Part 3
As in the foregoing Figure, so in this also is shewn what is to be done, where the Plans AA lie so oblique, as to cause Confusion; especially in the Parallel-lines which give the Breadths. The like Inconvenience often happens in elevating the Lengths in Perspective; when by their too near Approach to the Point of Sight, the Contour of the several Mouldings can’t be distinctly delineated: For avoiding which, instead of B you may make use of the Elevation C, which is not only more distinct than the former, but better than either of the two intermediate ones D or E, by so much as it is more remote from the Point of Sight.
In designing the finish’d Pedestal, the Breadths are taken from the lowest Plan, by setting one Point of the Compasses in the perpendicular Line OL: the Heights are taken from the Elevation C, by placing one Point of the Compasses in the Ground-line, as has been shewn before.
FIGURA Duodecima.
Deformatio stylobatæ Corinthii, cum duabus pilis.
_Ornatus gratiâ, stylobatæ Corinthio additæ sunt pilæ, quæ pone columnas locari solent. Ut autem pilæ clariùs appareant, columna omissa est, cujus deformandæ rationem nondum tradidimus. Mensuras omnes ex Barozzio acceptas esse demonstrat ipsum schema, in quo elevatio geometrica stylobatæ est ~A~; vestigium ejus geometricum est ~B~: pilæ ~CC~. Vestigium opticè contractum est ~D~, elevatio longitudinis stylobatæ opticè contracta est ~E~, ac methodo consuetâ ex iis eruetur stylobata nitidus cum suis pilis._
The Twelfth Figure.
_The ~Corinthian~ Pedestal, with its Pilasters, in Perspective._
For Ornaments sake, we have added to this _Corinthian_ Pedestal the Pilasters, which are usually placed behind Columns: And that they may be the more perspicuous, have left out the Column, not having yet shewn the Manner of putting it in Perspective. The Scheme shews the Measures are taken from _Vignola_; in which the Geometrical Upright of the Pedestal is A; the Geometrical Plan of the same is B; that of the Pilasters CC. The Plan in Perspective is D, the Elevation in Perspective is E; from which the finish’d Pedestal and Pilasters are drawn by the usual Method.
Figura Decimatertia.
Projectio stylobatæ, ordinis Compositi.
_Quum pagina non caperet integrum stylobatam tantæ molis, fingere oportuit detractum illi esse aliquid de trunco; ac partem supremam stylobatæ sustentari ab infima, non immediatè, sed per quatuor asseres; eisque impositam fuisse adjumento funium suspensorum ex trochlea. Elevatio geometrica stylobatæ est ~B~; vestigium geometricum est ~A~. Ex his eruitur optica delineatio vestigii ~C~ & elevationis ~D~. Ac postea formatur stylobata nitidus ~E~, accipiendo latitudines ex vestigio ~C~, altitudines ex elevatione ~D~._
The Thirteenth Figure.
_The Projection of a Pedestal, of the Composite Order, in Perspective._
Wanting Room in this Page to describe so large a Pedestal entire, we imagine it to have lost part of its Trunk, and the upper part to be set on the lower; not immediately, but on four Cross-pieces that intervene; and for placing it thereon, we suppose the Assistance of Ropes and a Pulley. The Geometrical Elevation of the Pedestal is B; its Plan A; from whence are found their Projections in Perspective D and C. Then taking the Breadths from the Plan C, and the Height from the Elevation D, you complete the finish’d Pedestal E.
Figura Decimaquarta.
Deformatio circulorum.
_Ut stylobatis imponere liceat columnas cum suis basibus & capitellis, docendus est modus qui servandus est in projectione optica circulorum, tum singularium, tum duplicium aut multiplicium circa idem centrum._
_Vestigium geometricum ~A~ constat quadrato in quatuor partes æquales diviso, cui circulus inscribitur, additis diagonalibus: & ubi hæ secant circulum, fiunt rectæ parallelæ ad singula latera ipsius quadrati. Deinde quadratum cum omnibus divisionibus opticè imminuitur; ac tum per quatuor puncta ubi tres lineæ rectæ se intersecant, tum per quatuor extrema reliquarum duarum diametrorum circuli, ducetur cum venustate circumferentia circuli ~B~. Si addere velimus alium circulum, vestigio geometrico ~C~ inscribetur aliud quadratum; indeque habebitur optica delineatio duplicis circuli ~D~. Inter hos duos quomodo liceat describere tertium, per octo sectiones quadratorum, ostendunt figuræ ~E~ & ~F~. Uno verbo, circuli describuntur per quadrata, adhibendo sectiones visualium cum parallelis ad lineam plani; ac nullum est punctum in quadratis & circulis ~A~, ~C~, ~E~, cui per sectiones illas nequeat inveniri punctum correspondens in quadratis & circulis ~B~, ~D~, ~F~. Nihilominus ubi opus habeas pluribus circulis, autor tibi sum ne multiplices quadrata, plus confusionis allatura tibi quam adjumenti._
The Fourteenth Figure.
