FIG. XXI.
FIG. XXI.
Optica imminutio capitelli Etrusci.
Eâdemcum reliquis formâ, eâdemque methodo capitella delineanda sunt: quum habeant ipsa quoque suum cimatium quadratum, & sint rotunda. Linea plani solet in iis fieri altior lineâ horizontali: quia quum capitella imponenda sint columnis homine altioribus, plerumque apparent sublimiora nostris oculis.
TheTuscanCapital in Perspective.
TheManner before deliver’d concerning Bases, is of the same Use in delineating Capitals; forasmuch as these also have their squareAbacus, and their round Members. The Ground-line in Capitals is usually plac’d above the Horizon; because when they are set upon Columns which exceed a Man’s Height, they are generally represented above the Eye.
Fig. xxii.
Fig. xxii.
Optica projectio capitelli Dorici.
Capitellumhoc pluribus membris constat, adeóque operosius est quàm præcedens. Nihilominus accurata delineatio vestigii geometrici omnes difficultates complanabit.
The Projection of aDorickCapital, in Perspective.
ThisCapital consisting of more Members than the foregoing, will be more troublesom to put in Perspective; but an accurate Delineation of the Geometrical Plan will certainly remove many seeming Difficulties.
Fig. xxiii.
Fig. xxiii.
Deformatio capitelli Ionici.
CapitellumIonicum poscit duas elevationes geometricas distinctas, alteram faciei, alteram lateris; ex iisque conflatur vestigium geometricumA, quod opticè contrahitur, translatis inBpunctis latitudinisC, & inEpunctis longitudinisDmore consueto: ut ex punctisBlatitudinis, lineæ tendant ad punctum oculi; ex punctis veròElongitudinis, lineæ tendant ad punctum distantiæ.
Ex vestigio capitelli opticè contracto eruenda est elevatio longitudinis ut in figura. Ex utrisque verò juxta morem fiet capitellum nitidum, acceptis latitudinibus ex vestigio, altitudinibus ex elevatione longitudinis. Hæc quoque dabit maximam latitudinem singularum volutarum.
Modum delineandi capitellum Ionicum, in quo helices volutarum obliquentur, dabimus infra figurâ trigesimâ.
TheIonickCapital in Perspective.
TheIonickCapital requires two distinct geometrical Elevations, one of the Front, the other of the Side; from both which is found the geometrical Plan A, which is put in Perspective by transferring into B the Points of Breadth C, and into E the Points of Length D, after the usual Manner; that from the Points of Breadth B, Lines may be drawn towards the Point of Sight; and from the Points of Length E, towards the Point of Distance.
From the Plan of the Capital in Perspective, is to be drawn the Upright of the Length, as in the Figure; and from both, as usual, the finish’d Capital is wrought, by taking the Breadths from the Plan, and the Heights from the Elevation; this giving the utmost Height, and that the utmost Breadth of each of the Volutes.
The Manner of describing theIonickCapital, whose Volutes lie obliquely, we shall hereafter treat of in the Thirtieth Figure.
FIG. XXIV.
FIG. XXIV.
Optica projectio capitelli Corinthii.
CapitellumCorinthium absolvere non poteris, nisi elevatione geometrica ejusque vestigio exactissimè delineatis juxta regulas Barozzii.
Ad formandum ex vestigioBvestigiumE, rectis occultis fient quadrata necessaria ad contractionem opticam quatuor vel trium saltem circulorum; translatis in lineamDdivisionibus lineæC, & aliis, more consueto. Contrahentur deinde lineis occultis vestigia foliorum, & absolventur cætera quæ posita sunt in vestigioE.
Ut fiat optica elevatio longitudinisF, in lineam perpendicularemHtransferentur ex elevationeAomnes ejus divisiones. Complebitur autem per lineas rectas, quæ ex punctis divisionum ducantur ad punctum oculi, ac per rectas ex circulorum summitate ac profunditate, quæ rectæ sint parallelæ ad lineamD, ac perveniant ad visualemG; indeque descendant, ac sint parallelæ ad lineam perpendicularemH.
Capitellum nitidum exordieris ab infimo circuloI, ostendente ambitum columnæ. Succedent folia1,2, quorum latitudines accipientur ex vestigioEper circinum, positâ unâ ejus cuspide in lineaH; altitudines verò accipientur ex elevationeF, posita una cuspide circini in lineaD. Idipsum dico tum de foliis3,3,4,4, tum de folio5, ac de aliis, & demum de cymatio. Descensus verò lineæ curvæ ipsius cymatii incipiet ex acieL.
TheCorinthianCapital in Perspective.
