Chapter V: THAT the Author’s Advice of taking the Figures in Course, be strictly (2)

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.

The Upright of the Length of the Cornice and Pedament, is made by producing Parallels to the Ground-line AS; till they intersect the Visual AC; and thence continuing Lines parallel to the Perpendicular P, as was directed in the Thirty-first Figure. Into the same Perpendicular P are transferr’d the Divisions of the Line DR in the Thirty-second Figure; and also the Heights which the Points KXZ have above VA in the same Figure. From all which, Visuals are drawn to the Point of Sight; which being intersected by the Perpendiculars, give six Points on the _Cima_ of the Pedament, which answer to the said Points KXZ of the Thirty-second Figure, doubl’d: By these the outward Arch is form’d. And by the same Rule, you find Points for all the others.

You will more easily draw the Cornice, the greatest Part of it consisting of visual Lines to the Point of Sight: Moreover, all the Members, except the upper _Cima_, are common both to the Cornice of the Entablature, and to the Pedament; so that the corresponding Points, in the Out-lines of their several Members, from whence the Breaks and Contours of the finish’d Piece are taken, are found in the same Parallels to the Perpendicular P.

Figura Trigesimaquinta.

Deformatio coronicis Compositæ, ad latus inspectæ.

_Artificium nitidæ coronicis, ex vestigio & elevatione figuræ trigesimæquartæ eruendæ, non differt ab eo quod sæpè traditum est. Itaque supposito, quòd linea plani & horizontis, ac puncta oculi ac distantiæ, habeant in hoc schemate situm omnino eundem, quem habent in præcedenti; ope duorum circinorum, invenientur distantiæ, quas anguli necessarii ad integram delineationem coronicis, habent à linea plani, & à linea normali ad ipsam lineam plani. Nam ducendo lineas visuales, aliasque lineas parallelas ad ipsum perpendiculum, cum terminis & flexibus qui conveniunt singulis membris, complebitur delineatio._

_In fastigio visuales sunt penitus occultæ: puncta autem similia ~H~ & ~L~, ex quibus fastigium incipit introrsum flecti, incidunt in unam eandemque visualem. Idipsum dico de aliis punctis similibus. Nam lineæ rectæ omnes, quæ in figura trigesimatertia sunt parallelæ ad lineam plani, in figuris trigesimaquarta & trigesimaquinta sunt partes linearum visualium._

The Thirty-fifth Figure.

_A Side-View of the ~Composite~ Cornice, in Perspective._

The Manner of drawing this finish’d Cornice, from the preceding Plan and Elevation, is the same with that so often shewn you. Admitting therefore, that the Lines of the Plan and Horizon, and the Points of Sight and Distance, have the very same Position in this, that they had in the preceding Scheme; all the Angles necessary for delineating the entire Cornice, are readily found by the help of two pair of Compasses; taking their Distances one way from the Ground-line; and the other way from a Line perpendicular to the same: Then drawing the visual and perpendicular Lines, and keeping the Place and Contour of the several Mouldings, you complete your Design.

In the Pedament the visual Lines are wholly occult; and the Points H and L, where the Pedament begins to break back, being of like Height, are found in one and the same Visual: And the same may be said of all Points that are of equal Height from the Plan; for all the right Lines, which in the Thirty-third Figure are Parallels to the Ground-line, in the Thirty-fourth and Thirty-fifth Figures are Parts of the visual Lines.

FIGURA Trigesimasexta.

Præparatio ad figuram trigesimamseptimam.

_In vestigio geometrico ~C~, & in ejus elevatione ~AB~, præcipuas tantùm lineas adnotavi, ne figuram confunderem, & ut studiosorum industriæ aliquid relinquerem. Linea plani ~EG~ habet divisiones latitudinis ~P~, & longitudinis ~Q~, vestigii geometrici ~C~. Ex punctis latitudinis ducentur more solito visuales ad ~O~ punctum oculi; ex punctis longitudinis fient occultæ ad punctum distantiæ, quod extra lineam ~AB~ protenditur modulis quatuordecim: & ubi occultæ ex divisionibus longitudinis secant visualem ~FO~ fiunt parallelæ ad lineam plani ~EF~, adhibitis sectionibus talium parallelarum cum visualibus, ad complendam deformationem vestigii._

_Eædem lineæ quæ in vestigio deformato sunt parallelæ ad ~EF~, prolongantur usque ad visualem ~EO~, & continuantur cum aliis parallelis ad perpendiculum ~DE~. Fiunt quoque visuales ad punctum oculi ex divisionibus elevationis ~AB~ translatis in perpendiculum ~DE~; adhibitis sectionibus talium parallelarum cum visualibus, ad complendam deformationem longitudinis elevationis._

