Light fix one End of a Thread in the Point O; and extending the
other to the Vault, make use of it as a Ray from the Lamp or Candle, for
describing the Place of the Shadows. It will be also of great use, to
second the Motion of the Thread with the Light of a Candle you may have
by you on the Scaffold, holding the same near the Thread itself. By this,
and other such Helps, which your own Industry will suggest, you may lay
these Shadows in Colours, and complete the third Net-work requir’d. The
Frame of Threads may also be fix’d nearer the Vault at some Distance
above the Cornice, as at GH, where the painted Architecture begins; for
the Shadows thrown on the Arch will by that means become more visible and
distinct.
You must be very careful, that the Measures of your Copy are exactly the
same with those of the Vault, that the Net-work thrown into the Angles,
Arches and Lunettes of the Vault, may perfectly correspond with that of
your Copy. Lastly, if you would not run into inextricable Errors; assure
yourself, that all these Rules of horizontal Perspective are as strictly
to be observ’d in the Figures of Men or Animals, as in painting Columns,
Cornices, or the like.
_Ut Perspectivæ Tyronibus consulerem, qui fortasse non adeo facilè
percipient duodecim primas figurarum explicationes, totidem novas
explicationes hic addo._
For the greater Help to Beginners, and those who are less conversant in
the Art of Perspective, I here subjoin a farther Explanation of the first
twelve Figures of this Book.
FIGURA PRIMA.
Explicatio linearum plani, & horizontis, punctorum oculi, & distantiæ; de
hoc ultimo pressiús.
_Tres lineæ diversi inter se nominis, & muneris, item, & duo puncta
præcipuè necessaria sunt, ut delineatio quælibet opticè reddi queat:
prima vocatur linea plani, secunda horizontalis ubi est punctum oculi;
de tertia loquar in elevationibus: alterum de duobus punctis assignatur
oculo, & vulgò dicitur punctum oculi; alterum verò assignatur distantiæ,
à qua nomen habet. Punctum oculi notissimum est, punctum verò distantiæ
non ità; in hujus igitur explicatione morabor, & ut clariùs ostendam
quid sit, & quomodo formandum sit, selegi descriptionem Ecclesiæ
geometricè habitam, quam in tres partes divisi, in vestigium, sectionem,
& interiorem faciem, in qua facie velit quis pingere, seu delineare
aliquid opticè, ut elongetur ad mensuram aperturæ quadrati ~P~, ut habes
in vestigio, & ad mensuram profunditatis ~Q~, quam habes in sectione._
_Super faciem ~CCCC~ quam puta esse delineamentum, habes rationem, qua
debes disponere supradicta puncta, & lineas. ~HI~ erit linea plani: ~NON~
erit linea horizontalis, quæ fieri solet distans à linea plani altitudine
hominis, ut vides in ~B~. Punctum oculi erit in ~O~; punctum distantiæ
erit in ~N~, ex qua parte malueris. Hoc punctum ~N~ debet tantum abesse
à puncto ~O~, quantum tuo arbitratu tu vis procul esse ut videas
profunditatem illius quadrati ~PQ~, sicut vides in exemplo vestigii, &
sectionis; ubi rem velut in suo statu naturali exhibeo; in iis enim tam
abest ~N~ ab ~O~, quam abest homo ab ~A~ ad ~DE~, & homo ~B~ in sectione,
ab ~FG~, ubi est murus in quo pingendum, vel delineandum est._
_Si ulteriùs curiosè descriptionem hanc consideres, videbis quam bene
respondeat quadratum ~P~ in plano, & elevatio ~Q~, ut naturalis status
rei in sectione Perspectivæ positæ in facie ~CCCC~, quæ est delineatio.
Videbis enim visuales, quæ secant in plano spatium ~RS~, ita pariter
secare spatium ~TV~ in elevatione: & segmentum visualium ~XZ~ in sectione
respondere ~YK~ in elevatione, quod demonstratione non caret._
FIRST FIGURE.
_An Explanation of the Lines of the Plan and Horizon, and of the Points
of Sight and Distance; but more especially of this last._
For beginning any Design in Perspective, there are principally requir’d
three Lines, and two Points: One Line where the Feet stand, which is
call’d the Line of the Plan, or Ground-line: The second where the Eye is
plac’d, call’d the horizontal Line: I shall speak of the third in the
Elevations. Of the Points, one is assign’d to the Eye, the other to the
Distance. The first of these is generally known, the latter not so well
understood, though of great Use for giving the Removal or Depth of every
Object. I shall therefore insist a while on the Explanation of the Point
of Distance; and that I may more clearly shew what it is, I have chosen
the Geometrical Description of a Church, which is divided into three
Parts; _viz._ the Plan, Profile, and inner Face; in the midst of which
Face one would paint a Piece of Perspective, that should seem to recede
as much as the Square P in the Plan, and the Depth Q in the Profile.
On the Face CCCC, which suppose that of the Design, you see the Manner
of disposing the two Lines and the two Points. HI is the Ground-line.
NON is the horizontal Line, which is usually made a Man’s Height above
the Ground line, as in B. The Point of Sight is O, the Point of Distance
N, on which side you will. This Point N must be as far from O, as the
Distance you determine to place yourself at for viewing the Depth of the
Square PQ; as is exemplify’d in the Plan and Profile, where you see the
thing as in its natural Position: And in them N is distant from O, as far
as the Man in A is remov’d from DE; or the Man B in the Profile from FG,
which is the Wall to be drawn or painted on.
If you farther and more strictly examine this Description, you’ll discern
how well the Square of the Plan P, and the Elevation Q, correspond as if
naturally put into Perspective on the Face CCCC, which is the Draught.
For you see the Visuals which cut the Space RN in the Plan, cut the
same Space TV in the Upright; and the Segment of the Visuals XZ in the
Profile, answer that of YK in the Elevation; which needs no Demonstration.
FIGURA SECUNDA.
Quadratum opticè delineatum.
_Postquam descripseris in papyro separata quadratum geometricum A, facies
duas lineas parallelas inter se distantes altitudine, quam dederis
puncto oculi; linea inferior erit linea plani, linea superior erit linea
horizontalis, super quam ponuntur puncta oculi ~O~, & distantiæ ~E~,
quod sit ex parte quam mavis: linea distantiæ non debet esse brevior
magnitudine rerum describendarum. Transfer posteà circino latitudinem
quadrati ~A~ in ~CB~, unà cum visualibus ad punctum ~O~; & similiter
transfer longitudinem ipsius quadrati in ~DC~, ducens lineam à puncto
~D~ ad punctum distantiæ ~E~, transeuntem per visualem ~CO~, & ubi illa
secat, habebis terminum quadrati optici ~GFCB~, ducens parallelam ad
lineam plani in ~F~._
_Ut autem hoc idem citiùs absolverem, sæpius chartam complicavi, ut habes
in ~A~._
SECOND FIGURE.