Thereis no Completing theCorinthianCapital, unless you most accurately describe its Geometrical Elevation and Plan, according to the Rules ofVignola.
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 theAbacusalso; the Sinking of the Horns whereof answers that of the visual Line L.
FIG. XXV.
FIG. XXV.
Optica descriptio capitelli Compositi.
Exiis 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.
TheCompositeCapital in Perspective.
Fromwhat has been said of theCorinthianCapital, may be learnt the Manner of putting theCompositealso 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.
Fig. xxvi.
Fig. xxvi.
Deformatio coronicis Etruscæ.
Postcapitella 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.
TheTuscanEntablature in Perspective.
AfterCapitals we proceed toEntablatures, which because they are square, are less difficult than the former. And of all Entablatures, that of theTuscanOrder 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.
Fig. xxvii.
Fig. xxvii.
Optica delineatio coronicis Doricæ.
Infaciendâ 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.
TheDorickEntablature in Perspective.
Inmaking theDorickEntablature, 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.
Fig. xxviii.
Fig. xxviii.
Præparatio figuræ sequentis.
Infigurâ vigesimaoctavâ, quæ continet vestigium & elevationes geometricas figuræ vigesimænonæ, oportuit latusCdelineare seorsim à facieB; quia facies exhibet latitudinem ædificii, latus verò exhibet longitudinem; atque una non est alteri æqualis. In vestigio geometrico solidus paries estA: circuli referunt summum scapum columnarum. Cætera dant projecturas coronicis, cum suis mutulis.
Preparatory to the following Figure.
Inthis 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.
FIG. XXIX.
FIG. XXIX.
Optica projectio ædificii Dorici.
Habesin 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.
BOest linea horizontis;ACest linea plani; in quam, ex lineisD&Cfiguræ vigesimæoctavæ, transferuntur puncta latitudinis & longitudinis duarum elevationum; prolongando versusCipsam lineam plani, ut oportet. Operaberis autem, ut diximus figurâ vigesimatertia; nimirum, in punctoVdesinet 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 visualemVO, fient parallelæ ad lineamAC, cum cæteris quæ necessaria sunt ad complendam delineationem opticam vestigii.
ElevatioCfiguræ vigesimæoctavæ opticè contrahetur more consueto, translatis in lineamABdivisionibus lineæEvelF, ex quibus fient visuales ad punctum oculi; ac demissis ex linea visualiAOperpendicularibus ad lineamAC, ita ut lineæ parallelæ ad lineam planiACcontinuentur cum aliis lineis parallelis ad lineamAB.
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.
A Projection of theDorickOrder in Perspective.
Inthis 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 theDorickOrder, 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.
Fig. xxx.
Fig. xxx.
Optica projectio ædificii Ionici; ubi de modo jungendi fictum cum vero.
Sitibi 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, estA; elevatio geometrica coronicis, & reliquorum quæ delineanda sunt, estB; vestigium geometricum estC. Porrò, tum vestigium tum elevatio longitudinis opticè contrahentur more consueto, ut vides inC&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 sectionemAtransferre inD, ducendo visuales ex punctis terminativis membrorum sectionisD, usque dum occurrant lineis latitudinis eorundem membrorum. Quod si colores in telarium scitè inducantur, angulus inE, 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.
AnIonickWork 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 atRomeandMilan, 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.
Fig. xxxi.
Fig. xxxi.
Optica projectio coronicis Corinthiæ, cum capitello & summitate columnæ.
Inhoc schemate linea plani estCIE, horizontis estDFO; punctum oculi estO, distantiæ estD. Elevatio geometrica capitelli Corinthii cum sua coronice estA, quorum divisiones cernuntur in perpendiculariCD. Vestigium geometricumBhabet longitudinem æqualem latitudini: opticè autem contrahitur methodo consueta. Nimirum, translatis divisionibus latitudinis & longitudinis in lineam planiCIE; 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 inGN,HL: lineæ latitudinum, parallelæ ad lineam plani fiunt ex punctis in quibus lineæ tendentes ad punctum distantiæ secant visualemHO, ut vides inNL. Porro, si tantundem prolongaretur horizontalisDO, ita ut haberet duo puncta distantiæ remota æqualiter abO, medietas diagonalium, quæ sunt in quadrato majoriGNLHopticè deformato, & in quadratis ejus minoribus, tendent ad unum punctum distantiæ; altera medietas ad aliud punctum distantiæ.
