Part 4
Being to form the Plan E from the Plan B, you must, with occult Lines, make the Squares necessary for bringing four, or at least three of the Circles into Perspective; transferring into the Line D the Divisions of the Line C, and the rest as usual. Then, with other occult Lines, contract the Plans of the Leaves, and finish what’s farther requisite in the Plan E.
To make the Optick Elevation of the Length F, you must transfer into the Perpendicular H all the Divisions of the Elevation A; and complete the same, by Lines drawn toward the Point of Sight, till they meet their respective Perpendiculars; which proceeding from all parts of the Circles parallel to the Line D, intersect the Visual G; from whence they descend, Parallels to the Perpendicular H.
In working the clean Capital, you should begin with the lowest Circle I, which denotes the Compass of the Column. Then make the Leaves 1, 2, by taking their Breadths from the Plan E, with the Compasses, and keeping one Point of them upon the Line H; and their Heights from the Elevation F, keeping one Point on the Line D. The same must be done, as well by the Leaves 3, 3, 4, 4, as by the Leaf 5, and the others; and last of all, by the _Abacus_ also; the Sinking of the Horns whereof answers that of the visual Line L.
Figura Vigesimaquinta.
Optica descriptio capitelli Compositi.
_Ex iis quæ diximus de capitello Corinthio, didiceris modum faciendi capitellum Compositum. Velim autem tibi persuadeas, cum lectione harum regularum quæ sunt magistri inanimes, circini usum perpetuò conjungi oportere. Hic enim vivi magistri defectum unicè supplere potest._
The Twenty-fifth Figure.
_The ~Composite~ Capital in Perspective._
From what has been said of the _Corinthian_ Capital, may be learnt the Manner of putting the _Composite_ also into Perspective. I wish I could prevail with you, that to the Reading of the Rules, which in themselves are but lifeless Masters, you would constantly add a diligent Practice of the Figures by the Compasses; this being the only way to supply the Want of a living Master.
Figura Vigesimasexta.
Deformatio coronicis Etruscæ.
_Post capitella sequuntur coronices, quæ utpote quadratæ, minimam habent arduitatem. Inter coronices verò, nulla est Etruscâ simplicior ac facilior. Ex elevatione geometricâ, more solito, formatur vestigium geometricum; ex eoque opticè contracto eruitur similis elevatio longitudinis. Demùm ex elevatione & vestigio componitur coronix nitida. Memineris autem duas esse lineas, quæ hinc inde terminant latitudinem elevationis opticæ. Linea quæ altior est, dat altitudinem anterioris faciei coronicis, alia quæ est depressior, dat altitudinem faciei posterioris. Et ita erit in posterum._
Twenty-sixth Figure.
_The ~Tuscan~ Entablature in Perspective._
After Capitals we proceed to _Entablatures_, which because they are square, are less difficult than the former. And of all Entablatures, that of the _Tuscan_ Order is the most simple and easie to be put in execution. From the Geometrical Upright is drawn, as usual, the Geometrical Plan; from the Plan put in Perspective is describ’d the Optick Elevation of the Length; and from both the latter is wrought the clean Entablature requir’d. You may observe, here are two Lines that terminate the Breadth of the Perspective on one side and the other. The Line which proceeds from the higher Corner of the Visual, gives the Height of the most advanc’d Part; that from the lower determines the Height of the Back-part. And so for the future.
Figura Vigesimaseptima.
Optica delineatio coronicis Doricæ.
_In faciendâ coronice Doricâ, quæ majorem operam poscit, ob denticulos & triglyphos; communis regula servanda est. Si autem libeat coronicem nitidam describere in papyro separatâ ab ejus præparationibus, id profectò licet, tum in hoc, tum in quocunque alio schemate._
Twenty-seventh Figure.
_The ~Dorick~ Entablature in Perspective._
In making the _Dorick_ Entablature, which has something more Work in it than the former, on account of its Dentels and Triglyphs; the common Rule is to be observ’d. And if you would delineate the finish’d Entablature in a Paper distinct from that of its Preparations, you are at liberty so to do, either in this or any other Figure.