_A Square in Perspective._
After you have drawn, on a separate Paper, the Geometrical Square A,
make two parallel Lines as much distant one from the other, as you would
have the Height of the Eye. The under Line is the Plan or Ground-line;
the upper Line is that of the Horizon, on which are plac’d the Points
of Sight O, and of Distance E, on which side you please. The Line of
Distance should not be shorter than the Extent of the thing to be
describ’d in Perspective. Then with your Compasses set the Breadth of
the Square A on CB, and draw Visuals to the Point O; and from the Length
of the Square transferr’d into DC, draw a Line from the Point D to the
Distance E; and where that cuts the Visual CO, by drawing a Line parallel
to GF, you describe the Square in Perspective GFCB.
For the more quick Dispatch of this, I commonly fold the Paper, as you
see in A.
FIGURA TERTIA.
Rectangulus altera parte oblongior opticé.
_Quidquid in proximo quadrato vidisti, facies in præsenti. Transferres
latitudinem ~BC~ in ~BC~, & longitudinem in ~CD~, ducens latitudinem ~BC~
ad punctum oculi ~O~, & longitudinem ~CD~ ad punctum distantiæ ~E~. Ubi
vero hæc linea secat visualem ~CO~, erit terminus rectanguli supradicti
~FG, BC,~ ducens parallelam, ut supra._
THIRD FIGURE.
_An Oblong Square in Perspective._
What was done in the preceding, repeat in this Third Figure. Transfer the
Breadth BC into BC, and the Length into CD, drawing the Breadth BC to the
Point of Sight O, and the Length CD to the Point of Distance E. Where
this cuts the Visual CO, you terminate the Square FG, BC, by drawing the
Parallel, as before.
FIGURA QUARTA.
Quadratum duplex opticé.
_Eodem modo construes quadratum duplex ~A~, transferens circino, aut
duplicando chartulam, latitudinem cujuscumque lineæ, ut vides in punctis
~1~, ~2~, ~3~, ~4~, ~5~, ~6~, super lineam plani in iisdem numeris, & ab
istis transferes visuales ad punctum ~O~. Postea transfer longitudinem
~7~, ~8~, ~9~, ~10~, super lineam plani in iisdem pariter numeris, & ab
istis duc lineas ad punctum distantiæ ~E~. Ubi hæ lineæ secant lineam ~6,
7, O,~ fiunt lineæ parallelæ ad lineam plani, & quadratum conficitur;
parem constructionem facies de quadrato secundo, & tertio, facilè ex
dictis._
FOURTH FIGURE.
_A double Square in Perspective._
The double Square A is made after the same manner as the former, by
transporting, either with the Compasses, or folded Paper, the Breadth of
every Line, as you see the Points 1, 2, 3, 4, 5, 6, on the Ground-line
mark’d with the same Numbers; and from these draw Visuals to the Point
of Sight. Then transfer the Points of Length 7, 8, 9, 10, into the
Ground-line, as you see also in the same Numbers; and direct their Lines
to the Point of Distance E. Where these intersect the Visual 6, 7, O,
make Parallels to the Ground-line, and the Square is complete. The same
is done in describing the middle Square, and that on the other Side.
FIGURA QUINTA.
Quadratorum vestigia cum elevationibus.
_Figuram hanc in duas partes divisi; in superiori parte vides tria
quadrata optica aliquantulum adumbrata, eaque tam inter se distantia,
quanta est distributio super lineam plani. ~BC~ erit quadratum primum.
Secundum erit in ~EF~. Si ergo posueris longitudinem quadrati in ~BC~,
eamque duxeris ad distantiam, secabit in ~DD~ visualem ~AO~. Si pariter
posueris alterum spatium longitudinis ejusdem quadrati in ~EF~, & duxeris
ad lineam distantiæ, habebis secundum quadratum opticé. Idem facies de
tertio, & de aliis, quæ distribuenda sunt._
_In secunda parte. Si desideres supra totidem vestigia formare
elevationes cuborum, & stylobatarum, ut in inferiori figuræ parte
vides, satis erit ex omni vestigiorum angulo elevare lineas occultas,
& apparentes, determinando altitudinem faciei ~L~ primo cubo, & anguli
ejusdem faciei dabunt altitudinem omnium aliorum._
_Immò etiam totidem cubos formare potes sine lineis occultis, ducendo
solùm apparentes, ut vides in tribus expositis adumbratis, & nitidis,
quorum perpendiculares sumuntur ab angulis vestigiorum, ut in superiori
figura habes in ~H~, & lineæ plani translatæ sunt ab angulis elevationis,
ut videtur in ~F~._
FIFTH FIGURE.
_Several Plans of Squares, with their Elevations._
I have divided this Figure into two Parts; In the uppermost you have
three Squares in Perspective a little shadow’d, distant one from another,
according to their Distribution on the Ground-line. BC is the first
Square; EF the second. If you then set the Length of a Square on BC, and
draw Lines to the Point of Distance, they will intersect the Visual AO
in DD. In like manner, if you set another Length of the said Square on
EF, and draw to the Point of Distance, you’ll have the second Square in
Perspective. The same you may do in the third, and as many as you have
occasion for.
In the second Part you see, that if upon the fore-mention’d Plans the
Elevations of Cubes or Pedestals were requir’d, it would suffice to
elevate the occult and visible Lines from every Angle of the Plan; and
determining the Height of the Face L of the first Cube, the Angles of
that Face drawn to the Point of Sight, give the Height of all the others.
You may form the same Cubes without occult Lines, drawing only those
that are apparent, as you see in the three Cubes that are finish’d and
shadow’d; the Perpendiculars of which are taken with the Compasses from
the Angles of the Plan, as is shewn in HI of the upper Figure; and the
level Lines are transferr’d from the Angles of the Elevation, as in FG of
the same Figure.
FIGURA SEXTA.
Modus delineandi opticè sine lineis occultis.
_Desiderans facili methodo figuram hanc exponere, dabo rationem elevandi
corpora sine lineis occultis, ut in superiori tetigi; ostendam igitur
hic, quomodo quinque cubi adumbrati desumantur ab eorum vestigiis, &
elevationibus._
_Duas debes facere præparationes, si libeat, in chartis etiam separatis.
