Fig. vi.
Fig. vi.
Modus opticæ delineationis, absque lineis occultis.
Inhac figura sexta, vestigium geometricumBseorsim posui ab elevatione geometricaA, ut deinceps faciemus. VestigiumBopticè contractum inEestNMRS; elevatio contracta longitudinis vestigii estFTSN. Posito autem quòd altitudinesFN,1, 5,2, 6, sint æquales; latitudinesNM,1, 2,5, 6, sint æquales; & rectæNM,5,6, sint in lineaXplani; rectæFN,1, 5, sint in perpendiculoV: anguli3&4basisChabent eandem elevationem seu distantiam à lineaXplani, quam habet angulusT: anguli1&2habent elevationem, quam angulusF: anguli3&7habent eandem latitudinem seu distantiam à perpendiculoV, quam habet angulusR: anguli2&6habent eandem latitudinem, quam habet angulusM.
The Manner of designing in Perspective, without occult Lines.
Inthis sixth Figure, I have design’d the Geometrical Plan B separately from the Geometrical Elevation A, as I shall always do hereafter. The Plan B optically contracted, or put in Perspective, in E, is NMRS; the Elevation of its Length in Perspective is FTSN. Then supposing the Heights FN, 1,5, 2,6, equal; and the Breadths NM, 1,2, 5,6, equal; the Lines NM, 5,6, to be in the Line of the Plan X; and the Lines FN, 1,5, in the Perpendicular V: the Angles 3 and 4 of the Base C have the very same Elevation or Distance from the Line of the Plan X, as has the Angle T: the Angles 1 and 2 have the same Elevation with the Angle F: the Angles 3 and 7 have the same Breadth or Distance from the Perpendicular V, as the Angle R has: the Angles 2 and 6 have the same Breadth, as the Angle M has.
Fig. vii.
Fig. vii.
Aliud exemplum vestigii geometrici, cum elevatione longitudinis.
Sidelineanda sit basis dissecta in quatuor partes, fiat vestigiumAcum suis divisionibus longitudinisED& latitudinisCD. Easdem vero divisiones latitudinis habebit inEFelevatioBquæ pertingit usque adX. Porro ad contractionem opticam vestigii adhibebitur papyrus complicata in latum & in longum, transferendo in lineam plani latitudinem & longitudinem vestigii. Deinde nullo negotio fiet optica deformatio elevationis, ut clarè positum est in figura. Quomodo autem ex vestigio & ex elevatione longitudinis opticè imminutis eruatur basis nitida sine lineis occultis, ex præcedentibus manifestum est. Optarem ut per assiduam circini tractationem in hac methodo exercenda operam sedulò ponas; quum ex ea pendeat omnis facilitas delineationum opticarum.
Another Example of a Geometrical Plan and Upright, put in Perspective.
Fordrawing in Perspective a Pedestal, or Base, divided into four Parts, make the Plan A with its Divisions of Length ED, and of Breadth CD; and the same Divisions of Breadth EF, in the Elevation B, prolong’d to X. Then make the Perspective-Plan, by transferring the Breadth and Length into the Ground-line, by means of your Paper folded cross-wise. From which Plan the Perspective-Upright is very easily made, as may be plainly seen in the Figure. How the Base below, without occult Lines, is made from the Perspective-Plan and Upright, is manifest from what has been said before. I could wish you would be very diligent in the Practice of this Method by the Compass; because the Dispatch of Perspective-Delineations chiefly depends thereon.
Fig. 8.
Fig. 8.
Optica projectio stylobatæ.
Silibitum fuerit delineare stylobatam, cum projecturis in summo & imo, incipies ab elevatione geometricaA, ducendo occultas ad id necessarias, tum versus perpendicularemL, tum deorsum pro vestigio geometricoB, cujus distantiæ transferentur in spatiumG. Si mensuræ longitudinis distent spatioCà mensuris latitudinis, vestigium deformatum videbitur distare à lineaKplani, quantum est idem spatiumC. In construenda optica elevationeD, visuales ex punctis lineæLdabunt lineas latitudinis; lineas vero altitudinis accipies ex lineis vestigii contracti, ut in figura. In formando stylobata nitidoEF, locum anguliHdabit concursus latitudinis ex lineaLusque adM, & altitudinis ex lineaKusque adI. Concursus tum ejusdem altitudinis, tum latitudinis exLusque adO, dabit angulumN. Demum altitudinem anguliPaccipies exKusque adQ; latitudinem exLusque adR.
The Projection of a Pedestal in Perspective.