Figura Vigesimaoctava.
Præparatio figuræ sequentis.
_In figurâ vigesimaoctavâ, quæ continet vestigium & elevationes geometricas figuræ vigesimænonæ, oportuit latus ~C~ delineare seorsim à facie ~B~; quia facies exhibet latitudinem ædificii, latus verò exhibet longitudinem; atque una non est alteri æqualis. In vestigio geometrico solidus paries est ~A~: circuli referunt summum scapum columnarum. Cætera dant projecturas coronicis, cum suis mutulis._
Twenty-eighth Figure,
_Preparatory to the following Figure._
In this Twenty-eighth Figure, which contains the Plan and Geometrical Elevations of the Twenty-ninth Figure, it was requisite to delineate the Side C separately from the Front B; because the Front, which signifies the Breadth of the Building, and the Side, which shews its Length, are not equal one to the other. In the Geometrical Plan the solid Wall is A: the Circles express the Nakeds of the Pillars Shafts at top. The rest is the Projecture of the Cornice, with its Mutules.
Figura Vigesimanona.
Optica projectio ædificii Dorici.
_Habes in hac figura vigesimanona, opticam delineationem vestigii, & unius ex elevationibus figuræ vigesimæoctavæ; nimirum, elevationis longitudinis; ex quibus eruitur imago nitida ædificii Ordinis Dorici, cum summitatibus & capitellis trium columnarum; ejusque epistylium, zophorus, & corona._
BO _est linea horizontis; ~AC~ est linea plani; in quam, ex lineis ~D~ & ~C~ figuræ vigesimæoctavæ, transferuntur puncta latitudinis & longitudinis duarum elevationum; prolongando versus ~C~ ipsam lineam plani, ut oportet. Operaberis autem, ut diximus figurâ vigesimatertia; nimirum, in puncto ~V~ desinet latitudo vestigii, incipiet longitudo; & ex punctis latitudinis lineæ tendent ad punctum oculi; ex punctis longitudinis lineæ occultæ tendent ad punctum distantiæ. Ubi verò hæ lineæ secant visualem ~VO~, fient parallelæ ad lineam ~AC~, cum cæteris quæ necessaria sunt ad complendam delineationem opticam vestigii._
_Elevatio ~C~ figuræ vigesimæoctavæ opticè contrahetur more consueto, translatis in lineam ~AB~ divisionibus lineæ ~E~ vel ~F~, ex quibus fient visuales ad punctum oculi; ac demissis ex linea visuali ~AO~ perpendicularibus ad lineam ~AC~, ita ut lineæ parallelæ ad lineam plani ~AC~ continuentur cum aliis lineis parallelis ad lineam ~AB~._
_Hic quoque locum habet observatio illa, cujus meminimus figura vigesimasexta, de lineis quæ deorsum excurrunt, & hinc inde terminant membra elevationis opticæ. Ex iis autem desumuntur projecturæ omnes coronicis & capitellorum._
Twenty-ninth Figure.
_A Projection of the ~Dorick~ Order in Perspective._
In this Twenty-ninth Figure, you have in Perspective the Plan, and one of the Uprights of the Twenty-eighth Figure; namely, that of the Length; from whence is drawn this finish’d Piece of the _Dorick_ Order, which has the upper Part and Caps of three Pillars, with their Architrave, Freeze, and Cornice.
BO is the Horizontal-line; AC that of the Plan; into which, from the Lines D and C of the Twenty-eighth Figure, are transferr’d the Points of Breadth and Length of the two Elevations; first prolonging the Line itself, as much as is needful, through C. The Work is then perform’d, as was shewn in the Twenty-third Figure; namely, the Divisions of the Breadth of the Plan end in the Point V, at which those of Length begin. From the first, Lines are drawn to the Point of Sight; and from the latter, occult Lines are directed to the Point of Distance: And where these cut the Visual VO, Lines are drawn parallel to AC; with those that are farther necessary for completing the Plan in Perspective.