The Six and thirtieth Figure,

_Preparatory to the Thirty-seventh._

In the Geometrical Plan C, and in the Elevation thereof AB, I have only mark’d the principal Lines, as well for avoiding Confusion in the Figure, as that something might be left to the Industry of the Studious. The Line of the Plan EG has the Divisions of Breadth P, and of Length Q, of the Geometrical Plan C. From the Points of Breadth are drawn, as usual, Visuals to the Point of Sight O; From the Points of Length occult Lines are produc’d to the Point of Distance, which lies fourteen Modules without the Line AB: And where the occult Lines from the Divisions of Length cut the Visual FO, Parallels are made to the Ground-Line EF; and from the Intersections of those Parallels with the Visuals, you complete the Delineation of the Plan in Perspective.

The Lines which in the Plan are parallel to EF, being prolong’d to the Visual EO, are then continu’d parallel to the Perpendicular DE. And from the Divisions of AB, produc’d to DE, visual Lines are drawn to the Point of Sight; which intersecting the Perpendiculars aforesaid, you from thence find the Length of the Elevation in Perspective.

FIGURA Trigesimaseptima.

Deformatio columnæ Etruscæ.

_Ex præparatione quam exhibuimus figurâ trigesimasextâ, eruitur columna hæc nitida Ordinis Etrusci, opticè imminuta per latitudines & altitudines partium singularum; quæ accipiuntur ope duorum circinorum, ut sæpiùs dictum est._

The Thirty-seventh Figure.

_A ~Tuscan~ Column in Perspective._

From the Preparation exhibited in the Thirty-sixth Figure, is drawn this complete Piece of the _Tuscan_ Order, brought into Perspective by means of the Breadths and Heights of the several Parts, exactly taken off with the Compasses, as has been often said.

FIGURA Trigesimaoctava.

Præparatio ad figuram trigesimamnonam.

_Hæc figura est simillima figuræ trigesimæsextæ. In vestigio ~P~ limes prominentiæ coronicis est ~R~; coronæ verò in stylobatâ est ~T~. soliditas stylobatæ est ~V~. ambitus columnæ in imo est ~X~, in summo ~Z~._

The Thirty-eighth Figure.

_Preparatory to the Thirty-ninth._

This Figure is very much the same with the Thirty-sixth. In the Plan P, the utmost Projecture of the Cornice is R; that of the Cap of the Pedestal is T; the Trunk of the Pedestal is V; the naked Shaft of the Column at bottom is X, at top is Z.

FIGURA Trigesimanona.

Deformatio ædificii Dorici.

_Habes hoc loco ædificium Doricum, addito statuæ unius ornamento. Velim autem, ut si figuram aliquam ex his desumptam, delineandam assumas, aliquid mutes saltem in loco punctorum oculi aut distantiæ. Hoc modo majores in hac arte progressus facies; & si alicubi cælator aberraverit, ex lapsu illius nullum senties detrimentum._

The Nine and thirtieth Figure.

_A Piece of ~Dorick~ Architecture in Perspective._

In this Plate you have a _Dorick_ Composition, with the additional Ornament of a single Statue; but I would advise, when you undertake to work after any of these Designs, you would at least place the Points of Sight and Distance somewhat differing from those here given; which Practice will both greatly further your Progress in this Art, and prevent any Inconvenience, that may arise from a Mistake of the Engraver.

FIGURA QUADRAGESIMA.

Vestigium geometricum ædificii Ordinis Dorici.

_Vt studiosorum, qui sedulò se exercuerint in praxibus hucusque traditis, & ad majora inhient, utilitati serviam, delineandam suscepi medietatem arcûs cum tribus columnis, ac totidem statuarum loculamentis. Ad vitandam autem confusionem, ea dumtaxat membra in vestigio adumbrantur, quæ recensuimus figurâ trigesimaoctavâ, & ostendunt characteres ~A~, ~B~, ~C~, ~D~, ~E~._

The FORTIETH FIGURE.

_The Geometrical Plan of a Design, of the ~Dorick~ Order._

For the Benefit of the Studious, who, having reduc’d to Practice the Rules hitherto laid down, aim at yet greater Things; I have here undertaken to delineate half an Arch adorn’d with three Columns, and as many Niches for Statues. But to avoid Confusion, I have given full Lines to those Members only, which were mention’d in the Thirty-eighth Figure, and which are here denoted by the Characters A, B, C, D, E.

FIGURA Quadragesimaprima.

Elevatio geometrica ædificii Dorici.

_Ex vestigio geometrico eruitur hæc elevatio geometrica longitudinis ædificii nostri. Et iccircò figura ista quadragesimaprima, cujus mensuræ omnes desumptæ sunt ex Barozzio, congruit longitudini figuræ quadragesimæ._

The Forty-first FIGURE.

