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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.