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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.