The Elevation C of the Twenty-eighth Figure is put in Perspective, as usual, by transferring the Divisions of the Line E, or F, into that of AB in this Plate; from whence drawing Visuals to the Point of Sight, they are intersected by Perpendiculars let fall from those Divisions of AO made by the Parallels to the Ground-line AC, and again continu’d parallel to the Perpendicular AB.
The Observation, mention’d in the Twenty-sixth Figure, is also pertinent in this place; That the Lines, which, in the Perspective-Elevation, tend downward, give the Advance and Recess of the several Members of the Work; and from them are taken all the Projectures of the Entablature and Capitals.
FIGURA Trigesima.
Optica projectio ædificii Ionici; ubi de modo jungendi fictum cum vero.
_Si tibi Pictor quum sis, occasione apparatûs quadraginta horarum, vel sepulcri Domini, mutare ad tempus libeat formam architecturæ alicujus Ecclesiæ jungendo fictum cum vero, ut mihi sæpius contigit Mediolani ac Romæ, cum ingenti spectatorum delectatione & admiratione; paucis ostendam tibi modum quem servare debeas in operando._
_Sectio coronicis veræ, quæ, ut suppono, videri debet continua esse cum coronice picta in telario, est ~A~; elevatio geometrica coronicis, & reliquorum quæ delineanda sunt, est ~B~; vestigium geometricum est ~C~. Porrò, tum vestigium tum elevatio longitudinis opticè contrahentur more consueto, ut vides in ~C~ & ~B~: ex iisque formabitur in telario coronix nitida cum columna & anta; ipsumque telarium depictum, normaliter coagmentandum erit veræ coronici._
_Ut fiat ea pars longitudinis, quæ coronicem pictam continuare videatur cum vera, & erui non potest ex elevatione deformata; oportet sectionem ~A~ transferre in ~D~, ducendo visuales ex punctis terminativis membrorum sectionis ~D~, usque dum occurrant lineis latitudinis eorundem membrorum. Quod si colores in telarium scitè inducantur, angulus in ~E~, quamvis merè depictus, videbitur verus; & ex adverso, anguli quos telarium ipsum depictum facit cum diversis adeò crepidinibus coronicis veræ, nusquam apparebunt, præterquàm in quadra simæ dumtaxat; & unio architecturæ veræ cum ficta dignosci non poterit._
The Thirtieth Figure.
_An ~Ionick~ Work in Perspective; with the Manner of reconciling the fictitious to the solid Architecture._
If, being a Painter, you were requir’d, against the Solemnity of the Holy-Week, to alter for a while the Architecture of some Altar-piece, by joining Painting to the real Work; as I have often done, both at _Rome_ and _Milan_, to the great Satisfaction and Surprize of the Beholders: I shall briefly shew the Method to be observ’d in performing the same.
The Dissection of the solid Cornice, which I here suppose shall appear continu’d in that painted on the Canvass, is A; the Geometrical Elevation of the Cornice, and other Parts to be drawn, is B; the Geometrical Plan is C. The Plan and Elevation of the Length are put in Perspective after the usual manner, in C and B; from those the finish’d Cornice, with the Pillar and Pilaster, are delineated on the Canvass; and the Picture is then conjoin’d, at right Angles, to the true Cornice.
For adjusting the Members so, that the painted Cornice may seem to be the real one continu’d, (which can’t be done by the Perspective Upright) you must transfer the Section A to D; and from the terminating Points of the several Members thereof, draw visual Lines, till they meet those of their respective Members in the Perspective. And if the Colours are laid by a skilful Hand, the Angle at E, tho’ painted only, will appear as real; and on the contrary, the Angles which the Members of the painted Cornice make with the different Projectures of those of the true, will never be discern’d, unless in the very uppermost Fillet; but the Conjunction of the real with the painted Architecture, will be altogether imperceptible.
Figura Trigesimaprima.
Optica projectio coronicis Corinthiæ, cum capitello & summitate columnæ.
