Chapter V: THAT the Author’s Advice of taking the Figures in Course, be strictly (3)

By casting your Eye on the Figure, you’ll readily apprehend the Manner of erecting the several Ranges of Frames. This Tabernacle last describ’d needs only two of them; the Frame next the Eye represents the outer Face, and the hinder Frame the inner Face thereof. I have here describ’d but the Half-Breadth of the said Frames, that you might have a Sight of the Poles and Braces which support them. The Line LS is the Line of the Plan, or Ground-line; the Line DG is that of the Horizon; and the Point of Distance, which falls without the Page CG prolong’d, is as far from the Point C, as the Point of Distance is from the Point of Sight in the upper Part of the Fifty-ninth Figure. The Horizontal DG is cut perpendicularly in C by the Line EF, which is the Section of the outer Face of the Tabernacle; and from the Point C begin the equal Divisions for the Net-work of the foremost Frame, as is shewn in the Sixty-second Figure. The Line IL, which is the Section of the inner Face of the Tabernacle, may at pleasure be set nearer or farther from the Line EF, to which it is parallel. By the Divisions of the Line EF (as M, N, O) Lines are drawn from the Point of Distance to the Perpendicular IL, for the Net-work of that Frame; for the Distance DC obliges the Parts of D to be painted larger, otherwise they will appear less than they really ought. And from hence you may discern, why the Arch, which in the foremost Frame would reach only to B, does in the hindmost rise up to H.

In the following Figure is shewn the Manner of delineating the inner Frame, from the Net-work of the outer Face; for the better understanding of which, make the Line HP in this Figure parallel to DC, and let the Line BC be divided into as many equal Parts, as the Line PC was.

FIGURA Sexagesimasecunda.

De reticulandis telariis, quæ repræsentent ædificia solida.

_Duo exemplaria tabernaculi quæ seorsim delineanda sunt, conjunctim habes in ~A~. Utrisque deservit eadem reticulatio, quam suis numeris insignivimus. Postquam ergo designaveris amplitudinem totius ædificii, cum proportione ad ipsam reticulabis pavimentum ~B~ aulæ cujuspiam quod capiat rem totam, ascriptis eisdem numeris quos habet exemplar: ejusque retis ope, ducentur in pavimento lineæ terminativæ totidem membrorum, quot futura sunt telaria exprimentia faciem externam tabernaculi. Ubi hæc parata fuerint, singula disponentur exactè suis locis in ipsomet pavimento; ac funiculis colore nigro imbutis, repetetur in telariis eadem reticulatio, additis ad libitum pluribus visualibus; quarum adjumento dum seorsim pinguntur telaria, duci queant rectæ tendentes ad punctum oculi seu perspectivæ. Alia quoque reticulatio super pavimento necessaria est pro internâ facie tabernaculi: ac duæ reticulationes pavimenti eam inter se proportionem habebunt, quam habent divisiones rectarum ~IL~, ~EF~, figuræ sexagesimæprimæ. Hujus retis ductu fient lineæ terminativæ telariorum cum reliquis, ut jam indicavimus._

_Juxta hanc methodum nequeunt duci lineæ terminativæ interioris faciei, nisi fiat in pavimento aliud rete deleto priori, quod esset valdè laboriosum. Postquam ergo ex vestigio figuræ quinquagesimænonæ eruta sint duo exemplaria, in exemplar faciei externæ transferatur recta ~PC~ figuræ sexagesimæprimæ, in exemplar faciei internæ transferatur recta ~BC~. Si autem recta ~PC~ divisa fuerit in quindecim partes æquales, dividetur ~BC~ in quindecim partes æquales, atque ope harum divisionum reticulare oportebit utrumque exemplar. Porrò licet quadrata in reti exemplaris faciei externæ sint majora quadratis exemplaris internæ faciei, nihilominus idem rete pavimenti deserviet pro ducendis lineis terminativis utriusque faciei. Quæ dicta sunt de duobus exemplaribus, valent de aliis quotcunque. Exempli gratiâ; si construere placeat quinque ordines telariorum, fient quinque exemplaria in papyro. Si in omnibus exemplaribus usurpetur eadem reticulatio, in pavimento facere oportet quinque diversas reticulationes. Si autem in exemplaribus fiant quinque diversæ reticulationes, in pavimento sufficit una reticulatio._

_Curandum est ut singula retis quadrata in telariis sint exacta, omnesque illorum anguli sint recti. Modus expeditissimus faciendi angulos rectos est hujusmodi. Posito uno crure circini in puncto ~F~ lineæ rectæ ~EF~, alioque crure posito ubilibet in ~O~, fiet circulus ~GFI~, & ex puncto ~G~ diameter ~GI~. Si recta ~HF~ transeat per puncta ~I~ & ~F~, est normalis ad ~EF~._

The Sixty-second FIGURE.