Prima erit formare geometricè vestigium, & elevationem, ut vides in ~B~
& ~A~. Secunda erit distribuere super lineam plani latitudinem vestigii
~B~, puta in ~NM~, & in duabus proximis: Illius longitudo ~MX~ ducta ad
distantiam ~D~, secat visualem ~MO~ in ~R~. Spatium autem obliquatum ~E~
utile etiam est aliis duobus quadratis positis super eamdem lineam plani;
anguli quorum translati ad distantiam ~B~, totidem angulos dabunt inter
visuales ~NO~, ~MO~. Hoc posito, duces perpendicularem ad angulum ~N~,
quæ in elevationibus geometricis semper necessaria est, eaque tertia
linea est, quam supra dixi. Transfer postea altitudinem ~A~ in ~NF~, cum
visualibus ~FO, NO,~ & invenies altitudinem ~ST~. Hoc pariter de cæteris
eveniet._
_Sciendum superest quonam modo supradicta præparatione uti possis ad
construendos stylobatas adumbratos, & inornatos._
_Super aliam igitur chartam dispone situm cum duabus lineis, plani
scilicet, & horizontis, una cum puncto oculi ~O~, & perpendiculari ~V~,
ejusdem mensuræ cum supradicta præparatione, & faciens uti me fecisse
vides. Experire postea circino ~NF~ æqualia esse ~1, 5,~ & ~2, 6~. Metire
pariter ~ST~, & invenies æqualia ~7~ & ~3~; facies postea lineas planas,
& visuales ad punctum oculi, & habebis planum superius cubi in ~1~, ~2~,
~3~, ~4~. Hoc idem faciendum est de aliis. Uno verbo: anguli vestigiorum
dabunt tibi lineas perpendiculares, & anguli elevationis dabunt lineas
planas; atque hoc semper erit._
SIXTH FIGURE.
_The Manner of designing in Perspective without occult Lines._
Being desirous to make this Rule as easy as possible, I shall give a
farther Account of raising Solids without the Help of occult Lines, which
I only touch’d upon in the foregoing Figure. I therefore here shew you,
how the five shadow’d Cubes of this Figure are taken from their Plans and
Elevations.
Two things preparatory are to be done, and, if you please, on separate
Papers. The first is, to describe the Geometrical Plan and Elevation,
as you see in B and A. The second is, to dispose on the Ground-line the
Breadth of the Plan B; as, for Example, in NM, and the two next to it.
The Length thereof MX, drawn to the Point of Distance D, cuts the Visual
MO in R; and the Foreshortning E serves also for the other two Squares
plac’d upon the same Ground-line, whole Angles being directed to the
Distance D, give as many Angles on the Visuals NO, MO. This done, erect a
Perpendicular on the Angle N, which in Geometrical Elevations is always
necessary, and is the third Line mention’d in the first Figure. Then
carry the Height A on NF, drawing the Visuals FO, NO, which determine the
Height ST, and that of the other Squares.
It remains to be known, how to make use of the foresaid Preparation for
the Construction of the shadow’d Pedestals.
On another Paper therefore dispose the Horizontal and Ground-lines,
together with the Point of Sight O, and the Perpendicular V, keeping the
same Measures as in the aforesaid Preparation, and doing as I have done.
You may prove by the Compasses, that NF is equal to 1, 5, and 2, 6, and
measuring ST, you’ll find it equal to 7, 3, then drawing the level Lines,
and the Visuals to the Point of Sight, you have the upper Face of the
Cube C in 1, 2, 3, 4. The same must be done in the others. In a word, the
Angles of the Plan give you the perpendicular Lines, and the Angles of
the Elevation give the level Lines, or those parallel to the Ground-line;
and this you are always to understand for the future.
FIGURA SEPTIMA.
Aliud exemplum construendi vestigium geometricum, cum elevatione
longitudinis.
_Vides hic stylobatam ~P~ in quatuor partes divisum, & adumbratum. Si
illum opticè delineare velis, construere debes supradictas præparationes,
geometricam nempe, & opticam. Nomine geometricæ intelligo vestigium
~A~, & elevationem ~B~; nomine vero opticæ, totum id quod includitur in
~GCDEO~._
_Transfer igitur latitudinem geometricam ~CD~ vestigii ~A~ super lineam
plani pariter ~CD~, & transfer longitudinem ~DE~ super lineam plani
pariter ~DE~, operans more solito; & habebis vestigium opticé. Transfer
posteà elevationem ~HX~ in ~CG~ perpendicularis; ducens visualem ~GO~,
eleva ad lineam ~GO~ omnem angulum, quem planum facit in linea ~CO~, &
habebis altitudinem necessariam etiam sectionis._
_Transferes denique circino in aliam chartam angulos vestigii, qui dabunt
tibi lineas perpendiculares, & anguli sectionis dabunt lineas planas:
Visuales vero duces ad punctum oculi._
SEVENTH FIGURE.
_Another Example of a Geometrical Plan, with the Elevation of its
Length._
If you would delineate in Perspective the Pedestal P, which you here
see divided into four Parts, and shadow’d; you must make the two
foregoing Preparations; namely, the Geometrical and the Perspective.
By the _Geometrical_, I mean the Plan A, and the Elevation B; By the
_Perspective_, all that’s contain’d within G, C, D, E, O.
Then transfer the Geometrical Breadth CD of the Plan A, into CD of
the Ground-line; and the Length DE of the said Plan into DE of the
Ground-line working after the usual manner; and you will have the Plan in
Perspective. Again, set the Elevation HX on CG of the Perpendicular, and
drawing the Visual GO, elevate thereto every Angle made by the Plan on
the Line CO, and you have all the Heights necessary for the Profile.
Lastly, by the Compasses you transport on a clean Paper the Angles of the
Plan, which give the perpendicular Lines; and those of the Profile, which
give the level Lines. The Visuals you draw to the Point of Sight.
FIGURA OCTAVA.
Stylobata opticé.
_Hic etiam postquam feceris supradictas præparationes, geometricam
scilicet, & opticam; facies præsentem stylobatam adumbratum, transferens
circino angulos vestigii, ut construas perpendiculares; & angulos
sectionis, ut formes lineas planas, ut supra. Nam sic duo anguli
vestigii ~MO~ dabunt lineas perpendiculares ~EF~; angulus vestigii ~R~
dabit perpendicularem ~P~, & sic reliqui anguli dabunt reliquas lineas
perpendiculares. Similiter à sectione angulus ~I~ dabit lineam planam
~HN~. Breviter, primus terminus sectionis ~ID~ dabit altitudinem linearum
planarum in facie stylobatæ adumbrati ~EFHN~. Secundus terminus ~Q~ dabit
altitudinem faciei oppositæ, & occultæ ~P~._
_Duo tamen moneo; primum, ut faciens vestigia geometrica, ducas ab
elevatione ~A~ totidem lineas ad latera vestigii ~B~, quot angulos
invenies in prominentiis supradictæ elevationis ~A~, ut manifestè vides
in lineis quas ex punctis composui, illæ enim à stylobata ~A~ cadunt
super vestigium ~B~; quare prominentia major in elevatione ~L~ facit
lineam majorem ~L~ in vestigio._
_Secundum quod moneo sit, ut volens elongare vestigium opticè delineatum
~MOR~ à linea plani ~K~, quantum erit spatium ~C~ in eadem linea plani,
tantumdem elongabitur spatium ~G~ à linea ejusdem plani._
EIGHTH FIGURE.