_Circles in Perspective._
That upon Pedestals you may be able to place Columns with their Bases and Capitals, it is requisite you should know the Manner of putting Circles into Perspective; whether single, double, or many concentrick.
The Geometrical Plan A consists of a Square with a Circle inscrib’d, whose Diameters divide it into four equal Parts; and the Diagonals being drawn where they intersect the Circle, continue Lines parallel to each Side of the Square. The Square, with all its Divisions, being put in Perspective; by the four extreme Points of the Diameters, and by those of the Intersection of the Diagonals, you neatly trace by hand the Circumference B. If you would add another Circle, you must inscribe another Square, as in the Plan C; from whence you find in Perspective the double Circle D. Between these two Circles, you may, by the eight Intersections of the Squares, describe a third; as is evident by the Figures E and F. In a word, all Circles are described by the Help of Squares, tracing them by the Intersections of the visual Lines, with those parallel to the Ground-line: Nor is there any Point in either the Squares or Circles A, C, E, whose correspondent Point may not be readily found by such Sections, in the respective Squares and Circles B, D, F. Nevertheless, where your Work requires many Circles, I would advise you to use as few Squares as possible; lest they perplex, rather than assist you.
Figura Decimaquinta.
Optica delineatio Columnæ.
_Descripturi frustum cylindricum ~I~ uniforme, fiet elevatio ~A~, & vestigium geometricum ~B~, saltem quoad medietatem. Ex hoc opticè deformato, ut vides in ~C~, ducendæ sunt parallelæ tum latitudinis ad visualem ~D~, tum elevationis ad visualem ~E~; ex quibus describentur circuli opticè contracti ~F~ & ~L~, accipiendo latitudines ex vestigio ~C~, altitudines ex perpendiculari ~M~; & juxta hanc methodum circuli ~F~ & ~L~ fiunt sine ope quadratorum. Demum ducendæ sunt perpendiculares ~G~ & ~H~, quæ tangant circulos ~F~ & ~L~ in punctis terminativis maximæ latitudinis._
_Nullum est punctum in vestigio ~C~, cui per lineas latitudinis & elevationis nequeat inveniri locus correspondens in circulo ~F~. Exempli gratia; locus puncti ~7~ est punctum ~6~. Hunc autem locum habemus per tres lineas, ~CD~, ~DE~, ~E7~._
_In delineandis duobus frustis cylindricis, cum summo & imo scapo, eandem regulam servare oportebit._
The Fifteenth Figure.
_A Column in Perspective._
Being to describe Part of the Shaft of a Pillar without Projectures, make the Elevation A, and the Geometrical Plan B, at least to the middle: From this brought into Perspective, as you perceive in C, must be drawn Parallels both of Breadth to the Visual D, and of Elevation to the Visual E; from which are described the Circles in Perspective F and L, taking the Breadths from the Plan C, and the Heights from the Perpendicular M: And according to this Method the Circles F and L are made, without the Help of Squares. Lastly, draw the Perpendiculars G and H, by the Points which terminate the greatest Breadth of the Circles F and L.
There is not a Point in the Plan C, but what, by means of the Lines of Breadth and Elevation, may be found in the Circle F. For Instance; the Place of the Point 6 is 7, which is found by the three Lines CD, DE, E7.
In designing the two Pieces of a Pillar, with the Projecture of the Fillet at Head and Foot, you must observe the very same Rule.
Figura Decimasexta.
Optica projectio basis Etruscæ.