_In hoc schemate linea plani est ~CIE~, horizontis est ~DFO~; punctum oculi est ~O~, distantiæ est ~D~. Elevatio geometrica capitelli Corinthii cum sua coronice est ~A~, quorum divisiones cernuntur in perpendiculari ~CD~. Vestigium geometricum ~B~ habet longitudinem æqualem latitudini: opticè autem contrahitur methodo consueta. Nimirum, translatis divisionibus latitudinis & longitudinis in lineam plani ~CIE~; ex punctis latitudinis fiunt visuales ad punctum oculi; ex punctis verò longitudinis fiunt occultæ ad punctum distantiæ: hoc modo habes quicquid necessarium est ad contractionem opticam vestigii. Nam lineæ longitudinum sunt partes visualium, ut patet in ~GN~, ~HL~: lineæ latitudinum, parallelæ ad lineam plani fiunt ex punctis in quibus lineæ tendentes ad punctum distantiæ secant visualem ~HO~, ut vides in ~NL~. Porro, si tantundem prolongaretur horizontalis ~DO~, ita ut haberet duo puncta distantiæ remota æqualiter ab ~O~, medietas diagonalium, quæ sunt in quadrato majori ~GNLH~ opticè deformato, & in quadratis ejus minoribus, tendent ad unum punctum distantiæ; altera medietas ad aliud punctum distantiæ._
_Elevatio longitudinis opticè contrahitur ductis parallelis ad ~CE~, quæ ubi pervenerint ad visualem ~IO~, continuentur cum aliis parallelis ad ~IK~. Præterea, translatis in lineam ~IK~ divisionibus lineæ perpendicularis ~CD~, ex punctis divisionum fiunt visuales ad punctum oculi, ac ducuntur singula membra ipsius elevationis, cujus latitudines sunt partes visualium, altitudines verò sunt partes linearum parallelarum ad ~IK~. Demùm ex vestigio & ex elevatione longitudinis, formatur coronix nitida cum capitello. Ut autem faciliùs delineentur mutuli, primùm fient quadratâ formâ, ut in ~M~; deinde congruus flexus in singulos inducetur._
The Thirty-first Figure.
_The Optick Projection of a ~Corinthian~ Cornice, with the Capital and PART of the Column._
In this Figure the Line of the Plan is CIE, that of the Horizon is DFO; the Point of Sight is O, the Point of Distance D; the Geometrical Elevation of the _Corinthian_ Capital, with its Entablature, is A; whose Divisions are seen in the Perpendicular CD. The Length and Breadth of the Geometrical Plan B are equal, and the Plan is put into Perspective after the usual Method; to wit, by transferring the Divisions of Breadth and Length into the Line CIE; from the Points of Breadth drawing Visuals to the Point of Sight; and from those of Length occult Lines to the Point of Distance: by which Intersections you have all that’s necessary for putting the Plan into Perspective. For the Lines of Length are Parts of visual Rays, as is manifest by GN, HL; and the Lines of Breadth are made Parallels to the Ground-line, from the Intersections before-mention’d, as is seen in NL. Moreover, if the Horizontal-line DO were so prolong’d, as to receive another Point of Distance equidistant from O; half the diagonal Lines of the great Square GNLH, and of the lesser Squares contain’d therein, would tend to one Point of Distance, and the other half to the other.
The Elevation of the Length is put in Perspective, by continuing the Parallels to CE, till they cut the Visual IO; and from thence dropping Lines parallel to IK: Then transferring into IK the Divisions of the Perpendicular CD, from them make visual Lines to the Point of Sight, and draw the several Members of the Upright; whose Breadths are Parts of Visuals, and their Heights Parts of Perpendiculars, or Lines parallel to IK. Lastly, from the Plan and Elevation of the Length, you delineate the finish’d Cornice and Capital: But that you may more easily draw the Modillions, first make them in a square Form, as in M; and that will very much assist you to give the Scroll of each a more agreeable Turn.
Figura Trigesimasecunda.
Delineatio geometrica coronicis, Ordinis Compositi.