_Of making the Net-work on Frames, for representing the Architecture as solid._

You have jointly in A, the two Designs of a Tabernacle, which are to be drawn separately; the same Net-work serving for both, which is also mark’d with Numbers. When you have therefore resolv’d on the Size of your Work, on the Pavement of some Room capacious enough make a Net-work answerable, and affix thereto the Numbers, as in your Copy: By the Help of which, you may on the Pavement describe the Out-line of all those Members that are requisite to the outer Frame of the Tabernacle. This being done, let the Frame be laid exactly in its place on the said Pavement, and with a black Line strike thereon the same Net-work; adding as many visual Lines as you please, which will be of Use for drawing Lines to the Point of Sight, when you come to paint the Frames asunder. Another Net-work on the Pavement is also necessary for the inner Face of the Tabernacle, which should bear such Proportion to this, as the Divisions of the Line IL do to those of EF in the Sixty-first Figure; and by this means the Out-lines of the inner Frame, _&c._ may be drawn, as has been shewn already.

Thus the Out-line of the inner Face can’t be describ’d, without rubbing out the first Net-work, and making a second on the Pavement; which would be very troublesom. Wherefore, from the Plan of the Fifty-ninth Figure, take the two Designs, and transfer the Line PC of the Sixty-first Figure on the outer Face, and the Line BC on the inner Face. Then if PC were divided into fifteen equal Parts, BC shall be divided in the same manner, and by these Divisions make the Net-work on each Design. And although the Squares of the outer Face be larger than those of the inner one, the same Net-work may nevertheless serve for giving the Out-line of both. What has been said of these two Designs, may be understood of many. For Instance; if five Ranges of Frames were requir’d, five Designs must be made in Paper. If in all the Designs the same Net-work be us’d, then five several Net-works must be made on the Pavement; but if the Designs have five different, then one Net-work on the Pavement will suffice.

You must be very careful that all the Squares of the Net-work be exactly divided, and at right Angles. The ready way of making a right Angle is thus: Placing one Foot of the Compasses in the Point F of the Line EF, and the other at pleasure in O, describe the Circle GFI; and from the Point G draw the Diameter GI. The Line FH drawn by the Points FI, shall be perpendicular to FE.

FIGURA Sexagesimatertia.

Vestigia ædificii quadrati.

_Vestigium geometricum ~A~ hujus ædificii habet in ~B~ suam deformationem. Discrimen inter pilas ~C~ & ~D~ oritur ex eo, quòd in ~C~ posita sint vestigia stylobatarum, in ~D~ autem posita sint vestigia coronicum._

The Sixty-third FIGURE.

_The Plan of a square Design._

The Geometrical Plan of this Design A, is brought into Perspective in B. The Difference between the Parts C and D arises from hence, that the Plan of the Pedestals is plac’d in C, and that of the Cornice in D.

FIGURA Sexagesimaquarta.

Ædificium quadratum.

_Ex deformatione vestigii & elevationis, methodo consuetâ eruitur imago totius ædificii, quæ potest esse exemplar aræ maximæ alicujus Ecclesiæ. Hanc machinam, non sine communi approbatione, aliquoties adhibui, in apparatu quadraginta horarum; locum in medio vacuum occupantibus Angelis cum nubibus, additâ figurarum aliquot copiâ in parte inferiori. Modus faciendi in telariis remotioribus ab oculo partem tholi rotundi quam hic vides, deducitur ex iis quæ tradidimus in projectione circulorum._

The Sixty-fourth FIGURE.