_Ex elevatione geometrica ~A~ eruitur vestigium ~B~. Hoc autem deformato in ~C~ & ~D~, ex circulis vestigii ~C~ habentur latitudines columnæ, quadræ, ac tori triplicis basis: & eodem modo ex vestigio ~D~ habentur latitudines quadræ ac tori ultimæ basis. Ex maximis latitudinibus circulorum vestigii ~C~ ereximus perpendiculares ad partes quæ ipsis respondent in basi; ut agnoscas quænam sint puncta maximæ latitudinis in eisdem partibus. Hæc puncta (quæ in circulo maximo vestigii ~C~ sunt ~M~ & ~N~) invenientur tangendo circumferentiam uniuscujusque circuli regulâ parallelâ ad lineam perpendicularem ~E~, nam si figura exactè delineata fuerit, regula tanget singulos toros trium basium in punctis maximæ hinc inde latitudinis._
_Magis laborandum erit in reperiendis altitudinibus quatuor basium. Verum si sedulò inspiciatur deformatio elevationis ~F~, aliarumque duarum, (quæ factæ sunt, notatis in linea perpendiculari ~E~ divisionibus desumptis ex elevatione geometrica ~A~) constabit, nullum esse punctum in circulis vestigii ~C~, cui nequeat inveniri punctum correspondens in toro & quadra ipsius basis, ut ostendunt lineæ occultæ, quæ incipiunt ex ~M~ & ~N~. Earum quælibet ex vestigio ~C~ pervenit ad lineam visualem, & continuatur cum linea altitudinis ex visuali ad elevationem ~F~, & cum alia linea latitudinis ex elevatione ~F~ ad basim. Porrò ex figura constat, superficiem superiorem quadræ subduci oculis à columna, & aliquid ex parte postica tori quod cæteroqui conspiceretur, abscondi à quadra. Proinde torus, qui ex punctis maximæ latitudinis retrorsum flectitur, eousque delineandus est, quoad hinc inde occurrat quadræ ipsum cooperienti. Præstaret autem singula membra ita exactè delineari, quasi essent diaphana; ut partes oculis imperviæ, omnino cohæreant cum partibus quæ ipsis conspicuæ sunt._
_Completâ delineatione, si figuram tuam ex perpendiculo puncti oculi ex debita distantia contemplatus fueris, omnes defectus facilè deteges & statim corriges. Præcipuam diligentiam pones in formando & emendando toro, qui habet duas rotunditates; unam quatenus ambit columnam; alteram quatenus caret angulis, ut ostendit elevatio geometrica in ~I~._
The Sixteenth Figure.
_The ~Tuscan~ Base in Perspective._
From the Geometrical Elevation A, is drawn the Plan B; which being put into Perspective, as you see in C and D, from the Circles of the Plan C you have the Breadths of the Column, and of the List, and _Torus_ of the three Bases: And after the same manner, by the Plan D, you have the Breadth of the List and _Torus_ of the last Base. From the greatest Breadth of the Circles of the Plan C, we have erected Perpendiculars to the Parts that answer them in the Base, to the end that you may see where the Points fall, which terminate the greatest Breadth of those Parts. These Points (which in the biggest Circle of the Plan C are M and N) are found by touching the Extremity of the Circumference with a Line parallel to the Perpendicular E: for if the Figure were exact, that Line would touch every _Torus_ of the three Bases in the extreme Points of their Breadth.
The Heights of the four Bases are something more difficult to be found. Nevertheless, if you consider well the Elevation F, and the other two G and H, (which are made by transporting the Divisions of the Elevation A upon the Perpendicular E) it will plainly appear that there is no Point in the Circles of the Plan C, to which there may not be a correspondent Point found in the _Torus_ and List of the said Base; as the occult Lines shew, that arise from M and N; each of which is a Continuation of three Lines: The first of Breadth, from the Plan C to the Visual; the second of Height, from the Visual to the Elevation F; the third of Breadth, from the Elevation F to the Base. Now, tho’ it’s plain by the Figure, that the Body of the Column prevents the Sight of good part of the Fillet, and the same Fillet takes off from part of the _Torus_, which would otherwise be visible; for which Reason the Back-part of the _Torus_ is continu’d only till it meet the same: Yet it’s certainly best to draw every Member complete, as tho’ the Work were transparent; that the Parts hidden from the Eye may the better agree with those that are expos’d to it.
When your Draught is finish’d, if you view it at the due Distance, and perpendicularly to the Point of Sight; you’ll readily discover and rectify what’s amiss. Your chief Care will be employ’d in shaping the _Torus_, difficult by reason of its Roundness both ways; namely, in the Contour of its Moulding, as in the Elevation I; and in the Circuit it makes about the Column.
Figura Decimaseptima.
Deformatio basis Doricæ.