_The Geometrical Elevation of the foregoing Design._

This Upright is drawn from the foregoing Geometrical Plan; and therefore all the Parts of this Design, whose Measures are taken from _Vignola_, exactly answer those of the Fortieth Figure.

FIGURA Quadragesimasecunda.

Modus vitandi confusionem, in contractione vestigiorum, & elevationum.

_Contractiones vestigii figuræ quadragesimæ, & elevationis figuræ quadragesimæprimæ, ob nimiam obliquitatem quam habent, valde confusæ sunt. Medebimur tamen incommodo isti, uti fecimus figuris decimâ & undecimâ. Et ostendit chartula, exhibens in parvo tum figuram hanc quadragesimamsecundam, tum quatuor sequentes._

The Forty-second FIGURE.

_The Manner of avoiding Confusion, in reducing Plans and Elevations into Perspective._

The Reducing into Perspective the Plan of the Fortieth Figure, and the Upright of the Forty-first Figure, would become very confus’d, through the great Obliquity of the Rays: We have therefore remedy’d the Inconveniences of both, by the Methods explain’d in the Tenth and Eleventh Figures. And this Plate contains in little, what is more at large describ’d in Parts, as well in this, as the four subsequent Figures.

FIGURA Quadragesimatertia.

Contractio vestigii figuræ quadragesimæ.

_Linea plani multò remotior est à lineâ horizontali in hoc schemate, quàm in præcedenti. Ideo istud vestigium vacat omni confusione. Cætera patent ex iis quae sæpiùs dicta sunt, & ex figuræ hujus inspectione. Oportet autem, rectas parallelas ad lineam plani, prolongari usque ad visualem ~TO~, (quæ cadit extra paginam) ut adminiculo parallelarum, fiat elevatio longitudinis nostri ædificii, de quâ dicemus figurâ quadragesimaquartâ._

The Forty-third FIGURE.

_The Plan of the Fortieth Figure in Perspective._

By placing the Ground-line in this, much more remote from the Horizontal, than it is in the foregoing Figure, all Confusion is here avoided. The rest is evident from what has been often said on this Head, and a bare Inspection of the Figure. Parallels to the Ground-line must nevertheless be continu’d to the Visual TO, which falls without this Page; that from them may be rais’d the Elevation of the Length of this Design, which we shall handle in the next Figure.

FIGURA Quadragesimaquarta.

Contractio elevationis figuræ quadragesimæprimæ.

_Rectæ parallelæ ad lineam plani figuræ quadragesimætertiæ, ubi pervenerint ad visualem ~TO~, continuandæ sunt, more solito, cum parallelis ad lineam perpendicularem. In hanc autem transferre oportet omnes divisiones, quas ex Barozzio habet elevatio hujus ordinis; ac ducere visuales. Quomodo autem, adminiculo visualium & parallelarum, compleatur elevatio, constat ex figura, & clarius ex chartula figuræ quadragesimæsecundæ. Numeri ~1~, ~2~, ~3~, ~4~, geminati, ostendunt centra & altitudines semicirculorum seu arcuum figuræ quadragesimæquintæ; videlicet, numerus inferior designat centrum, superior verò designat altitudinem semicirculi._

The Forty-fourth FIGURE.

_The Elevation of the Forty-first Figure in Perspective._

When the Parallels to the Ground-line in the Forty-third Figure, are prolong’d to the Visual TO, they are then, as usual, to be continu’d Parallels to the Perpendicular: On which Perpendicular, those Divisions given by _Vignola_, for the Proportions of this Order, are to be transferr’d; and Visuals drawn from them to the Point of Sight. How by these Visuals and Parallels the Elevation is rais’d in Perspective, is manifest in part from this Figure, but more clearly from the Forty-second Figure. The Numbers 1, 2, 3, 4, which you here see doubl’d, give the Centers and Heights of Semicircles of the Arches in the Forty-fifth Figure; the lower Numbers denoting the Centers, and the upper Numbers the Heights of the Semicircles of the same.

FIGURA Quadragesimaquinta.

Dimidium ædificii Dorici opticè deformati.

_Huic figuræ delineandæ plures præiverunt, ejusdemque latitudines mutuati sumus ex figura quadragesimatertia, altitudines ex quadragesimaquarta. Superest autem, ut lumina & umbræ scitè inducantur in singulas partes ædificii._

The Forty-fifth FIGURE.

_One Half of the ~Dorick~ Design in Perspective._

The foregoing Figures being preparatory to this, the Breadths are taken from the Forty-third, and the Heights from the Forty-fourth Figure. It only remains, that the Lights and Shades be skilfully dispos’d to each Part of the Work.