_A square Design in Perspective._

From the Plan and Upright in Perspective, this finish’d Piece of the whole Work is delineated after the usual Manner, and may serve for the Design of a great Altar in a Church. I have sometimes, for the Solemnity of the _Forty Hours_, expos’d this painted on a Machine, with an universal Satisfaction; Angels with Clouds possessing the higher part of the Hemisphere within, and Groups of Figures the lower part. The Manner of designing on the inner Frame, that part of the said _Cupola_ which you here see, is deduc’d from what has been before said of putting Circles into Perspective.

FIGURA Sexagesimaquinta.

Vestigium ædificii rotundi opticè imminutum.

_Qui sedulam operam in circulis deformandis non posuerint, eosque minimo negotio ex usu describere nequiverint, frustra conabuntur projicere vestigia ædificiorum rotundorum. Ad vitandam confusionem, proderit in vestigio notare primùm lineas occultas membrorum præcipuorum; iisque translatis in elevationem, addere sensim reliquas. Hac industriâ ego ipse in hoc schemate usus sum. Quum autem experimento didicerim summam arduitatem harum descriptionum, aliam regulam adhibere jamdiu cœpi, quam, ut suprà diximus, in aliud Opus reservamus._

The Sixty-fifth FIGURE.

_The Plan of a Circular Work in Perspective._

They that have not diligently apply’d themselves to the putting Circles into Perspective, and, by a constant Practice, render’d the Work familiar to them, will in vain attempt that of the Plans of round Buildings. To prevent Confusion, you’ll do well, first to mark the occult Lines of the principal Members; and after those are transferr’d into the Upright, then proceed to the rest, as I myself did in this Figure. But having found by Experience, the great Difficulty of describing these round things, I have long since made use of another Method, which, as I said before, is reserv’d for another Volume.

FIGURA Sexagesimasexta.

Projectio ædificii rotundi.

_Mirifice oculis imponunt imagines rerum rotundarum, si omnibus resectis quæ ad eas non pertinent, exactè delineatæ ac depictæ fuerint. Hanc figuram ex vestigio eruere oportebit methodo consuetâ, eamque in Templo S. Ignatii Collegii Romani construxi pro feriâ V & VI Hebdomadæ sanctioris. Intra arcum, super altari, locus erat urnæ sepulcrali, cum Venerabili Sacramento. Sub altari visebatur simulacrum Christi Domini è Cruce depositi: in medio columnarum, imago Beatæ Virginis dolentis; super balaustiis Angeli lugentes, cum instrumentis cruciatuum Salvatoris._

The Sixty-sixth FIGURE.

_A Circular Design in Perspective._

The Appearance of round things, if well design’d, masterly painted, and the Frame cut away to the Out-line of the Work, do wonderfully deceive the Eye. This Figure is drawn from the Plan, as usual; and was put in execution by me, in the Church of S. _Ignatius_ of the _Roman_ College, for the _Thursday_ and _Friday_ of the Holy Week. Within the Arch, on the Altar, was plac’d a sepulchral Urn containing the Holy Sacrament. Beneath the Altar was laid a Figure of our Saviour Christ taken down from the Cross. In the midst of the Tambour, was a Picture of the Blessed Virgin in extreme Sorrow; and on the Ballustrade, Angels mourning, bearing the Instruments of the Passion.

FIGURA Sexagesimaseptima.

Vestigium geometricum, ac prima præparatio ad figuram septuagesimamprimam.

_Egregiam adeò speciem præsetulit, atque oculis adeò imposuit machina quam construxi anno 1685, pro supplicatione quadraginta horarum, in Templo Urbis Farnesiano, ut decreverim satisfacere Studiosis, publici juris faciendo non modò imaginem totius ædificii, sed etiam illius vestigia & elevationes: quæ omnia eâ diligentiâ delineavimus, veluti Opus ipsum non pennicillo colorandum, sed lapidibus extruendum fuisset. Spatia nigrantia soliditatem designant parietum & columnarum. Cæteræ lineæ sunt crepidines stylobatarum & coronicum. Initium delineationis fiet ab iis membris, ex quibus oriuntur lineæ occultæ positæ in ~A~, (quæ autem dicuntur de hac medietate, intelligi debent de aliâ) ne multitudo linearum confusionem pariat. In ~B~ lineæ curvæ occultæ sunt vestigium tholi qui complet summitatem ædificii. Vestigium ~C~ exhibet ambulacrum interius. Omisimus autem vestigium theatri, quia paginæ angustia illud non capit._

The Sixty-seventh FIGURE.

