Part 8
_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._