Ifyou would draw a Pedestal, with the Projecture of its Cap and Base, you must begin with the Geometrical Elevation A, by drawing such occult Lines as are necessary, as well sideways to the Perpendicular L, as downwards for making the Geometrical Plan B, whose Distances must be transferr’d, and carry’d into the Space G. If the Measures of the Length be placed the Distance of the Space C, from those of the Breadth, the Perspective-Plan will then appear removed within the Ground-line K, as much as the said Space C is. In the Construction of the Perspective Elevation D, the Visuals drawn from the Points of the Line L give the Lines of the Breadth; and those of the Height are taken from the Lines of the Perspective-Plan, as in the Figure. In delineating the clean or finish’d Pedestal EF, the Intersection of the Breadth from L to M, with the Height from K to I, gives the precise Place of the Corner H. The Intersection of the same Height with the Breadth LO gives the Angle N. Lastly, the Angle P is found by the Intersection of the Height KQ, with that of the Breadth LR.
Fig. ix.
Fig. ix.
Optica delineatio Architecturæ Jacobi Barozzii; & primum, de Stylobata Ordinis Etrusci.
Perspectivanusquam clariùs emicat, quàm in Architectura. Iccirco tibi ob oculos pono Architecturam Jacobi Barozzii, quem à patria nuncupantIl Vignola, reliquis fortasse usitatiorem; in eaque continetur elevatio geometrica singulorum quinque Ordinum, qui vocantur, Etruscus, Doricus, Ionicus, Corinthius, & Romanus, vel Compositus; delineando seorsim partes cujuscunque Ordinis in figuris grandioribus. Elevationi geometricæ suum vestigium nos addemus; ex vestigio autem & ex elevatione opticè deformatis, eliciemus apparentias solidorum juxta regulam traditam. Exempli gratia, si delineare velis stylobatam quadratum & pilam Ordinis Etrusci, præter elevationem geometricamAdelineare oportet vestigium geometricumB; ex ambobus autem opticè contractis formatur stylobata nitidusD, cum anta & pila existente ad latus, accipiendo altitudines à linea plani, latitudines à linea perpendiculari ad ipsum planum. In alia delineatione posuimus pilam ex adverso, ut eis omni modo delineandis assuescas.
Ad vitandam confusionem linearum, proderit ut figuræ fiant his nostris multò grandiores: in quem finem singulis paginis apposita est scala modulorum. Hoc nomine intelliguntur partes æquales, in quas dividuntur lineæ latitudinis & altitudinis elevationum geometricarum; ac lineæ latitudinis & longitudinis vestigiorum geometricorum. Si moduli sint parvi, subdividuntur singuli in duodecim partes; ac prout fuerint grandiores, subdividuntur in partes triginta, vel sexaginta, vel centumviginti.Modulos Etruscum Doricúmque in partes duodecim; reliquos autem in octodecim partiti sunt.
The Architecture ofVignolain Perspective; and first, of his Pedestal of theTuscanOrder.
Perspectivenever appears more graceful, than in Architecture; for which Reason I present you with that ofJames Barozzi, from his Country generally call’dVignola; which perhaps is more in use than any other; and contains the Geometrical Upright of each of the five Orders,viz.theTuscan,Dorick,Ionick,Corinthian, and theRoman, orComposite; together with a separate Delineation of the Parts of each Order, in larger Figures. To this Geometrical Elevation we shall add the Plan, and, from both of them reduc’d into Perspective, shall draw the Appearances of Solids, according to the Rule before laid down. For Example: If you would draw the squareTuscanPedestal, and its Pilaster, you must, from the Geometrical Elevation A, make the Geometrical Plan B; and from both of them reduc’d in Perspective, draw the finish’d Pedestal D, with that of its Pilaster on the Side, by taking the Heights from the Ground-line, and the Breadths from a Line perpendicular to the same. On the other Side we have placed the Pilaster on the Back-part, that you may practise the Drawing them in any manner.
For avoiding the Confusion of Lines, I advise you to make the Figures as much larger than ours as you can; for which purpose there is annex’d a Scale of Modules to each Figure. By this Name we understand the equal Parts, into which the Lines of the Breadth and Height of the Geometrical Uprights, and of the Breadth and Length of the Geometrical Plans, are divided. If the Modules are small, they are subdivided into twelve Parts; and according as they are larger, into thirty, sixty, or an hundred and twenty Parts.I have divided theTuscanandDorickModule into twelve Parts, and that of the other Orders into eighteen.
Fig. 10.
Fig. 10.
Optica deformatio stylobatæ Dorici; ubi de modo vitandi confusionem, in vestigiis delineandis.