_The Geometrical Plan, and first Preparation to the Seventy-first Figure._

The Machine which I erected in the Year 1685, in the Church _Farneze_, or _Jesuits_ Church at _Rome_, for the Devotions of the _Forty Hours_; had so admirable an Effect, and so pleasantly deceiv’d the Eye, that I resolv’d to gratify the Studious, not only with a general View, but with the Plan and Elevation thereof; all which was perform’d with such Exactness, that the Work itself seem’d rather to consist of solid Stones, than to be wrought by the Painter’s Hand. The hatch’d Part denotes the Solidity of the Walls and Columns. The other shews the Breaks and Projectures of the Pedestals and Cornices. Lest many Lines should cause Confusion, begin with those Members, which produce the occult Lines on the Side A; understanding the same also of the other half. In B the occult curv’d Lines are the Plan of the _Cupola_ which crowns this Structure. The Plan C is that of the inner Vestibule, but that of the Theater is here omitted, through Want of Room in the Page.

FIGURA Sexagesimaoctava.

Elevatio geometrica vestigii præcedentis, & secunda præparatio ad figuram septuagesimamprimam.

_In hoc schemate habes elevationem ædificii sectam in longum, quam figurâ septuagesimâ opticè projiciemus: eisdemque membris constare videbis elevationem deformatam, quibus constat elevatio geometrica. Hinc disces ad excogitandas hujusmodi machinas, eandem Architecturæ scientiam in Pictore necessariam esse, quæ ad construenda solida ædificia exigitur in Architecto._

The Sixty-eighth FIGURE.

_The Geometrical Elevation of the foregoing Plan, and second Preparation to the Seventy-first Figure._

In this Figure you have the Elevation of the aforesaid Structure dissected lengthwise; the Perspective thereof is describ’d in the Seventieth Figure; and you may observe that both of them consist of the same Members: whence you may perceive, that for designing things of this kind, the Painter ought to have no less Skill in Architecture, than is requir’d for the Execution of solid Works.

FIGURA Sexagesimanona.

Deformatio vestigii figuræ sexagesimæseptimæ, & præparatio tertia ad figuram septuagesimamprimam.

_Artificium projectionis vestigii hujus, explicatum à nobis est figurâ quadragesimasecundâ. Nimirum, ut parallelæ sint invicem distantiores, lineam plani deorsum protraximus, ut ex intuitu figuræ statim cognosces._

The Sixty-ninth FIGURE.

_The Plan of the Sixty-seventh Figure in Perspective, and third Preparation to the Seventy-first Figure._

The Artifice us’d in projecting the Perspective of this Plan, has been already shewn in the Forty-second Figure; namely, that for giving the greater Distance between the Parallels, the Ground-line is drawn much lower than its true Place; as is manifest on Inspection of the Figure.

FIGURA SEPTUAGESIMA.

Deformatio elevationis figuræ sexagesimæoctavæ, & præparatio quarta ad figuram septuagesimamprimam.

_Quæ dicta sunt de projectione vestigii nostri ædificii, habent locum in elevatione. Nimirum, ut parallelæ invicem notabiliter distarent, usi sumus industriâ quam declaravimus figurâ quadragesimasecundâ._

The Seventieth FIGURE.

_The Perspective of the Elevation of the Sixty-eighth Figure, and the fourth Preparation to the Seventy-first Figure._

What has been said of the Perspective-Plan of this Structure, is also here practis’d in the Elevation; namely, that the Parallels might be sufficiently distinct, the Perpendiculars are drawn more remote from the Point of Sight, as was shewn in the Forty-second Figure.

FIGURA Septuagesimaprima.

Theatrum repræsentans Nuptias Canæ Galilææ, constructum Romæ, anno 1685. in expositione Ven. Sacramenti in Templo Farnesiano Societatis JESU.