_A Pedestal in Perspective._
Here also, after you have made the two foregoing Preparations, the
Geometrical and the Perspective; this shadow’d Pedestal is made by
taking with the Compasses the Angles of the Plan, for drawing the
Perpendiculars, and the Angles of the Profile for the level Lines, as
before. Thus the two Angles of the Plan MO, give the perpendicular Lines
EF. The Angle of the Plan R, gives the Perpendicular P; and the other
Angles give their respective Perpendiculars. So likewise in the Profile,
the Angle I gives the level Line HN. In short, the first Out-line of
the Profile ID gives the Height of the level Lines on the Front of the
shadow’d Pedestal. The other Out-line Q gives the Height of the occult
and back part thereof.
Nevertheless, two things are to be observ’d; first, that in making the
Geometrical Plan, you draw from the Elevation A, as many Lines to the
Side of the Plan B, as you have Angles in the Projectures of the said
Elevation; as is manifest in the pointed Lines, which fall, from the
Upright A, on the Plan B, where that of the greatest Projecture L in the
Elevation makes the outer Line L of the Plan.
The second thing to be observ’d, is, That if you would have the
Perspective-Plan MOR as far within the Ground-line K, as the Breadth
of the Space C on the same Line, the Space G will then be the Distance
thereof from the said Ground-line.
FIGURA NONA.
Optica delineatio Architecturæ Jacobi Barozzii: & primum, de stylobata
Ordinis Etrusci.
_Quandoquidem omnibus nota est Architectura Barozzii, eam hic penitus
immutatam cum suis regulis particularibus, & generalibus expono; Metieris
autem illam modulis ut fieri solet; qui igitur illam desiderat, in
sequentibus figuris inveniet totam, simulque discet opticè reddere. Cum
autem non minus Opticæ studioso quam Architecturæ necesse sit, efficere
delineamenta rei construendæ, ab hoc verè, ab illo fictè, id est, cum
uterque facere debeat vestigium, elevationem, sectionem, & faciem, ob id
delineavi hic stylobatam Ordinis Etrusci cum suo vestigio, quem vides
in ~AB~, ut faciliùs percipias quod in proxima figura dixi, à totidem
scilicet angulis prominentiarum elevationis, totidem ducendas esse
lineas super lineam vestigii; cum hoc necesse sit ad inveniendum illorum
angulorum cum istis lineis concursum in suis degradationibus. Nota,
longitudinem, quam voco ~F~ ductam in ~G~ esse illam, à qua non solùm
nascitur vestigii obliquitas, verùm etiam ab illa nascitur obliquitas
illius quam voco sectionem ~E~. Ob id in altero hujus ejusdem figuræ
stylobata totum id è contrario videbis._
_Non ampliùs repetam quonam modo eruatur nitida delineatio, de qua
superiùs pluries; dicam tamen angulos primi termini sectionis ~E~
daturos lineas planas faciei ~D~, & angulos vestigii daturos omnes
perpendiculares._
NINTH FIGURE.
_The Architecture of ~Vignola~ put in Perspective; and first, the
Pedestal of the ~Tuscan~ Order._
Since every one is acquainted with _Vignola_’s Architecture, I determine
not to alter it, but to explain it, with its general and particular
Rules; measuring the same with Modules, after the usual manner. He
therefore that has it not, may find it in the following Figures, and
at the same time learn the Method of putting it in Perspective. And
whereas the Drawing the Plan, Elevation and Profile of what’s to be
built, is no less necessary for him that studies Perspective, than for
the Architect, the first performing in Appearance, what the latter does
in Reality; I have therefore here delineated the _Tuscan_ Pedestal, with
its Plan, as you see in AB, that you may the better apprehend what I said
in the foregoing Figure, That from all the Angles of Projecture in the
Elevation, Lines must be let fall on the Plan; this being of absolute
necessity for finding the Correspondence of the Angles with the Lines in
the Perspective Projection. Observe, that what I always call Length, as
from F to G, is that from which proceeds not only the Foreshortning of
the Plan; but also that which I call the Profile E. Wherefore, in the
opposite Pedestal of the same Figure, you’ll see a contrary Disposition
of the Whole.
I shall not here repeat, how the finish’d Pedestal is taken from these;
having so largely spoken of that before; but briefly tell you, that the
Angles of the first Out-line of the Profile E give the level Lines of the
Face D, and the Angles of the Plan give all the Perpendiculars.
FIGURA DECIMA.
Stylobata Doricus, & ratio vitandi difficultatem quamdam, quæ occurrit
inter illum opticè delineandum.
_Hic oritur difficultas hæc. Vestigium ~A~ opticè translatum in ~C~
adeò contrahitur, ut distinctè videri nequeat ubi collocetur circini
pes, ut transferri possint perpendiculares stylobatæ adumbrati; totaque
hæc difficultas oritur à propinquitate quam habet linea horizontalis,
seu punctum oculi cum linea plani. Ut igitur illam vincas: Duces lineam
plani inferiùs quantum libuerit, & super illam feres denuò latitudinem, &
longitudinem more solito, retinendo puncta oculi, & distantiæ ~OF~, & sic
videbis vestigia magis minusve distincta; Vestigium enim ~E~ distinctius
est vestigio ~D~, & ~D~ distinctius est vestigio ~C~._
TENTH FIGURE.
_A ~Dorick~ Pedestal, with the Manner of shunning a Difficulty, which
occurs in putting the same in Perspective._
In this Figure a Difficulty arises, which is this; That the Plan A put
in Perspective in C, is so foreshorten’d, that one can’t see distinctly,
where to place the Compasses, for transferring the Perpendiculars on
the shadow’d Pedestal; which is caus’d by the too near Approach of the
horizontal Line to the Ground-line. For avoiding this Difficulty, draw
another Ground-line as much below the first as you please, and carry the
Breadth and Length thereon, after the usual manner, still keeping the
same Points of Sight and Distance O and F: And according to the Removal
of the Ground-line, the Plans will be more or less distinct; as you see
the Plan E is more distinct than D, and D is more so than C.
