Part 5
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~._