_Ex antecedentibus præparationibus eruimus projectionem nobilis hujus Architecturæ, quæ oculos implebat tum ad lucem solis diurnam, tum præcipuè ad lumen candelarum; ex quibus multæ palam erant expositæ, aliæ omnino latebant, ut illuminarent sex diversos ordines telariorum quibus tota machina constabat, non computando in hoc numero telaria, quæ in medio arcûs maximi exprimebant nubes refertas Angelis adorantibus Venerabile Sacramentum. Nubes istas omisimus, ne absconderentur partes interiorum ædificiorum. In disponendis autem ordinibus telariorum, servatus est modus quem declaravi figurâ sexagesimaprima & sexagesimasecunda; ac præterea in eligenda eorum distantia curatum fuit, ut candelæ in parte postica telariorum collocatæ, illuminarent faciem telariorum interiorum. Porrò quot membra præcipua in duabus faciebus majoribus, totidem distincta telaria numerabantur, quorum proinde connexiones discerni vix poterant; eorumque aliquot paria ferreis hamulis copulata erant, ut explicari ac replicari possent, ad faciliorem tractationem diuturnioremque conservationem._

_Qui hucusque sequuti me fuerint, nihil dubito quin suum iter felicissimè sint prosequuturi; atque Opera his nostris majora melioraque inventuri._

The Seventy-first FIGURE.

_A Theater representing the Marriage of ~Cana~ in ~Galilee~, erected in the ~Jesuits~ Church at ~Rome~, in the Year ~1685~; for the Solemnity of exposing the Holy Sacrament._

From the foregoing Preparations, is drawn the Perspective of this noble Piece of Architecture; which struck the Eye when seen by Day-light, but was more especially surprizing by Candle-light; many of the Candles being expos’d to Sight, and others altogether hidden, to illuminate the six different Ranges of Scenes, of which the whole Work consisted, without reckoning that in the midst of the great Arch, representing Clouds fill’d with Angels adoring the blessed Sacrament. Those Clouds are here omitted, that the inner Parts of the Work might be the better seen. In disposing the several Ranges of Scenes, the same Method was observ’d, which was deliver’d in the Sixty-first and Sixty-second Figures; and great Care was also taken in their Distances, that the Candles plac’d on the Back of one of them might illuminate the Face of the other behind it. Moreover, each Scene consisted of as many parts, as there were principal Members in the two greater Façades; so that the Joints were scarcely discernible: and some Pairs of them being coupl’d with Hinges, folded and unfolded, for the more easy managing and preserving them.

I doubt not but those who have follow’d me thus far, will be encourag’d so to prosecute their Studies, as to be able to design even greater and more noble Works, than these of mine.

FIGURA Septuagesimasecunda.

De theatris scenicis.

_Theatris quæ jam delineavimus affinia sunt theatra scenica: in his tamen non adeò facilè reperitur punctum oculi seu perspectivæ. Præterea, quia ex obliquitate canalium intra quos moventur scenæ, oritur ut lineæ rectæ quæ videri debent parallelæ ad lineam plani, non debeant esse parallelæ sed obliquæ, harum delineatio difficultate non caret. Incommodum istud vitari posset adhibendo canales parallelos ad poscenium, ut alicubi fieri solet, præsertim in Germaniâ. Nihilominus usus Italicus affert hoc adjumentum, ut illi quibus incumbit suggerere actoribus, vel scenas movere, aliisque similibus præesse, facilius lateant & liberius fungantur munere suo._

_Ut brevem summam habeas eorum quæ deinde latius declaraturi sumus, hanc figuram contemplare. ~1~, ~2~, ~3~, ~4~, est vestigium aulæ quæ habet in longitudine centumviginti palmos Romanos, in latitudine sexaginta palmos; ut ostendit scala ~S~ triginta palmorum. Medietatem loci occupat theatrum, medietatem obtinent podia & loca spectatorum. ~O~ punctum in quo uniuntur lineæ visuales, ~D~ locus pro apparentiis rerum magis ac magis distantium. ~BC~ locus poscenii. ~HH~ sunt canales obliqui, quorum latitudo est dupla latitudinis scenarum. ~FG~ frons & facies theatri. ~AO~ ejus profunditas aut longitudo. ~E~ locus pro psaltibus, tibicinibus, & fistulatoribus. ~K~ spatium pro spectatoribus. ~I~ vestigium podiorum. ~L~ scalæ podiorum. ~N~ ipsorum elevatio. ~M~ declivitas tabulati, cum sectione & elevatione theatri, & scenis ex latere inspectis, quæ cum suis canalibus congruunt, ut demonstrant lineæ occultæ. ~OO~ linea normalis ad lineam horizontalem. ~P~ & ~Q~ elevatio scenarum coram inspectarum, quæ introrsum flectuntur; & in latitudine congruunt cum canalibus vestigii ~B~, in altitudine cum sectionibus elevationis ~M~; ut constat ex lineis occultis. In eâdem elevatione ~M~ pars altitudinis tribuenda est scenis, pars laquearibus ~R~, per quæ jungitur unumquodque par telariorum. ~VV~ lineæ ad explorandum an detur vacuum inter scenas & laquearia, vel inter scenas, vel inter laquearia. In quibusdam autem scenis, loco laquearium pinguntur nubes & aer._