FIGURA UNDECIMA.
Stylobata Ionicus, & ratio vitandi aliam difficultatem in elevationibus.
_In elevationibus etiam sectionis opticè potest accidere, ut si visualis
~LK~ nimis recta sit, sectio ~B~ restringatur. Elongando lineam plani ab
~L~ ad ~M~, visualis ~MN~ erit inclinatior, & consequenter sectio ~C~
erit latior, & distinctior._
_Nota, difficultatem hanc sæpe sæpiùs te habiturum in figuris præcipuè,
quæ multas lineas habent, ut in figura quadragesimasecunda, ubi pariter
rationem vitandi confusionem reddam._
_Neque tibi molestiæ sim, quod in hac figura lineam horizontalem infra
lineam plani collocaverim, id enim feci, ut illarum diversos effectus
videas, utque tu in tuis studiis mutes, & discas._
ELEVENTH FIGURE.
_The ~Ionick~ Pedestal, and the Way to shun another Difficulty in the
Elevations._
In Elevations of the Profile in Perspective, it may sometimes happen,
that the Visual LK may be so direct, as to render the Profile B too close
and narrow; wherefore prolonging the Ground-line from L to M, make the
Visual MN, which being much more oblique, does consequently render the
Profile C more broad and distinct.
And observe, that this Difficulty will very often occur; especially in
Figures that have many Lines, as the Forty-second Figure has, where I
speak also of the manner of avoiding the same.
Nor let it trouble you, that in this Figure I have plac’d the horizontal
Line below the Ground-line; which I have done, that you might see their
different Effects, and by changing the Disposition of your Designs,
improve and learn.
FIGURA DUODECIMA.
Stylobata Corinthius cum suis pilis.
_Fecisse septimam figuram magno tibi documento erit ad construendum,
& dividendum stylobatam ~A~, & vestigium ~B~; cum nihil addere debeas
præter pilas ~C~ cum coronice, quæ duo latera ambit. Opticè hoc vestigium
delineabis in ~D~, quæ delineatio distinctior est, quia inferiùs duxi
lineam plani; & distinctior etiam est sectio ~E~, cum elongaverim
visualem ~FG~. Sic semper agam, ut detur locus figuræ adumbratæ, & ut
etiam videas perpendiculares stylobatæ adumbrati cadere super angulos
vestigii, & lineas planas incidere è diametro super angulos sectionis
~E~. Iterùm libenter moneo, ut facias supradictas præparationes in
chartulis separatis, ut initio assuescas transferendis figuris nitidis
circino; facile enim tibi postea erit integras machinas Perspectivæ
jucundioris delineare, ut videbis: in hoc enim tota regulæ hujusce, &
totius operis facilitas sita est._
TWELFTH FIGURE.
_A ~Corinthian~ Pedestal, with its Pilasters._
The Performance of the Seventh Figure will be a great Assistance to you,
in the Construction and Division of this Pedestal A, and the Plan B;
since you have nothing more to add here, but the Pilasters C, and the
Mouldings which surround the two Sides. This Plan is put in Perspective
in D, and becomes more distinct by my sinking the Ground-line lower;
and the Profile E is also more distinct by the Removal of the Visual
FG, as mention’d in the foregoing Chapter. This I shall always do, that
there may remain Room for the shadow’d Figure, and that you may also see
that the Perpendiculars of the shaded Pedestal fall directly upon the
Angles of the Plan, and that the level Lines directly answer the Angles
of the Profile E. I repeat my Advice, that you would make the foresaid
Preparations on several Papers, and accustom yourself at the beginning
to take off the finish’d Figures with the Compasses; for it will become
very easy to you afterward, to design entire Machines of delightful
Perspectives, as you’ll see hereafter. And indeed in this Practice, the
Facility of this Rule, and of all that follows in this Work, does chiefly
consist.
_Respondetur objectioni factæ circa punctum oculi opticum._
Non omnium sensus est, uni optico operi unicum tantùm punctum
assignare, _e. g._ toti spatio fornicis, tholi, & tribunæ, quam
vocant, expressæ in figura nonagesimatertia, nolunt concedi
unicum punctum, volunt concedi plura.
_Respondeo, objectionem hanc dupliciter intelligi posse: vel enim
intelligi posset, non esse assignandum unicum punctum toti illi spatio;
atque in hoc sensu vera est; cum enim spatium illud valde oblongum sit,
dividi debuit in partes, atque assignanda tribunæ, quam dicunt, tholo,
& fornici, propria puncta; cum hoc communiter doceant, ubi situs nimium
est longus, & parùm altus. Vel potest intelligi de qualibet ex dictis
partibus, & sic intellecta penitùs falsa est. Primò, quia præstantiores
fornices aularum, & templorum, qui optico artificio ornati sint, si
unicum opus reddunt, à suismet authoribus determinatum idemque unicum
punctum accepisse compertum est. Secundò, quia cum ars optica sit mera
veri fictio, non id pictor facere potest, ut à qualibet parte simulet
veritatem, verùm ab uno determinato puncto id ostendit. Tertiò, quia si,
~e. g.~ fornici, qui uno integroque optico opere ornetur, plura puncta
assignaveris, nullum reperies locum, unde integrum opus spectare possis,
& ad summum ex quolibet puncto tantùm partem illius spectabis, nusquam
verò totum opus. Ex dictis igitur rationibus concludo ab inducentibus
plura puncta in eodem opere induci malum majus eo, quod unicum punctum
inducit; quare hoc omnino necessarium est situi in quo unicum opus
formandum sit, ad quod collimare debeant ex omni operis parte figuræ
simul & architectura. Quo posito, negari rationabiliter nequit, à
me etiam concedi unicum punctum spectando fornici amplo, aptoque ad
repræsentandum unicum opus, qualis est fornix in D. Ignatii templo. Si
verò propter situm irregularem, ut dicimus, architectura extra punctum
aliquantulum deformetur, & figuræ pariter operi optico intermixtæ extra
commune punctum aliquam patientur deformitatem, præterquam quod à
supradictis rationibus excusatur, nequaquam id vitio arti est, sed laudi;
quandoquidem ars à suo puncto exhibet, proportione positâ, ut rectum, ut
planum, ut concavum, id quod tale non est._
An Answer to the Objection made about the Point of Sight in Perspective.