FIGURA Quadragesimasexta.

Alterum dimidium ejusdem ædificii.

_Supersedere poteram delineatione alterius medietatis ædificii nostri. Verùm operæ non peperci, ut ostenderem diversitatem luminum & umbrarum, quæ conveniunt partibus cæteroqui omnino similibus._

The Forty-sixth FIGURE.

_The other Half of the same Design._

I might very well have omitted this Half of the Design, but that I spar’d no Pains, to shew the Diversity of the Lights and Shadows, that must be given to those Parts of the Work, which in other Respects are alike.

FIGURA Quadragesimaseptima.

Vestigia ædificii Ionici.

_Vestigium geometricum ~A~ ædificii Ionici, sub se habet suam deformationem ~B~. Hæc autem ut evadat distinctior, lineam plani, quæ in sequentibus figuris habebit distantiam ~PE~ ab horizontali ~OE~, deorsum protraximus in ~CD~, ut etiam fecimus figurâ quadragesimasecundâ & quadragesimatertiâ. Linea visualis ~OM~ eundem habet usum, quem visualis ~OT~ figuræ quadragesimætertiæ; videlicet, ut in ea terminentur parallelæ ad lineam plani ex membris vestigii ~B~, eademque continuentur cum aliis parallelis ad rectam ~EC~, pro deformandâ elevatione quam apponemus figurâ quadragesimanonâ._

The Forty-seventh FIGURE.

_The Plan of an ~Ionick~ Building._

The Geometrical Plan of this _Ionick_ Work is A, underneath is its Perspective B; to render which more distinct, the Ground-line that in the following Figures has only the Distance PE from the Horizontal EO, is here remov’d downward to CD, as was done in the Forty-second and Forty-third Figures foregoing. The visual Line OM is of the same use as that of OT in the Forty-third Figure; namely, to terminate the Lines which are drawn from the Members of the Plan B parallel to the Ground-line; from whence they are again continu’d parallel to the Perpendicular EC, for making in Perspective the Elevation inserted in the Forty-ninth Figure.

FIGURA Quadragesimaoctava.

Elevatio geometrica ædificii Ionici.

_Ex hac elevatione quæ clarè ostendit membra totius ædificii secundum longitudinem dissecti, desumuntur altitudines ac terminationes membrorum singulorum. Peritiores tamen hac figurâ delineandâ supersedere solent, quia terminationes haberi possunt ex vestigio ~A~ figuræ quadragesimæseptimæ, altitudines verò ponendæ iterum sunt figurâ sequenti._

The Forty-eighth FIGURE.

_The Geometrical Upright of the foregoing ~Ionick~ Design._

From this Figure (which distinctly shews the Composition of the whole Work, in respect of its Length) are taken the Heights and Terminations of the several Members thereof. But those that are skill’d in this Art, usually omit the delineating these Elevations; because the Terminations may be taken from the Plan A in the Forty-seventh Figure; and the Heights must be repeated in the following Figure.

FIGURA Quadragesimanona.

Deformatio elevationis ædificii Ionici.

_Hæc figura continens deformationem præcedentis elevationis, perficitur methodo illa, quam ostendimus figurâ quadragesimasecundâ; nimirum, ex vestigio ~B~ figuræ quadragesimæseptimæ, ducere oportet parallelas ad lineam plani ~CD~, quæ ubi pervenerint ad visualem ~OM~, continuandæ sunt cum aliis parallelis ad lineam ~EC~. Easdem parallelas in hanc figuram translatas secant visuales ex linea recta ~AB~, in qua positæ sunt altitudines ædificii Ionici, desumpta vel ex figura præcedenti, vel ex Barozzio. Nullum autem est punctum in membris hujus elevationis, quod non inveniatur per sectiones visualium ex linea ~AB~, cum parallelis ad eandem lineam._

The Forty-ninth FIGURE.

_The Elevation of the ~Ionick~ Design in Perspective._

This Plate containing the Perspective of the foregoing Upright, is drawn by the Method laid down in the Forty-second Figure; to wit, from the Plan B of the Forty-seventh Figure, Parallels to the Ground-line CD are prolong’d to the Visual OM; and thence are continu’d Parallels to the Perpendicular EC. These being transferr’d into this Figure, are intersected by the visual Lines that proceed from AB, which contains the Heights of this _Ionick_ Composition, agreeable to the foregoing Figure, and the Rules deliver’d by _Vignola_. Now there is no Point in any Member of this Upright, but may be found by the Intersection which the visual Line from AB makes with its respective Perpendicular.

FIGURA Quinquagesima.

Architectura Ionica.