ElevatiogeometricaBstylobatæ Dorici continet eandem symmetriam partium quæ habetur apud Barozzium; ex eaque eruitur vestigium geometricumAper lineas occultas, quæ descendant ex punctis terminativis præcipuarum projecturarum. Earundem projecturarum distantiæ transferendæ sunt in lineam elevationis, notando puncta quæ necessaria sunt ad deformandam elevationem longitudinis stylobatæ.
Si ob propinquitatem lineæ plani ad lineam horizontis, vestigium evadat confusum, fiant in distantia congrua sub linea plani aliæ lineæ planorum ipsi parallelæ, cum suis vestigiis. Quid autem emolumenti afferat distantia major præ minori, ostendit vestigiumEdistinctiùs vestigioD. Singula hæc vestigia fiunt notando in linea cujuslibet plani mensuras latitudinis & longitudinis vestigiiA, & ducendo lineas ad eadem puncta oculi ac distantiæ.
Stylobatam nitidum descripsimus ex parteG, tum ex necessitate, tum ut videas, pro distantiaFO, usurpandam esse distantiamGOpenitus æqualem.
ADorickPedestal in Perspective; with the Manner of avoiding Confusion, in designing the Plans.
TheGeometrical Elevation B has the same Members and Proportions, as theDorickPedestal ofVignola; and the Geometrical Plan A is form’d, by letting fall occult Lines from the principal Projectures of the Upright. Occult Lines are also to be continued to the Perpendicular F, from the several Members requisite for elevating in Perspective the Length of the Pedestal.
When, by reason of the too near Approach of the Ground-line to that of the Horizon, the Plan becomes thereby confus’d; draw at a convenient Distance underneath, other Ground-lines parallel to the first; together with the Plans in Perspective. And of what Advantage the Removal of the Ground-line is, is evident from the Plan E, which is much more distinct than the Plan D. Each of these Plans is made, by marking upon its respective Ground-line the Measures of the Breadth and Length of the Plan A, and by drawing Lines to the same Points of Sight and Distance, which were first assign’d.
We have placed the finish’d Pedestal on the Side G, partly for want of Room, and partly to shew, that the Point of Distance G is there made use of, GO being equal to FO.
Fig. xi.
Fig. xi.
Stylobatæ Ionici deformatio; ubi de vitanda confusione in elevationibus.
Tumin figura præcedenti, tum rursus in hac, ostendimus quid agendum sit ubi vestigiaAAnimium obliquentur, unde oritur confusio; præcipuè in lineis parallelis quæ exhibent latitudines. Non minor difficultas interdum occurret in elevationibus longitudinis opticè deformandis; quòd videlicet, ob nimiam earum obliquitatem, pervium non sit altitudines singularum projecturarum probè discernere ac designare. Ad scopulos istos declinandos, loco elevationisBadhibebitur elevatioC, quæ distinctior est, tum illâ, tum duabus intermediisD&E, ob majorem distantiam quam habet à puncto oculi.
In delineando stylobata nitido, latitudines accipientur ex ultimo vestigio, ponendo unam cuspidem circini in linea perpendiculari, quæ proxima est literæO: altitudines accipientur ex elevationeC, ponendo unam cuspidem circini in linea plani, ut in præcedentibus ostensum est.
TheIonickPedestal in Perspective; with the Manner of avoiding Confusion, in Elevations.
Asin 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.
FIG. XII.
FIG. XII.
Deformatio stylobatæ Corinthii, cum duabus pilis.
Ornatusgratiâ, 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 estA; vestigium ejus geometricum estB: pilæCC. Vestigium opticè contractum estD, elevatio longitudinis stylobatæ opticè contracta estE, ac methodo consuetâ ex iis eruetur stylobata nitidus cum suis pilis.
TheCorinthianPedestal, with its Pilasters, in Perspective.
ForOrnaments sake, we have added to thisCorinthianPedestal 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 fromVignola; 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.
FIG. XIII.
FIG. XIII.
Projectio stylobatæ, ordinis Compositi.
Quumpagina 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 estB; vestigium geometricum estA. Ex his eruitur optica delineatio vestigiiC& elevationisD. Ac postea formatur stylobata nitidusE, accipiendo latitudines ex vestigioC, altitudines ex elevationeD.
The Projection of a Pedestal, of the Composite Order, in Perspective.
WantingRoom 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.
Fig. xiv.
Fig. xiv.
Deformatio circulorum.
Utstylobatis 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 geometricumAconstat 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 circuliB. Si addere velimus alium circulum, vestigio geometricoCinscribetur aliud quadratum; indeque habebitur optica delineatio duplicis circuliD. Inter hos duos quomodo liceat describere tertium, per octo sectiones quadratorum, ostendunt figuræE&F. Uno verbo, circuli describuntur per quadrata, adhibendo sectiones visualium cum parallelis ad lineam plani; ac nullum est punctum in quadratis & circulisA,C,E, cui per sectiones illas nequeat inveniri punctum correspondens in quadratis & circulisB,D,F. Nihilominus ubi opus habeas pluribus circulis, autor tibi sum ne multiplices quadrata, plus confusionis allatura tibi quam adjumenti.