_Every one does not approve, that in a Perspective of great
Extent one Point of Sight only should be assign’d the whole
Work; as for Example, In the whole Length of the Nave, Cupola,
and Tribune, express’d in the Ninety-third Figure, they will by
no means allow of one single Point, but insist upon several._
I answer, This Objection may be understood two ways; either that one
Point alone is not sufficient for that whole Length, and in this sense
’tis true; for that Space being very long, it ought to be divided into
Parts, and proper Points assign’d to the Tribune, Cupola, and Vault
of the Nave; as is commonly taught, where the Situation is of a great
Length, and not very high. Or it may be understood of any One of the said
Parts, and so is altogether false. _First_, Because in the Vaults of
Halls or Churches painted by the greatest Masters, if they consist of one
Piece only, we find but one Point of Sight assign’d. _Secondly_, Since
Perspective is but a Counterfeiting of the Truth, the Painter is not
oblig’d to make it appear real when seen from _Any_ part, but from _One_
determinate Point only. _Thirdly_, Because, if in a Vault, for Example,
where you would paint one entire Design of Architecture and Figures, you
assign several Points of Sight, you will find no place whence you may
take a perfect View of the Whole, and at best you can only view each
Part from its proper Point. From all which Reasons I conclude, that the
Introduction of many Points into the same Piece, is more injurious to the
Work, than making use of one only: Wherefore ’tis absolutely necessary in
a regular Situation, and where the Work is all of a piece, so to place
the same, as that the Figures and Architecture may from every part of
the Design have respect thereto. This suppos’d, I confess that I myself
make use of one Point of Sight only, in very large Vaults that consist
of one Design, such as that of the Nave of the Church of S. _Ignatius_.
If therefore through the Irregularity of the Place, the Architecture
appear with some Deformity, and the Figures intermix’d therewith seem any
thing lame and imperfect when view’d out of the proper Point, besides
the Reasons just now given, it’s so far from being a Fault, that I look
upon it as an Excellency in the Work, that when view’d from the Point
determin’d, it appear, with due Proportion, streight, flat, or concave;
when in reality it is not so.
INDEX.
FIG.
_INSTRUMENTA paranda_, UTENSILS for Drawing.
_Explicatio linearum plani I. Explication of the Lines of
& horizontis, ac punctorum the Plan and Horizon, and of
oculi & distantiæ_, the Points of the Eye and of
the Distance.
_Modus delineandi opticè II. The Manner of delineating a
quadratum_, Square in Perspective.
_Optica delineatio III. The Delineation of an oblong
rectanguli, alterâ parte Square in Perspective.
longioris_,
_Optica descriptio quadrati IV. The Optical Delineation of a
duplicis_, double Square.
_Vestigia quadratorum cum V. Plans of Squares with their
elevationibus_, Elevations.
_Modus opticæ delineationis VI. The Manner of designing in
absque lineis occultis_, Perspective without occult
Lines.
_Aliud exemplum vestigii VII. Another Example of a
geometrici, cum elevatione Geometrical Plan and Upright
longitudinis_, put into Perspective.
_Optica projectio stylobatæ_, VIII. The Projection of a Pedestal
in Perspective.
_Optica delineatio IX. The Architecture of _Vignola_
Architecturæ Jacobi in Perspective, and first of
Barozzii, & primum de his Pedestal of the _Tuscan_
stylobata Ordinis Etrusci_, Order.
_Optica deformatio stylobatæ X. A _Dorick_ Pedestal in
Dorici; ubi de modo vitandi Perspective, with the Manner
confusionem in vestigiis of avoiding Confusion in
delineandis_, designing the Plans.
_Stylobatæ Ionici XI. The _Ionick_ Pedestal in
deformatio; ubi de vitanda Perspective, with the Manner
confusione in elevationibus_, of avoiding Confusion in
Elevations.
_Deformatio stylobatæ XII. The _Corinthian_ Pedestal, with
Corinthii, cum duabus pilis_, its Pilasters, in Perspective.
_Projectio stylobatæ Ordinis XIII. The Projection of a Pedestal
Compositi_, of the _Composite_ Order.
_Deformatio circulorum_, XIV. Circles in Perspective.
_Optica delineatio columnæ_, XV. A Column in Perspective.
_Optica projectio basis XVI. The _Tuscan_ Base in
Etruscæ_, Perspective.
_Deformatio basis Doricæ_, XVII. The _Dorick_ Base in
Perspective.
_Optica delineatio basis XVIII. The _Ionick_ Base in
Ionicæ_, Perspective.
_Optica imminutio basis XIX. The _Corinthian_ Base
Corinthiæ_, in Perspective.
_Basis Atticurga opticè XX. The _Attick_ Base in
imminuta_, Perspective.
_Optica imminutio capitelli XXI. The _Tuscan_ Capital in
Etrusci_, Perspective.
_Optica projectio capitelli XXII. The Projection of a
Dorici_, _Dorick_ Capital in
Perspective.
_Deformatio capitelli XXIII. The _Ionick_ Capital in
Ionici_, Perspective.
_Optica projectio capitelli XXIV. The _Corinthian_ Capital in
Corinthii_, Perspective.
_Optica descriptio capitelli XXV. The _Composite_ Capital in
Compositi_, Perspective.
_Deformatio coronicis XXVI. The _Tuscan_ Entablature
Etruscæ_, in Perspective.
_Optica delineatio coronicis XXVII. The _Dorick_ Entablature
Doricæ_, in Perspective.
_Præparatio figuræ XXVIII. Preparatory to the following
sequentis_, Figure.
_Optica projectio ædificii XXIX. A Projection of the _Dorick_
Dorici_, Order in Perspective.
_Optica projectio ædificii XXX. An _Ionick_ Work in
Ionici; ubi de modo jungendi Perspective, with the Manner
fictum cum vero_, of reconciling the fictitious
to the solid Architecture.
_Optica projectio coronicis XXXI. The Optick Projection of a
Corinthiæ, cum capitello & _Corinthian_ Cornice, with the
summitate columnæ_, Capital and part of the Column.
_Delineatio geometrica XXXII. The Geometrical Design of a
coronicis Ordinis Compositi_, Cornice of the _Composite_
Order.
_Deformatio coronicis XXXIII. A _Composite_ Cornice in
Compositæ_, Perspective.
_Præparatio ad figuram XXXIV. Preparatory to the
trigesimamquintam_, Thirty-fifth.
_Deformatio coronicis XXXV. A Side-View of the
Compositæ ad latus inspectæ_, _Composite_ Cornice in
Perspective.
_Præparatio ad figuram XXXVI. Preparatory to the
trigesimamseptimam_, Thirty-seventh.
_Deformatio columnæ Etruscæ_, XXXVII. A _Tuscan_ Column in
Perspective.
_Præparatio ad figuram XXXVIII. Preparatory to the
trigesimamnonam_, Thirty-ninth.