_Ad vitandam satietatem quam pareret nimia uniformitas, unam ex basibus invertimus. Utraque autem basis delineata est methodo quam tradidimus figurâ præcedenti. Eademque methodus adeò manifestè patet ex lineis occultis latitudinum & elevationum, ut superfluum futurum sit ipsam repetere._
The Seventeenth Figure.
_The ~Dorick~ Base in Perspective._
That you may not be tir’d with practising one and the same thing, I have here, for Variety-sake, inverted one of the Bases. Both of ’em are drawn after the Manner explain’d in the foregoing Figure; which is so evident from the occult Lines of the Plan and Elevation here given, that I think it superfluous to say any more of it.
Figura Decimaoctava.
Optica delineatio basis Ionicæ.
_Ex multitudine ac varietate figurarum hujus Operis, disces, mi Lector, modum deformandi res demissas & sublimes, magnas & parvas. In hac figura, linea cui bases duarum columnarum incumbunt, est conjunctim linea plani, & linea horizontalis; linea cui bases trium columnarum incumbunt, est altior linea horizontali. Quemadmodum autem, si linea plani sit inferior linea horizontali, lineæ quæ tendunt ad punctum oculi & ad punctum distantiæ, ascendunt sursum; ita si linea plani sit superior horizontali, lineæ quæ veniunt ad punctum oculi & ad punctum distantiæ, tendunt deorsum. Quòd si in eadem tabula sint plura plana, eorumque aliqua sint altiora, alia verò demissiora linea horizontali, lineæ omnes planorum, ac linea horizontalis, sunt invicem parallelæ; adeoque ex linea, quæ omnes eas normaliter secet, statim dignosci potest, in qua proportione, singula plana sint altiora vel profundiora linea horizontali. Velim quoque observes, latitudinem columnæ mediæ, minorem esse latitudine columnarum lateralium; & discrimen inter hujusmodi latitudines eò est majus, quò punctum distantiæ fuerit vicinius puncto oculi. Quæ dicta sunt de columnis, intelligere oportet de basibus, & de optica delineatione ambarum. Nihilominus, si figura ex debito puncto inspiciatur, columnæ pictæ habebunt eandem apparentiam, quam haberent columnæ solidæ, invicem æquales._
The Eighteenth Figure.
_The ~Ionick~ Base in Perspective._
By the Multitude and Variety of Figures in this Work, the Reader will be instructed in delineating things, however different in Size or Situation. In this Figure, the Line on which the two Columns rest, is both the Horizontal and the Ground-line; that on which the three Columns are plac’d, is so much higher than the Horizontal Line. And as, where the Ground-line is beneath the Horizontal, the Lines drawn to the Points of Sight and Distance tend upwards; so, where the same is above the Horizontal, the Lines to the Points of Sight and Distance tend downwards. If in the same Picture there are different Grounds, some higher, others lower than the Horizontal Line; yet are all those Ground-lines, and the Horizontal, parallel one to another; and therefore, by a Line cutting them all perpendicularly, you presently know in what proportion each Plan or Ground is higher or lower than the Horizontal. I would have you observe, That the Breadth of the middle Column is, by the Perspective, render’d less than that of the Side-Columns; and that this Difference is the greater, as the Point of Distance approaches nearer to the Point of Sight. What has been said of the Columns, is also to be understood of the Bases, and the Projections of all their Parts in Perspective: Nevertheless, if the Picture be view’d from its due Place, the Columns will have the same Effect, as if solid; and all appear equal one to the other.
Figura Decimanona.
Optica imminutio basis Corinthiæ.
_Hæc basis juxta regulas traditas opticè contracta est. Porrò altitudo superficiei ~A~ est eadem cum altitudine lineæ visualis ~CD~; latitudo crucis ~A~ est eadem cum latitudine crucis secundi circuli vestigii ~B~, incipiendo à minimo omnium. Duæ lineæ normaliter infixæ basi, ostendunt maximam latitudinem quam habere debet columna supra imum scapum. Maxima latitudo tori superioris & utriusque astragali, est eadem cum maxima latitudine tertii circuli. Maxima latitudo tori inferioris est eadem cum maxima latitudine ultimi circuli._
The Nineteenth Figure.