_Ut hoc schema grandius ac distinctius esset, ejus medietatem dumtaxat suscepi delineandam. ~PN~ est vestigium geometricum. ~M~ est solidus paries. ~OO~ spatia columnarum. In ~H~ sunt crepidines coronicis. Elevatio geometrica latitudinis ædificii constat epistylio ~T~, zophoro ~L~, & coronâ ~V~, supra quam eminet fastigium ~S~._
_Jam ut inveniatur centrum arcuum, distantiæ ~AV~ fiat æqualis distantia ~AC~. Positaque una cuspide circini in ~C~, alia extendatur usque ad ~V~: ita fient arcus, quorum ultimus est ~BD~, omnesque sunt concentrici. Elevatio ~F~ ostendit longitudinem ædificii ex parte ~GI~; elevatio ~E~ ostendit longitudinem ipsius ex parte ~DR~._
Thirty-second Figure.
_The Geometrical Design of a Cornice, of the ~Composite~ Order._
That this Figure might be larger and more distinct, I have here describ’d only the Half of it. PN is the Geometrical Plan. M is the solid Wall. OO are the Places of the Columns. H shews the Projectures of the Cornice. The Geometrical Elevation of the Breadth of the Frontispiece, consists of the Architrave T, the Freeze L, and the Cornice V, over which is rais’d the Pedament S.
For finding the Center of the arch’d Lines of the Pedament, make the Distance AC equal to that of AV; and placing one Point of the Compasses in C, extend the other to V, and describe the Arch. The other Arches, of which BD is the utmost, have all the same Center. The Elevation F shews the Length of the Work on the Side GI. The Upright E shews the Length of the same on the Front DR.
Figura Trigesimatertia.
Deformatio coronicis Compositæ.
_Figura hæc trigesimatertia minus ardua tibi videbitur, si ex ea delineandam primùm suscipias medietatem quæ respondet vestigio ~PN~ & elevationi ~BR~ figuræ trigesimæsecundæ; rejecto in ultimum fastigio, postquàm cætera compleveris. Linea ~BV~ est horizontalis. Punctum oculi est ~V~, punctum distantiæ remotum est ab ~V~ spatio ~BV~, additis modulis quatuordecim cum dimidio. Linea plani est ~AR~, in quam ex ~Q~ versus ~A~ transfertur latitudo ~P~; ex ~Q~ versus ~R~ transfertur longitudo ~N~, cum omnibus earum divisionibus; ut ex punctis latitudinis fiant visuales ad punctum oculi; & ex punctis longitudinis fiant occultæ ad punctum distantiæ. Ex his habes quicquid necessarium est ad projectionem opticam vestigii, ut ostendimus figurâ trigesimaprimâ. Eademque methodo, quam ibi servavimus, contrahes elevationem ~P~ longitudinis coronicis: ac tum ex illa, tum ex vestigio, eruetur coronix nitida more consueto._
_Ut delineetur fastigium, transferendæ sunt in lineam ~AB~ divisiones ipsius ex elevatione ~F~ figuræ trigesimæsecundæ, ac ducendæ visuales ad punctum oculi, additis lineis terminativis uniuscujusque membri, quæ accipientur ex vestigio ~Q~ opticè deformato. Centrum ~O~ arcuum fastigii nitidi, remotum est à summitate coronicis, medietate distantiæ, quam habent ungues quadræ cui fastigium ipsum incumbit. Ac proinde, si accipias ex elevatione ~P~ diversas altitudines membrorum fastigii; latitudines verò accipias ex vestigio ~Q~; opus tuum feliciter absolves._
The Thirty-third Figure.
_A ~Composite~ Cornice in Perspective._
This Thirty-third Figure will be found the less difficult, if you first attempt that Half which answers to PN in the Plan, and BR in the Upright of the Thirty-second Figure; leaving the Pedament, till all the rest be finish’d. The Line BV is the Horizontal. V is the Point of Sight; the Point of Distance is fourteen Modules and a half without the Point B, more than the Interval BV. The Line of the Plan is AR, in which from Q toward A you have the Divisions of Breadth of the foregoing Plan P; and from Q to R those of the Length thereof N: From the former, Visuals are drawn to the Point of Sight; and from the latter, occult Lines to the Point of Distance. And from these you have all that’s necessary for putting the Plan in Perspective; as was shewn in the Thirty-first Figure. By the Method there observ’d, you may also describe the Perspective-Elevation of the Length P; and from this, and the Plan, delineate the finish’d Cornice after the usual Manner.