_Ex vestigio figuræ quadragesimæseptimæ, & ex elevatione figuræ quadragesimænonæ, eruitur hoc ædificium Ionicum, quod esse poterit vel principium alicujus turris campanariæ, aut basis cujuspiam arcûs triumphalis. Vereor ut cælator suam diligentiam in hoc schemate satis probaverit. Ejus tamen errata facilè ipse deteges, & omni studio cavebis._

The Fiftieth FIGURE.

_A Design of ~Ionick~ Architecture._

From the Plan of the Forty-seventh Figure, and from the Upright of the Forty-ninth Figure, is drawn this _Ionick_ Piece; which might well serve for the lower Order of a Turret, or for part of a Triumphal-Arch. I fear the Engraver has not been so exact in this Scheme, as he ought; but you will readily discover his Mistakes, and carefully beware of them.

FIGURA Quinquagesimaprima.

Ordo Corinthius.

_Complectitur hæc pagina molem contractam Ordinis Corinthii, cum suis præparationibus. Vestigium ~A~ exhibet parietem pone columnas cavum instar canalis. Idem vestigium opticè deformatur in ~D~: omissâque elevatione geometricâ, per ejus altitudines notatas in lineâ ~BC~ projicitur elevatio; ac methodo consuetâ, ex vestigio & elevatione componitur ædificium, addito statuæ unius ornamento._

The Fifty-first FIGURE.

_A ~Corinthian~ Design in Perspective._

This Plate contains the Perspective of a _Corinthian_ Work, with its Preparations. The Geometrical Plan A shews the Wall wrought hollow behind the Columns. The said Plan in Perspective is D: and leaving out the Geometrical Elevation, the Perspective thereof is describ’d, by transferring the Heights of the former into the Line BC. From the Perspective-Plan and Upright the Design is finish’d after the usual Manner; to which is added the Ornament of a single Statue.

Figura Quinquagesimasecunda.

Delineatio columnæ spiralis, Ordinis Compositi.

_Posita elevatione geometrica columnæ rectæ, ac divisione illius in vigintiquatuor partes æquales, columna spiralis absolvitur per partes circumferentiæ circulorum, quorum diametri sunt æquales diversis latitudinibus columnæ rectæ, ut ostendit figura in ~A~. Ad projectionem opticam elevationis, notandæ sunt quatuor occultæ rectæ, quæ ex terminis convexitatis & concavitatis infimarum spirarum ejusdem elevationis ~A~, descendunt ac desinunt in duos circulos vestigii geometrici ~B~. Vestigium ipsum opticè imminutum habetur in ~C~: eædem autem sunt maximæ hinc inde latitudines, tum in circulo majori, tum in convexitate infimarum columnæ spirarum; eædem sunt maximæ latitudines, tum in circulo minori, tum in concavitate ipsarum spirarum; ut dignosces applicando regulam spiris simul & circulis. Ex quatuor punctis maximæ latitudinis duorum circulorum, incipiunt quatuor lineæ parallelæ ad lineam plani, quæ ubi pervenerint ad visualem ~ED~, continuandæ sunt cum parallelis ad perpendiculum ~DF~. In eandem lineam ~DF~, ex elevatione ~A~ transferre oportet vigintiquatuor partes æquales altitudinis columnæ, ac ducere visuales ad ~O~ punctum oculi. Per sectionem autem visualium cum prædictis quatuor parallelis ad lineam ~DF~, ducuntur lineæ undulatæ ~MN~, ~PQ~, ex quibus eruuntur lineæ utrinque terminativæ columnæ spiralis nitidæ. Ex linea verò ~GH~ habetur facies anterior stylobatæ, columnæ & coronicis; ex linea ~IL~ habetur facies eorum posterior._

The Fifty-second FIGURE.

_The Description of a wreath’d Column, of the Composite Order._

Having made the Geometrical Elevation of a streight Column, and divided the Height of its Shaft into Four and twenty equal Parts; the Wreathing is describ’d by Parts of the Circumference of Circles, whose Diameters are equal to the several Breadths, or Diameters, of the streight Column; as is shewn in the Figure A. For putting the Upright into Perspective, four streight occult Lines are of use, which descend from the Extent of the Swellings and Sinkings of the lower Wreaths of the Column A; and terminate in two Circles of the Geometrical Plan B. The said Plan laid down in Perspective is C. The utmost Extent of the greater Circle determines that of the Convex Parts of the lower Wreaths: The greatest Breadth of the lesser Circle gives that of the hollow Parts of the said Wreaths; as may be perceiv’d, by applying a Ruler from the Wreaths to the Circles of the Plan. From the four Points of greatest Breadth in those Circles, four Lines parallel to the Ground-line are continu’d to the Visual ED, and thence again continu’d parallel to the Perpendicular DF. From the Elevation A, the Four and twenty equal Parts of the Columns Height are transferr’d into the Line DF, and Visuals drawn from each to the Point of Sight O. By the Intersections of those Visuals with the four Perpendiculars aforesaid, are drawn the wav’d Lines MN, PQ; from which, both the Out-lines of the finish’d Column are describ’d. But the Fore-part of the Pedestal, Column, and Cornice, is taken from the Line GH; the Back-part of the same from the Line IL.