_The ~Corinthian~ Base in Perspective._
This Base is put in Perspective by the Rules before laid down. The Height of the Superficies A is the same with that of the visual Line CD; the Breadth of the Cross A is the same with that of the second Circle of the Plan B, beginning with the least. The two Lines that stand perpendicularly on the Surface of the Base, shew the greatest Breadth of the Columns Shaft above the Fillet. The Extent of the upper _Torus_ and the two Astragals, is the same with that of the third Circle; and the Extent of the lower _Torus_ is the same with that of the outward Circle.
FIGURA Vigesima.
Basis Acticurga opticè imminuta.
_Basis Acticurga Pictoribus præ reliquis familiaris est, quia cum omnibus ferè Ordinibus egregiè consentit. Porrò ex punctis ~E~ & ~F~ maximæ utrinque latitudinis extimi circuli vestigii, habetur maxima latitudo tori inferioris ~CD~. Ac cætera quæ spectant ad ipsum & ad torum ~AB~, petenda sunt ex dictis de basi Etrusca._
The Twentieth Figure.
_The ~Attick~ Base in Perspective._
The _Attick_ Base is more frequently made use of by Painters, than any other; because it suits well with most of the Orders. The Points E and F, the greatest Breadth of the outward Circle of the Perspective-Plan, give the greatest Breadth of the lower _Torus_ CD. And whatever else relates either to this or the upper _Torus_ AB, is to be sought in the same Manner, as has been shewn in the _Tuscan_ Base.
Figura Vigesimaprima.
Optica imminutio capitelli Etrusci.
_Eâdem cum 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._
The Twenty-first Figure.
_The ~Tuscan~ Capital in Perspective._
The Manner before deliver’d concerning Bases, is of the same Use in delineating Capitals; forasmuch as these also have their square _Abacus_, 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.
Figura Vigesimasecunda.
Optica projectio capitelli Dorici.
_Capitellum hoc pluribus membris constat, adeóque operosius est quàm præcedens. Nihilominus accurata delineatio vestigii geometrici omnes difficultates complanabit._
Twenty-second Figure.
_The Projection of a ~Dorick~ Capital, in Perspective._
This Capital 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.
Figura Vigesimatertia.
Deformatio capitelli Ionici.
_Capitellum Ionicum poscit duas elevationes geometricas distinctas, alteram faciei, alteram lateris; ex iisque conflatur vestigium geometricum ~A~, quod opticè contrahitur, translatis in ~B~ punctis latitudinis ~C~, & in ~E~ punctis longitudinis ~D~ more consueto: ut ex punctis ~B~ latitudinis, lineæ tendant ad punctum oculi; ex punctis verò ~E~ longitudinis, 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._
Twenty-third Figure.
_The ~Ionick~ Capital in Perspective._
The _Ionick_ Capital 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 the _Ionick_ Capital, whose Volutes lie obliquely, we shall hereafter treat of in the Thirtieth Figure.
Figura Vigesimaquarta.
Optica projectio capitelli Corinthii.
_Capitellum Corinthium absolvere non poteris, nisi elevatione geometrica ejusque vestigio exactissimè delineatis juxta regulas Barozzii._
_Ad formandum ex vestigio ~B~ vestigium ~E~, rectis occultis fient quadrata necessaria ad contractionem opticam quatuor vel trium saltem circulorum; translatis in lineam ~D~ divisionibus lineæ ~C~, & aliis, more consueto. Contrahentur deinde lineis occultis vestigia foliorum, & absolventur cætera quæ posita sunt in vestigio_ E.
_Ut fiat optica elevatio longitudinis ~F~, in lineam perpendicularem ~H~ transferentur ex elevatione ~A~ omnes 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 lineam ~D~, ac perveniant ad visualem ~G~; indeque descendant, ac sint parallelæ ad lineam perpendicularem_ H.
_Capitellum nitidum exordieris ab infimo circulo ~I~, ostendente ambitum columnæ. Succedent folia ~1~, ~2~, quorum latitudines accipientur ex vestigio ~E~ per circinum, positâ unâ ejus cuspide in linea ~H~; altitudines verò accipientur ex elevatione ~F~, posita una cuspide circini in linea ~D~. Idipsum dico tum de foliis ~3~, ~3~, ~4~, ~4~, tum de folio ~5~, ac de aliis, & demum de cymatio. Descensus verò lineæ curvæ ipsius cymatii incipiet ex acie ~L~._
Twenty-fourth Figure.
_The ~Corinthian~ Capital in Perspective._
There is no Completing the _Corinthian_ Capital, unless you most accurately describe its Geometrical Elevation and Plan, according to the Rules of _Vignola_.