The Seventy-second FIGURE.

_Of Scenes for the Stage._

Scenes for the Stage have very much Affinity with those lately describ’d, but the Point of Sight is not so easily found in these; and from the Obliquity of the Grooves in which the Scenes run, it comes to pass, that the right Lines which ought to appear parallel to the Line of the Plan, must not be drawn parallel thereto, but oblique; which is a Work of some Difficulty. This indeed may be avoided, by fixing the Grooves parallel to the Poscene; as is usual in some Places, especially in _Germany_. Nevertheless, the _Italian_ Manner has this Advantage; That those who are employ’d to prompt the Actors, and shift the Scenes, _&c._ are less expos’d to Sight, in the Performance of their Business.

In this Figure I have given you an Abridgment of those things, which shall hereafter be more enlarg’d on. The Numbers 1, 2, 3, 4, denote the Area of a Hall an hundred and twenty _Roman_ Palms in Length, and sixty in Breadth; as is manifest from the Scale of thirty Palms mark’d S. Half this Space is taken up by the Stage, the other half by the Spectators. O is the Point in which the visual Lines concenter. D is the Place of those things that are to appear most remote. BC is the Place of the Poscene. HH are the oblique Grooves, whose Lengths are double the Breadth of the Scenes. FG is the Front of the Stage. AO is its Depth or Length. E is the Place for the Musick. K is the Room for Spectators. I is the Plan of the Galleries. L the Stairs to the same. N is the Elevation of the Galleries. M shews the Declivity of the Floor, with the Section and Elevation of the Stage and Scenes view’d on the Side; answering their respective Grooves, as the occult Lines demonstrate. OO is a Line perpendicular to that of the Horizon. P and Q are the Elevation of the Scenes view’d in Front, turning inwards, in Breadth agreeing with the Length of the Grooves of the Plan B; and in Height answering that of the Sections of the Elevation M; as is evident from the occult Lines. In this Profile M, part of the Height belongs to the Scenes, and part to their Soffites, or Ceilings, R; where each Pair of these Frames are join’d. VV are the Lines by which is espy’d what Vacancy there is either between the Scenes and their Ceilings, between the Scenes themselves, or between their respective Ceilings; though in some Scenes the Place of these last is supply’d by painting therein the Air with Clouds, _&c._

FIGURA Septuagesimatertia.

Aliud vestigium theatri, ubi de modo inveniendi ejus punctum.

_Si pingendæ sint scenæ theatri alicujus antea constructi, delineare oportebit vestigium geometricum ex ipso erutum, (ad formam vestigii quod cernis in hac paginâ) ut inveniatur longitudo theatri, seu distantia quam ejus punctum habet à puncto ~A~: id autem nullo negotio fiet, accipiendo distantias ~BC~ inter primos canales, & ~DE~ inter ultimos, ac ducendo visuales ~MO, NO~: nam theatrum habebit longitudinem ~AO~, ac punctum perspectivæ in vestigio theatri erit ~O~. Præterea scire oportebit longitudinem & latitudinem canalium, eorumque numerum, distantias, & flexus; ac præcipuè curandum est, ut licet sint obliqui ad lineam ~MN~, sint invicem paralleli in unoquoque latere, ac singuli tangant lineas ~MO, NO~. Jam si rectæ ~AO~ fiat æqualis recta ~FA~, in ~F~ erit punctum distantiæ: adeoque si theatrum juxta methodum à nobis tradendam depictum fuerit, spectatori qui consistat in ~F~ apparebit veluti tabula picta juxta leges perspectivæ, posita in ~A~._

The Seventy-third FIGURE.