Fig. Quinquages. tertia A.

Ordines Architecturæ, desumpti ex Palladio & Scamozzio.

_De Ordinibus Architecturæ, præter Barozzium, egregiè scripserunt Palladius & Scamozzius; ac singuli, jure merito, suos habent asseclas & patronos. Ut ergò, etiam juxta laudatissimorum Autorum placita, opticas projectiones facere possis, omnes Ordines in hac paginâ exhibere volui, ut in eorum Libris inveniuntur._

The Fifty-third Figure A.

_The Orders of Architecture, taken from ~Palladio~ and ~Scamozzi~._

Besides _Vignola_, _Palladio_ and _Scamozzi_ have also written excellently well of the Orders of Architecture; and each of ’em have deservedly their Followers and Admirers. That you might therefore be enabl’d to make Designs in Perspective, after the Proportions of the most celebrated Masters, I have in this Plate given you the Measures of all the Orders, as deliver’d by them in their Books.

Fig. Quinquages. tertia B.

Modus triplex delineandi columnas spirales.

_Columnæ figuræ superioris carent ea concinnitate, qua præditæ sunt columnæ spirales æneæ celeberrimi Equitis Bernini ad sepulcrum S. Petri in Vaticano. Itaque methodum triplicem exhibeo ad minuenda spatia totius altitudinis columnæ._

1. _Recta ~OA~ sit æqualis altitudini ~AB~ columnæ. Fiat autem recta ~OB~, & arcus ~AP~ ex centro ~O~, divisus in partes duodecim æquales, ducendo rectas, quæ per puncta divisionum desinant in columnam rectam; ac demum fiant parallelæ ad basim: Spatia inter has parallelas dabunt aperturam circini pro triangulis æquilateris & pro spiris, ut ostendit columna ~1~._

2. _Translatâ in ~C~ tertiâ parte altitudinis columnæ ab ejus imo scapo, habeat circinus aperturam ~CD~; ac posito uno ejus crure prius in ~D~, postea in ~C~, fiant duo parvi arcus ad ~E~: sectio illorum arcuum erit centrum arcûs ~DC~, quem oportet dividere in duodecim partes æquales, & ex punctis divisionum ducere parallelas ad basim. Tum spatiis inter parallelas divisis in quatuor partes æquales, tres ex illis partibus dabunt longitudinem crurum pro triangulis isoscelibus; vertices autem triangulorum erunt centra singularum spirarum, ut ostendit columna ~2~._

3. _Ductâ ex medio summitatis ~G~ rectâ ~GF~, spatium ~HF~ transferatur in ~I~, & fiat recta ~IL~ parallela ad basim ~HF~; spatium ~IL~ transferatur in ~N~, ac fiat ~NM~, & sic deinceps. In parvis columnis triangula sine sensibili errore duci possunt per diagonales: in columnis tamen grandioribus, alterutrum ex modis antea explicatis adhibere necesse est._

The Fifty-third Figure B.

_Three different Ways of delineating wreath’d Columns._

The wreath’d Columns describ’d in the Fifty-second Figure, being divided into Twenty-four equal Parts, want very much of that Elegancy of Contour, which is visible in those brass Pillars, made by the famous Cavalier _Bernino_, for S. _Peter_’s Sepulcher in the _Vatican_. Wherefore I here lay before you three several Ways of diminishing the Spaces through the whole Height of the Column.

1. Make the right Line OA equal to AB the Height of the Column; then draw the Line OB, and on the Center O describe at pleasure the Arch AP, which divide into twelve equal Parts, and by the Divisions draw streight Lines from the Center O to the Line of the Column; and lastly continue the same Parallels to the Base. The Spaces between these Parallels, shall be the Sides of equilateral Triangles, wherewith you are to describe the Wreath of the Column, as is seen in Column 1.

2. Having set the third Part of the Columns Height, from the Bottom of the Shaft to the Point C; with the Interval CD, from the Centers D and C, describe the Parts of Arches intersecting at E. On the Center E, with the same Interval, describe the Arch DC, which divide into twelve equal Parts; and from the Points of those Divisions, draw Parallels to the Base. Then dividing each Space between the Parallels into four equal Parts; three of those Parts shall be the Sides of the _Isosceles_ Triangle; whose _Vertex_ is the Center whereon to describe each Wreath of Column 2.