Circles in Perspective.
Thatupon 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.
Fig. xv.
Fig. xv.
Optica delineatio Columnæ.
Descripturifrustum cylindricumIuniforme, fiet elevatioA, & vestigium geometricumB, saltem quoad medietatem. Ex hoc opticè deformato, ut vides inC, ducendæ sunt parallelæ tum latitudinis ad visualemD, tum elevationis ad visualemE; ex quibus describentur circuli opticè contractiF&L, accipiendo latitudines ex vestigioC, altitudines ex perpendiculariM; & juxta hanc methodum circuliF&Lfiunt sine ope quadratorum. Demum ducendæ sunt perpendicularesG&H, quæ tangant circulosF&Lin punctis terminativis maximæ latitudinis.
Nullum est punctum in vestigioC, cui per lineas latitudinis & elevationis nequeat inveniri locus correspondens in circuloF. Exempli gratia; locus puncti7est punctum6. Hunc autem locum habemus per tres lineas,CD,DE,E7.
In delineandis duobus frustis cylindricis, cum summo & imo scapo, eandem regulam servare oportebit.
A Column in Perspective.
Beingto 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.
Fig. xvi.
Fig. xvi.
Optica projectio basis Etruscæ.
Exelevatione geometricaAeruitur vestigiumB. Hoc autem deformato inC&D, ex circulis vestigiiChabentur latitudines columnæ, quadræ, ac tori triplicis basis: & eodem modo ex vestigioDhabentur latitudines quadræ ac tori ultimæ basis. Ex maximis latitudinibus circulorum vestigiiCereximus perpendiculares ad partes quæ ipsis respondent in basi; ut agnoscas quænam sint puncta maximæ latitudinis in eisdem partibus. Hæc puncta (quæ in circulo maximo vestigiiCsuntM&N) invenientur tangendo circumferentiam uniuscujusque circuli regulâ parallelâ ad lineam perpendicularemE, 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 elevationisF, aliarumque duarum, (quæ factæ sunt, notatis in linea perpendiculariEdivisionibus desumptis ex elevatione geometricaA) constabit, nullum esse punctum in circulis vestigiiC, cui nequeat inveniri punctum correspondens in toro & quadra ipsius basis, ut ostendunt lineæ occultæ, quæ incipiunt exM&N. Earum quælibet ex vestigioCpervenit ad lineam visualem, & continuatur cum linea altitudinis ex visuali ad elevationemF, & cum alia linea latitudinis ex elevationeFad 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 inI.
TheTuscanBase in Perspective.
Fromthe 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, andTorusof the three Bases: And after the same manner, by the Plan D, you have the Breadth of the List andTorusof 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 everyTorusof 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 theTorusand 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 theTorus, which would otherwise be visible; for which Reason the Back-part of theTorusis 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 theTorus, 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.
Fig. xvii.
Fig. xvii.
Deformatio basis Doricæ.
Advitandam 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.
TheDorickBase in Perspective.
Thatyou 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.
FIG. XVIII.
FIG. XVIII.
Optica delineatio basis Ionicæ.
Exmultitudine 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.
TheIonickBase in Perspective.
Bythe 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.
Fig. xix.
Fig. xix.
Optica imminutio basis Corinthiæ.
Hæcbasis juxta regulas traditas opticè contracta est. Porrò altitudo superficieiAest eadem cum altitudine lineæ visualisCD; latitudo crucisAest eadem cum latitudine crucis secundi circuli vestigiiB, 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.
TheCorinthianBase in Perspective.
ThisBase 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 upperTorusand the two Astragals, is the same with that of the third Circle; and the Extent of the lowerTorusis the same with that of the outward Circle.
Fig. xx.
Fig. xx.
Basis Acticurga opticè imminuta.
BasisActicurga Pictoribus præ reliquis familiaris est, quia cum omnibus ferè Ordinibus egregiè consentit. Porrò ex punctisE&Fmaximæ utrinque latitudinis extimi circuli vestigii, habetur maxima latitudo tori inferiorisCD. Ac cætera quæ spectant ad ipsum & ad torumAB, petenda sunt ex dictis de basi Etrusca.
TheAttickBase in Perspective.
TheAttickBase 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 lowerTorusCD. And whatever else relates either to this or the upperTorusAB, is to be sought in the same Manner, as has been shewn in theTuscanBase.