_Deformatio ædificii Dorici_, XXXIX. A Piece of _Dorick_
Architecture in Perspective.
_Vestigium geometricum XL. The Geometrical Plan of a
ædificii Ordinis Dorici_, Design of the _Dorick_ Order.
_Elevatio geometrica XLI. The Geometrical Elevation of
ædificii Dorici_, the foregoing Design.
_Modus vitandi confusionem XLII. The Manner of avoiding
in contractione vestigiorum Confusion in reducing Plans
& elevationum_, and Elevations into
Perspective.
_Contractio vestigii figuræ XLIII. The Plan of the Fortieth
quadragesimæ_, Figure in Perspective.
_Contractio elevationis XLIV. The Elevation of the
figuræ quadragesimæprimæ_, Forty-first Figure in
Perspective.
_Dimidium ædificii Dorici XLV. One half of the _Dorick_
opticè deformati_, Design in Perspective.
_Alterum dimidium ejusdem XLVI. The other half of the
ædificii_, same Design.
_Vestigia ædificii Ionici_, XLVII. The Plan of an _Ionick_
Building.
_Elevatio geometrica XLVIII. Geometrical Upright of the
ædificii Ionici_, foregoing _Ionick_ Design.
_Deformatio elevationis XLIX. The Elevation of the _Ionick_
ædificii Ionici_, Design in Perspective.
_Architectura Ionica_, L. A Design of _Ionick_
Architecture.
_Ordo Corinthius_, LI. A _Corinthian_ Design in
Perspective.
_Delineatio columnæ spiralis LII. The Description of a
Ordinis Compositi_, wreath’d Column of the
_Composite_ Order.
_Ordines Architecturæ LIII. A. The Orders of Architecture
desumpti ex Palladio & taken from _Palladio_ and
Scamozzio_, _Scamozzi_.
_Modus triplex delineandi LIII. B. Three different ways of
columnas spirales_, delineating wreath’d Columns.
_Vestigia ædificii Ordinis LIV. The Plan of a Design of the
Corinthii_, _Corinthian_ Order.
_Elevatio ædificii Ordinis LV. The Geometrical Elevation
Corinthii_, of a _Corinthian_ Work.
_Deformatio vestigiorum LVI. The Perspective-Plans and
& elevationis ædificii Upright of the _Corinthian_
Corinthii_, Design foregoing.
_Adumbratio figuræ LVII. The rough Draught of the
sequentis_, following Figure.
_Ædificium Ordinis Corinthii LVIII. Part of an Octangular Work
octangulare_, of the _Corinthian_ Order.
_Vestigia Tabernaculi LIX. The Plans of an Octangular
octangularis_, Tabernacle.
_Tabernaculum octangulare_, LX. An Octangular Tabernacle in
Perspective.
_Modus erigendi machinas quæ LXI. The Manner of erecting
constant pluribus ordinibus Machines that consist of
telariorum_, several Ranges of Frames.
_De reticulandis telariis, LXII. Of making the Net-work on
quæ repræsentent ædificia Frames, for representing
solida_, the Architecture as solid.
_Vestigia ædificii quadrati_, LXIII. The Plan of a square Design.
_Ædificium quadratum_, LXIV. A square Design in Perspective.
_Vestigium ædificii rotundi LXV. The Plan of a Circular Work
opticè imminutum_, in Perspective.
_Projectio ædificii rotundi_, LXVI. A Circular Design in
Perspective.
_Vestigium geometricum, ac LXVII. The Geometrical Plan, and
prima præparatio ad figuram first Preparation to the
septuagesimamprimam_, Seventy-first Figure.
_Elevatio geometrica LXVIII. The Geometrical Elevation of
vestigii præcedentis, & the foregoing Plan, and
secunda præparatio ad second Preparation to the
figuram septuagesimamprimam_, Seventy-first Figure.
_Deformatio vestigii figuræ LXIX. The Plan of the Sixty-seventh
sexagesimæseptimæ, & Figure in Perspective, and
præparatio tertia ad figuram third Preparation to the
septuagesimamprimam_, Seventy-first Figure.
_Deformatio elevationis LXX. The Perspective of the
figuræ sexagesimæoctavæ, & Elevation of the Sixty-eighth
præparatio quarta ad figuram Figure, and fourth Preparation
septuagesimamprimam_, to the Seventy-first.
_Theatrum repræsentans LXXI. A Theater representing the
nuptias Canæ Galilææ, Marriage of _Cana_ in
constructum Romæ anno _Galilee_, erected in the
1685, in expositione Ven. Jesuits Church at _Rome_,
Sacramenti, in templo 1685, for the Solemnity of
Farnesiano Societatis Jesu_, exposing the Holy Sacrament.
_De theatris scenicis_, LXXII. Of Scenes for the Stage.
_Aliud vestigium theatri; LXXIII. Another Plan of a Theater,
ubi de modo inveniendi ejus with the Method of finding
punctum_, the Point of Sight therein.
_Sectio scenarum theatri_, LXXIV. The Section or Profile of
Scenes for Theaters.
_Elevatio scenarum coram LXXV. The Elevation of Scenes in
inspectarum; ubi docetur Front, and how the oblique
artificium, ut scenæ obliquæ Scenes are made to appear
appareant rectæ_, direct.
_Modus delineandi exemplar LXXVI. The Manner of delineating
scenarum_, the Designs of Scenes.
_Modus reticulandi & LXXVII. The Manner of making the
pingendi scenas theatri_, Net-work or Squares, and
painting the Scenes of
Theaters.
_De projectionibus LXXVIII. Of horizontal Projections.
horizontalibus_,
_Projectiones vestigii & LXXIX. The Plan and Elevation of
elevationis mutuli_, a Corbel in Perspective.
_Horizontalis projectio LXXX. The horizontal Projection
mutuli inumbrati_, of a shaded Corbel.
_Stylobatæ Corinthii LXXXI. _Corinthian_ Pedestals in
horizontaliter contracti_, an horizontal Perspective.
_Columna Corinthia LXXXII. A _Corinthian_ Column in
horizontaliter deformata_, horizontal Perspective.
_Capitella Corinthia LXXXIII. A _Corinthian_ Capital in
horizontaliter contracta_, horizontal Perspective.
_Coronix Corinthia_, LXXXIV. A _Corinthian_ Cornice.
_Coronix Corinthia LXXXV. A _Corinthian_ Cornice in
horizontaliter contracta_, horizontal Perspective.
_Horizontalis projectio LXXXVI. A Column in horizontal
columnæ_, Perspective.