Elevatio longitudinis opticè contrahitur ductis parallelis adCE, quæ ubi pervenerint ad visualemIO, continuentur cum aliis parallelis adIK. Præterea, translatis in lineamIKdivisionibus lineæ perpendicularisCD, 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 adIK. Demùm ex vestigio & ex elevatione longitudinis, formatur coronix nitida cum capitello. Ut autem faciliùs delineentur mutuli, primùm fient quadratâ formâ, ut inM; deinde congruus flexus in singulos inducetur.
The Optick Projection of aCorinthianCornice, with the Capital and PART of the Column.
Inthis 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 theCorinthianCapital, 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.
FIG. XXXII.
FIG. XXXII.
Delineatio geometrica coronicis, Ordinis Compositi.
Uthoc schema grandius ac distinctius esset, ejus medietatem dumtaxat suscepi delineandam.PNest vestigium geometricum.Mest solidus paries.OOspatia columnarum. InHsunt crepidines coronicis. Elevatio geometrica latitudinis ædificii constat epistylioT, zophoroL, & coronâV, supra quam eminet fastigiumS.
Jam ut inveniatur centrum arcuum, distantiæAVfiat æqualis distantiaAC. Positaque una cuspide circini inC, alia extendatur usque adV: ita fient arcus, quorum ultimus estBD, omnesque sunt concentrici. ElevatioFostendit longitudinem ædificii ex parteGI; elevatioEostendit longitudinem ipsius ex parteDR.
The Geometrical Design of a Cornice, of theCompositeOrder.
Thatthis 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.
FIG. XXXIII.
FIG. XXXIII.
Deformatio coronicis Compositæ.
Figurahæc trigesimatertia minus ardua tibi videbitur, si ex ea delineandam primùm suscipias medietatem quæ respondet vestigioPN& elevationiBRfiguræ trigesimæsecundæ; rejecto in ultimum fastigio, postquàm cætera compleveris. LineaBVest horizontalis. Punctum oculi estV, punctum distantiæ remotum est abVspatioBV, additis modulis quatuordecim cum dimidio. Linea plani estAR, in quam exQversusAtransfertur latitudoP; exQversusRtransfertur longitudoN, 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 elevationemPlongitudinis coronicis: ac tum ex illa, tum ex vestigio, eruetur coronix nitida more consueto.
Ut delineetur fastigium, transferendæ sunt in lineamABdivisiones ipsius ex elevationeFfiguræ trigesimæsecundæ, ac ducendæ visuales ad punctum oculi, additis lineis terminativis uniuscujusque membri, quæ accipientur ex vestigioQopticè deformato. CentrumOarcuum fastigii nitidi, remotum est à summitate coronicis, medietate distantiæ, quam habent ungues quadræ cui fastigium ipsum incumbit. Ac proinde, si accipias ex elevationePdiversas altitudines membrorum fastigii; latitudines verò accipias ex vestigioQ; opus tuum feliciter absolves.
ACompositeCornice in Perspective.
ThisThirty-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.
Fig. xxxiv.
Fig. xxxiv.
Præparatio ad figuram trigesimamquintam.
Siplacuerit 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 exVversusR, & sunt eædem cum divisionibus rectæIGfiguræ trigesimæsecundæ. Divisiones longitudinis incipiunt exVversusS, & sunt eædem cum divisionibus rectæIPduplicatis. Ex divisionibus latitudinis fiunt visuales ad punctum oculi; ex divisionibus longitudinis fiunt rectæ ad punctum distantiæ; cum reliquis quæ necessaria sunt ad complendum vestigiumAVDC.
Elevatio longitudinis coronicis & fastigii, opticè contrahitur per lineas parallelas ad lineam planiAS; quæ ubi pervenerint ad visualemAC, continuentur cum aliis parallelis ad perpendiculumP, ut diximus figurâ trigesimaprimâ. In idem perpendiculumPtransferuntur ex figurâ trigesimasecundâ divisiones rectæDR; & insuper altitudines, quas punctaKXZhabent supra rectamVA; fientque visuales ad punctum oculi: sectiones autem visualium cum parallelis ad perpendiculumP, dabunt sex puncta simæ fastigii, respondentia punctisKXZduplicatis, 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 perpendiculumP.
Preparatory to the Thirty-fifth.
Ifyou please to compare the Thirty-third Figure with this Thirty-fourth Figure, you will perceive the Plan and Elevation of thisCompositeCornice 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 theCimaof 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 upperCima, 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.
FIG. XXXV.
FIG. XXXV.
Deformatio coronicis Compositæ, ad latus inspectæ.
Artificiumnitidæ 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 similiaH&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.
A Side-View of theCompositeCornice, in Perspective.
TheManner 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.