3. Having drawn from the midst of the Columns top G, the Line GF, make HI equal to HF, and draw IL parallel to the Base HF: Again, make IN equal to IL, and draw NM also parallel, and so on. In small Pillars, the Centers of the Diagonals of these Spaces may, without sensible Errour, serve for describing the Wreaths; but in greater Columns, either of the other two Methods is rather to be chosen.

FIGURA Quinquagesimaquarta.

Vestigia ædificii Ordinis Corinthii.

_Descripturi ædificium Corinthium octangulare, ponimus hic vestigia unius ex quatuor partibus pilarum, quibus imponetur fornix in modum tholi, ut constabit in figurâ quinquagesimaoctava. Ad faciliorem descriptionem, in parte inferiori paginæ posui vestigium geometricum stylobatæ, in superiori vestigium geometricum coronicis, cum latitudinibus & longitudinibus membrorum singulorum; ut eas transferendo in lineam plani more consueto, utrumque vestigium opticè deformetur. Ad vitandam confusionem, prius notare oportebit puncta quæ spectant ad membra propinquiora solido parieti, deinde alia._

The Fifty-fourth FIGURE.

_The Plan of a Design of the ~Corinthian~ Order._

Being to describe an Octangular _Corinthian_ Work, I have here inserted the Plan of one Quarter of the Composition; which is vaulted in Form of a _Cupola_, as is seen in the Fifty-eighth Figure. To render the Plan less confus’d, I have, in the lower part of the Plate, given the Geometrical Plan of the Pedestal; and in the upper part, that of the Cornice; with the Breadths and Lengths of each Member: so that by transferring the same into the Ground-line, after the usual Manner; you delineate each Plan in Perspective. For avoiding Confusion, ’twill be requisite first, to transfer the Points of those Members that are next the Solidity of the Wall; and then proceed to the others.

FIGURA Quinquagesimaquinta.

Elevatio ædificii Ordinis Corinthii.

_Elevatio geometrica ædificii octangularis congruit cum duobus ejus vestigiis figuræ antecedentis. Quia verò elevatio parietis abscondit secundam ex quatuor columnis, eademque in ædificio deformato conspicua futura est; iccircò eam lineis occultis designare oportuit._

The Fifty-fifth FIGURE.

_The Geometrical Elevation of a ~Corinthian~ Work._

The Geometrical Elevation of this Octangular Design, is wholly correspondent to the two Plans of the foregoing Figure: But because the Wall in this Upright takes off the Sight from the second of the four Columns, which is notwithstanding visible in the finish’d Perspective that follows; ’tis requisite to delineate the same with occult Lines, as in the Figure.

FIGURA Quinquagesimasexta.

Deformatio vestigiorum & elevationis ædificii Corinthii.

_In hac figurâ, lineam plani coincidere volui cum linea horizontis. Itaque videri non posset vestigium inferius, nisi ut alias deorsum protraxi lineam plani, hic è converso sursum promovissem lineam horizontis, quam constitui mediam inter lineas plani utriusque vestigii, ut ambæ projectiones essent æquè distinctæ. In elevatione, columna secunda, quam, ut dixi, paries abscondit, lineis occultis designanda est._

The Fifty-sixth FIGURE.

_The Perspective Plans and Upright of the ~Corinthian~ Design foregoing._

In this Figure, I have made the Ground-line coincident with that of the Horizon, in which case the lower Plan can’t be seen, unless the Ground-line be sunk lower, as before intimated; or contrariwise, the Point of Sight rais’d higher, as I have here done, keeping it in the midst between the Ground-lines of the two Plans, that the Perspective of both might be equally distinct. In the Elevation, the second Column, which I mention’d to be hidden by the Wall, should be design’d with occult Lines.

FIGURA Quinquagesimaseptima.

Adumbratio figuræ sequentis.

_Figuram hanc seorsim delineavi, ut videas quomodo facienda sit operis totius adumbratio, accipiendo altitudines membrorum singulorum ex elevatione; latitudines & longitudines ex vestigiis. Quæ omnia ex diagrammatis inspectione clarissimè apparent._

The Fifty-seventh FIGURE.

_The rough Draught of the following Figure._

I have drawn this Figure apart, that you may see the Manner of describing the Out-line of the whole Work, by taking the Heights of the several Members from the Elevation, and their Breadths and Lengths from the Plans; all which is very plain, upon Inspection of the Figure.

FIGURA Quinquagesimaoctava.

Ædificium Ordinis Corinthii octangulare.

_Hucusque descripsimus pilas anticas sinistras ædificii Corinthii. En hoc loco medietatem dexteram totius Operis. Integrum verò ædificium habebis figurâ sexagesimâ._

The Fifty-eighth FIGURE.