_Præparatio necessaria ad LXXXVII. The Preparation necessary to
sequentem figuram, & ad the following Figure, and to
projectiones horizontales all other horizontal
in laquearibus vel Perspectives, whether on flat
testudinibus_, or vaulted Ceilings.
_Horizontalis projectio LXXXVIII. The horizontal Projection
balustiorum figuræ of the Balustrade of the
octogesimæseptimæ, cum Eighty-seventh Figure, view’d
brevi distantia_, at a small Distance.
_Horizontalis projectio LXXXIX. A horizontal Piece of
Architecturæ in laqueari Architecture in a square
quadrato_, Ceiling.
_Horizontalis projectio XC. A Cupola in horizontal
tholi_, Perspective.
_Tholus figuræ nonagesimæ, XCI. The Cupola of Fig. 90, with
cum luminibus & umbris_, its Lights and Shades.
_Tholus octangularis_, XCII. An Octangular Cupola.
_Vestigium templi XCIII. The Geometrical Plan of S.
Ludovisiani S. Ignatii _Ignatius_’s Church at _Rome_.
almæ urbis_,
_Orthographia templi XCIV. The Orthography of S.
Ludovisiani_, _Ignatius_’s Church.
_Aliæ præparationes ad XCV. Other Preparations to
figuras 98 & 99_, the 98th and 99th Figures.
_Aliæ præparationes ad XCVI. Other Preparations to
figuras 98 & 99_, the 98th and 99th Figures.
_Alia præparatio ad figuras XCVII. Another Preparation to the
98 & 99_, 98th and 99th Figures.
_Quadrans Architecturæ XCVIII. Fourth-part of the
horizontalis in fornice, Architectonical Design on the
cum luminibus & umbris_, Vault of S. _Ignatius_’s
Church, with its Lights and
Shades.
_Alter quadrans totius XCIX. Another Quarter of the
operis_, whole Design.
_Modus reticulationis C. The Method of drawing the
faciendæ in testudinibus_, Net-work on Vaults.
_FINIS._
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_D^{r}. Adam Oatley, of Pickford, ArchD. of Salop and Hereford._
_M^{r}. Austin Oldesworth, Stationer._
_M^{r}. Dan^{l}. Osburn B.D. Exeter Coll._
His Grace the DUKE of ORMOND.
_S^{r}. James Oxenden, K^{t}. Bart._
P
_Ralph Palmer, Esqꝫ._
_M^{r}. Barth. Peisley, Oxon._
_M^{r}. Elias Pen Writing-M^{r}._
_M^{r}. Tho. Pestel, Jeweller._
_Clement Petit, Esqꝫ._
_Madam Dorothea Petit._
_M^{r}. James Petiver, Pharm. Lond. FRS._
_M^{r}. Edmund Powel, Printer._
_M^{r}. John Paine._
R
The R^{t}. Hon^{ble} The LORD RABY.
The R^{t}. Hon^{ble} Richard EARL of RANELAGH.
_Edw. Richards, Esqꝫ, LB. Exeter Coll._
_Benj. Robinson Sec. to the Dutchess of Bucclough._
_D^{r}. Tancred Robinson._
_M^{r}. Rich^{d}. Rogerson, Carpenter._
_Chr. Rawlinson, Esqꝫ, of Cark-Hall, Lanc._
S
The Right Hon^{ble} James EARL of SALISBURY, Christ Church Oxon.
_M^{r}. John Savage_, A. M.
_Edw. Sayer, Esq^{r}, of Barkhamsteed._
_M^{r}. Will. Scrimshire._
The Right Hon^{ble} The EARL of SEAFIELD, Chanc. of Scotland.
D^{r}. Hans Sloane, S.R.S.
_M^{r}. Joseph Smart, Town-Clerks-Office._
_M^{r}. Ralph Snow, Writing-M^{r}._
_Sam. Stebbins, Esq^{r}._
_Rob. Steel, Bookbinder, in little Britain._
_M^{r}. James Stone, Gent._
_M^{r}. John Stuart, Stationer._
_M^{r}. Jacob Sturt, of Woodhouse, Sussex._
T
_M^{r}. John Tallman._
_M^{r}. John Taylor._
_M^{r}. Lewis Thomas, Oxon._
_M^{r}. John Thorpe_, A.M. F.R.S.
_M^{r}. Edw. Thwaites_, A.M. Queens Coll.
_M^{r}. John Tijou._
_Andr. Tooke_, A.M. _Geom. Prof. Gresham Col._
_Benj. Tooke, Bookseller._
_M^{r}. Will. Townsend, Oxon._
_Lewis Tremayne, Esq^{r}._
_Capt. Edw. Tuffnall, S^{t}. Marg^{t}. Westm^{r}._
_M^{r}. John Tuffnall, Joyner, S^{t}. Marg^{t}. Westm^{r}._
_Cholmondley Turner, Esq^{r}._
V
_J. Vanbrugh, Compt^{ll}. of Her MA^{ties} Works &c._
W
_Sam^{l}. Waters, Gent._
_M^{r}. Jo^{n}. Wilbraham, Brazen-Nose-Coll._
_M^{r}. John Wilkinson, of the Excheq^{r} Gent._
_M^{r}. John White._
_M^{r}. Sam^{l}. Whitfield._
_M^{r}. Tho. Whitmore, Painter._
_M^{r}. John Williams, Printer._
_M^{r}. Waldive Willington._
_S^{r}. Francis Windham K^{t}._
_M^{r}. Henry Wise, M^{r}. Gardener._
_Nicol Wolstenholme, Esq^{r}._
S^{r}. Chr. Wren K^{t}. Surv^{r}. Gen^{l}. of Her MA^{TIES} Works.
Transcriber’s Note
The following is a list of changes made to the original text to correct
suspected printing errors:
Under the heading:
FIGURA QUARTA ~6~, ~7~, => ~6~, ~7~, ~O~
FIGURA OCTAVA. ex lilinea => ex linea
The Ninth Figure. yon must => you must
Figura Trigesimaprima. qudratâ => quadratâ
Figura Trigesimaquinta. denineationem => delineationem
The Seventy-second FIGURE. hundred an twenty => hundred and twenty
FIGURA OCTOGESIMA. qnam => quam
FIGURA Nonagesima. centrum => Centrum
Figura Nonagesimaprima. spospondit => spopondit
FIGURA SECUNDA. longitudidinem => longitudinem
FIGURA QUINTA. superoiri => superiori
INDEX. Doric => Dorick (twice, lines XL and XLV)
SUBSCRIBERS. Gr. D. of Tosoany => Gr. D. of Toscany
Respondetur objectioni... punctum aliqualem => punctum aliquam
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