_Another Plan of a Theater, with the Method of finding the Point of Sight therein._

If it be requir’d to paint the Scenes of some Theater already built, the Geometrical Plan thereof must first be carefully drawn, (as you see, for Example, in this Plate) that the Length of the Theater may be found; or the Distance of its Point from that of A; which is easily done, by taking the Interval BC of the first Grooves, and DE of the latter; and drawing the Visuals MO, NO: for AO is the Length of the Theater, and the Point of Sight, or Perspective, therein, is O. Moreover the Length and Breadth of the Grooves must be known, as also their Numbers, Distance, and Obliquity; and especial Care must be taken, that though they be oblique to the Line MN, that on each Side they be Parallels between themselves, and that they all touch the Lines MO, NO. If you then make AO equal to FA, the Point of Distance will be F; and if the Theater be painted according to the Rules hereafter given, it will appear to him that views it from F, as a regular Piece of Perspective plac’d in A.

Figura Septuages. quarta.

Sectio Scenarum Theatri.

_Præter vestigium Theatri delineanda est sectio scenarum. Itaque si acceptis mensuris altitudinis, quam punctum ~A~ unde incipit tabulatum, ac punctum ~D~ poscenii, habent supra planum horizontale ~FV~, fiant ex perpendiculo ~NV~ tum recta ~ADO~ ex qua innotescit declivitas tabulati, tum recta ~NO~, quæ sit parallela ad ~FV~ & æqualis rectæ ~AO~ figuræ septuagesimætertiæ; punctum theatri in elevatione est ~O~; in poscenio verò punctum theatri est ~Q~. Si maxima scenarum altitudo sit ~EB~, recta ~OE~ dat altitudinem omnium reliquarum. Vera tamen altitudo cujuslibet scenæ est illa quam habet linea major, ex minori autem dignoscitur quantum obliquitas cujusque scenæ apparenter minuat altitudinem extremæ illius lineæ. Porro excessus quo linea major superat minorem tum in summo tum in imo, diligenter notandus est, hinc enim pendet intelligentia figuræ septuagesimæquintæ. Punctum ~M~ quod est remotum ab ~N~ quantum in figura septuagesimatertia punctum ~F~ est remotum ab ~A~, designat locum unde Theatrum spectari oporteat, ut ibidem notavimus._

_In construendo tabulato solet servari hæc regula, ut altitudo puncti ~O~ sit æqualis altitudini oculi, & elevatio ex ~A~ usque ad ~D~ sit nona circiter vel decima pars ipsius longitudinis ~AD~. Expediret autem ad scenas facilius movendas, pavimentum ~F~ esse profundius pavimento ~G~, ut erecto corpore sub tabulato ambulari possit._

Seventy-fourth Figure.

_The Section or Profile of Scenes for Theaters._

Besides the Plan of the Theater, the Section of the Scenes is also to be delineated, for finding the Point of the Theater in the Elevation. Wherefore, setting the Measures of the Heights which the Point A, where the Floor of the Stage begins, and the Point D of the Poscene, have above the Level of the Horizontal FV; from the Perpendicular NV draw the right Line ADO, which gives the Declivity of the Stage; then make NO parallel to FV, and equal to AO of the Seventy-third Figure: The Point of the Theater in Elevation is O; the Point of the same on the Poscene is Q. If EB be the greatest Height of the first Scene, the Line OE determines the Height of all the others. The longest of the two Lines gives the true Height of each Scene; and the shorter discovers how much of that Height the Sight loses on the Out-line, by the oblique Position of the Scenes. Moreover, the Excess of the longer Line above the shorter, as well at top as at bottom, is to be well observ’d; for on this depends the right Understanding of the Seventy-fifth Figure. The Point M, which is as far distant from N, as that of F is from A in the Seventy-third Figure, denotes the Place from whence the Stage ought to be view’d; as is there mention’d.

In laying the Floor of the Stage, this Rule is commonly observ’d, That the Height of the Point O be made equal to the Height of the Eye, and that the Rise of the Floor from A to D, be about a Ninth or Tenth Part of the Length AD. ’Tis also requisite, for the better shifting the Scenes, that the Pavement F be sunk lower than that of G, that a Man may walk upright under the Floor thereof.

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._