_Part of an Octangular Work of the ~Corinthian~ Order._

Hitherto the nearest left-hand Quarter of this _Corinthian_ Design has been describ’d. In this Plate you have the right-hand Half of the whole Work; and in the Sixtieth Figure, the entire Perspective compleat.

FIGURA Quinquagesimanona.

Vestigia tabernaculi octangularis.

_Projectiones rerum octangularium sunt quadratis difficiliores: ideò in eis explicandis diligentiæ non peperci. Moles cujus vestigia vides in ~A~ & ~B~, convenit in multis cum eâ quam ereximus figurâ quinquagesimaoctavâ. Visualis ~CD~ recipit sectiones perpendicularium, quæ deserviunt pro elevatione figuræ sequentis, ut sæpius dictum est. Si facies interior delineanda sit seorsim à facie anteriori, illam perficies ope linearum ~CE~, istam ope linearum ~FD~._

The Fifty-ninth FIGURE.

_The Plans of an Octangular Tabernacle._

Octangular Figures being more difficult to be put in Perspective, than the Square; I shall use my best Endeavours to render the Method as plain as possible. The Composition whose Plans you see in A and B, has much Affinity with that describ’d in the Fifty-eighth Figure. The Visual CD receives the Sections, from which Perpendiculars are rais’d for the Elevation and Profile of the following Figure, as has been often said. If you would delineate the Back-part separate from the Fore-part, you may do the former by means of the Line CE, and the latter by that of FD.

FIGURA SEXAGESIMA.

Tabernaculum octangulare.

_Hoc tabernaculo aliquoties usus fui pro expositione quadraginta horarum. Si colores scitè inducti fuerint in duos ordines telariorum, resectis omnibus quæ ad molem ipsam non pertinent, spectatoribus imponet, & solida videbitur. Oportebit autem exemplar externæ faciei eruere ex parte ~DF~ vestigii & elevationis; exemplar interioris faciei eruere ex parte ~EC~, servando in omnibus regulas quas hucusque tradidimus._

The SIXTIETH FIGURE.

_An Octangular Tabernacle in Perspective._

I have sometimes made use of this Tabernacle for the Exposition of the _Forty Hours_. If the Colours are laid by a skilful Hand, on two Ranges of Cloth, and the Frame cut away according to the Out-line of the Work, they will wonderfully deceive the Eye, and appear as solid; but then the outer Range must be drawn after the Plan and Elevation of the Part DF in the foregoing Figure; and the inner Range after that of EC; in all things observing the Rules hitherto deliver’d.

FIGURA Sexagesimaprima.

Modus erigendi machinas, quæ constant pluribus ordinibus telariorum.

_Ex figuræ inspectione addisces modum erigendi machinas quæ constant pluribus ordinibus telariorum. Tabernaculum hoc nostrum indiget duobus tantum ordinibus; nam telaria propinquiora oculo exprimunt faciem externam, remotiora exhibent faciem internam. Ne autem lateant stipites quibus telaria sustinentur, medietatem telariorum adumbrare omisimus. Recta ~LS~ est linea plani, recta ~DG~ est linea horizontalis; ac punctum distantiæ quod cadit extra paginam in recta ~CG~ prolongatâ, debet esse remotum à puncto ~C~, quantum in superiori parte figuræ quinquagesimænonæ, punctum distantiæ est remotum à puncto oculi. Eadem horizontalis ~DG~ secatur normaliter in ~C~ à recta ~EF~, quæ est sectio externæ faciei tabernaculi, & ex ~C~ incipiunt divisiones in partes æquales pro reticulatione anterioris faciei telariorum, ut dicemus figurâ sexagesimasecunda. Recta ~IL~ quæ est sectio internæ faciei tabernaculi, distat ad libitum à recta ~EF~ cui est parallela. Porrò, per divisiones rectæ ~EF~ (ut vides in ~M~, ~N~, ~O~) ex puncto distantiæ ducendæ sunt visuales ad rectam ~IL~ pro reticulatione aliorum telariorum: distantia enim ~DC~ facit ut augere oporteat ea quæ in telariis pinguntur, alioquin justo minora viderentur. Atque hinc dignosces, cur arcus qui in telariis anterioribus pertingeret solum ad ~B~, in posterioribus elevetur usque ad ~H~._

_Figura sequenti proponemus modum delineandi faciem internam telariorum, adhibita reticulatione externæ faciei: ad intelligentiam verò illius methodi, fiat in hac figurâ recta ~HP~ parallela ad ~DC~, ac recta ~BC~ dividatur in totidem partes æquales, in quot partes divisa fuerit recta ~PC~._

The Sixty-first FIGURE.

_The Manner of erecting Machines, that consist of several Ranges of Frames._