For making the Pedament, the Divisions of the Elevation F in the Thirty-second Figure, must be transferr’d into the Line AB, and Visuals drawn from them to the Point of Sight; giving to each Member its proper Out-line and Contour, as may be taken from the Perspective-Plan Q. The Center O of the Arches in the finish’d Pedament, is plac’d below the upper Member of the Cornice, as much as half the Extent of the upper Fillet from whence the Pedament springs. And by taking the several Heights of the Members thereof, from the Elevation P; and the Breadths from the Plan Q; you will successfully finish and complete your Work.
Figura Trigesimaquarta.
Præparatio ad figuram trigesimamquintam.
_Si placuerit conferre figuram trigesimamtertiam cum præsenti figura trigesimaquarta, dignosces vestigium & elevationem coronicis Compositæ alio modo hic deformari, mutando scilicet longitudinem in latitudinem, & latitudinem in longitudinem. Propterea hæc figura tantum spatii occupat, ut eam seorsim à coronice nitida delineare oportuerit._
_Divisiones latitudinis in vestigio incipiunt ex ~V~ versus ~R~, & sunt eædem cum divisionibus rectæ ~IG~ figuræ trigesimæsecundæ. Divisiones longitudinis incipiunt ex ~V~ versus ~S~, & sunt eædem cum divisionibus rectæ ~IP~ duplicatis. Ex divisionibus latitudinis fiunt visuales ad punctum oculi; ex divisionibus longitudinis fiunt rectæ ad punctum distantiæ; cum reliquis quæ necessaria sunt ad complendum vestigium ~AVDC~._
_Elevatio longitudinis coronicis & fastigii, opticè contrahitur per lineas parallelas ad lineam plani ~AS~; quæ ubi pervenerint ad visualem ~AC~, continuentur cum aliis parallelis ad perpendiculum ~P~, ut diximus figurâ trigesimaprimâ. In idem perpendiculum ~P~ transferuntur ex figurâ trigesimasecundâ divisiones rectæ ~DR~; & insuper altitudines, quas puncta ~KXZ~ habent supra rectam ~VA~; fientque visuales ad punctum oculi: sectiones autem visualium cum parallelis ad perpendiculum ~P~, dabunt sex puncta simæ fastigii, respondentia punctis ~KXZ~ duplicatis, figuræ trigesimæsecundæ; earumque ductu formandus est supremus arcus. Eodem artificio fient reliqui omnes._
_Faciliùs delineabitur coronix, cujus maximam partem occupant lineæ visuales ad punctum oculi: porrò, membra omnia, exceptâ simâ, communia sunt coronæ & fastigio. Adeoque puncta similia in lineis terminativis membrorum singulorum, ex quibus desumuntur crepidines & ungues figuræ nitidæ, sunt parallela ad perpendiculum ~P~._
The Thirty-fourth Figure,
_Preparatory to the Thirty-fifth._
If you please to compare the Thirty-third Figure with this Thirty-fourth Figure, you will perceive the Plan and Elevation of this _Composite_ Cornice to be delineated differently from that; to wit, by making the Length of that the Breadth of this, and the Breadth of that the Length of this: On which account, this Figure takes up so much Room, that there was a necessity of drawing the finish’d Cornice on a separate Paper.
The Divisions of Breadth in the Plan begin from V toward R; and are the same with those of the Line IG in the Thirty-second Figure. The Divisions of Length are set from V toward S; and are the same with those of the Line IP in the Thirty-second Figure; which being the Half, is here doubl’d. From the Divisions of Breadth, Lines are drawn to the Point of Sight; and from those of the Length, Lines to the Point of Distance; with the farther Requisites for completing the Plan AVDC in Perspective.