Chapter V: THAT the Author’s Advice of taking the Figures in Course, be strictly (1)

follow’d in the Practice; which will be a great means to render the Whole easy and pleasant.

THIS is the Sum of what we thought most proper to advertise you; and have only this farther to request, That if any Mistakes may have escap’d the Press undiscover’d, as we well hope there are few or none, you will favourably correct and pardon them.

MONITA ad TYRONES.

_Concinnitatem ac symmetriam opticæ delineationes ædificiorum habere nequeunt, nisi utramque mutuentur ab Architectura. Proinde necesse est, ut in istius graphide ac intelligentia te aliquandiu exerceas, donec uniuscujusque elevationis vestigium formare didiceris, ex eoque eruere sectionem totius longitudinis, ut in Opere toto videre est, præsertim figuris sexagesimaoctava & septuagesima. Siquidem ex vestigio & ex sectione derivatur in opticas imagines congrua rerum singularum profunditas._

_Subjiciam his consilium summi momenti; videlicet, egregiè intelligas oportet figuram secundam, priusquam progrediaris ad tertiam, idemque de cæteris dictum velim; nam singulas eo disposuimus ordine, ut quæ præcedit, necessaria sit ad percipiendas eas quæ sequuntur. Si aliqua sint in explicatione, quæ initio non intelligas, ipsum schema sæpius diligenter inspicies; ac vicissim si aliqua desint in schematibus, ex declarationibus ea supplebis. Lapsus verò quos deprehenderis, facilè pro tua benignitate, mihi, ut spero, condonabis._

ADVICE to BEGINNERS.

The Perspective of Structures here treated of, can have no Grace or Proportion, without the Help of Architecture. ’Tis therefore absolutely necessary, that you employ yourself for some time in Drawing, and the Study of that Art; till you can readily describe the Plan of any Upright, and from thence project the Section or Profile, as is shewn through the whole Course of this Work; and more particularly, in the Sixty-eighth and Seventieth Figures: Forasmuch as the proper Depth of each Part of the Perspective, is determin’d by the Plan and Profile thereof.

I shall add this one thing more, which is indeed of the last Importance; to wit, that you endeavour to understand the Second Figure throughly, before you proceed to the Third; and so of the rest: they being dispos’d in such Order, that the Knowledge of the preceding Figure is always necessary to a right Understanding of that which follows. If you meet with any thing which at first seems difficult in the Description, a diligent Inspection of the Figure may relieve you: And on the other hand, if you find not in the Figure every thing you desire, you may have Recourse to the Explanation. What Errours you discover in the Work, I hope you’ll generously overlook and pardon.

AD

Lectorem Perspectivæ studiosum.

_Ars Perspectiva, oculum, licet sagacissimum inter sensus nostros exteriores, mirabili cum voluptate decipit; eademque necessaria est iis, quibus in pingendo, tum singulis figuris positionem ac deformationem suam congruè tribuere, tum colores & umbras, magis vel minus intendere aut remittere, prout oportet, curæ est. Ad id autem sensim sine sensu illi perveniunt, qui solo studio Graphidis non contenti, singulis Architecturæ Ordinibus exactè deformandis assueverint. Nihilominus, inter multos qui opus hujusmodi magno impetu aggressi hucusque fuerunt, paucos numeramus, qui animum ipso statim initio non desponderint, ob magistrorum librorumque penuriam, ordinatè ac perspicuè docentium opticas projectiones, à principiis hujus artis, usque ad omnimodam perfectionis consummationem. Quum autem sentiam, longâ multorum annorum exercitatione, me non minimam facilitatem in hac disciplina mihi parasse: censeo Studiosorum voluntati me satisfacturum, eorumque profectui consulturum, si methodos expeditissimas in lucem proferam, ad singulorum Architecturæ Ordinum opticas delineationes perficiendas, adhibitâ communi regulâ, ex qua omnia linearum occultarum offendicula sustulimus. Deinde, si tempus & vires ad aliud Opus conscribendum Bonitas Divina dederit, projectiones quascunque absolvemus regulâ qua in præsentia uti soleo, ac multò facilior & universalior est regula communi & vulgata, quamvis hæc sit fundamentum alterius. Itaque, Lector studiose, constanti animo negotium tuum suscipe; ac lineas omnes tuarum operationum, ad verum oculi punctum ducere, ad gloriam scilicet DEI O.M. tecum omninò decerne. Sic votis honestissimis, ut auguror tibi ac spondeo, feliciter potieris._

TO

The Lovers of Perspective.

The Art of PERSPECTIVE does, with wonderful Pleasure, deceive the Eye, the most subtle of all our outward Senses; and is very necessary to be known of all, who in Painting would give a due Place and Proportion to their Figures, and more or less Strength requisite to the Lights and Shades of the Picture. This might be insensibly attain’d, if Persons, not content with the Study of Drawing only, would accustom themselves exactly to delineate the several Orders of Architecture. Nevertheless, among many who have hitherto vigorously undertaken this Work, there have been but very few, who have not been in a manner quite discourag’d, through want of Masters and Books to teach them clearly and methodically the Rules of Perspective-Projections, from the first Principles of the Art, to the entire Perfection thereof. Wherefore, apprehending that by long and constant Practice in Works of this kind, I had acquir’d a Method to facilitate the same; I judg’d it might be for the Satisfaction and Advantage of the Studious, to publish the shortest way for designing in Perspective the several Orders of Architecture, by a common and easy Rule, free from the Incumbrances of occult Lines. But if it please God to give me Life and Health to compose another Book, I shall therein shew the Method of putting Works into Perspective by the Rule I make use of at present, which is more easy and general than the common way, though this be the Foundation of the other. Therefore, Reader, my Advice is, that you chearfully begin your Work, with a Resolution to draw all the Lines thereof to that true point, the Glory of GOD; and I durst predict, and promise you good Success in so honourable an Undertaking.

THE

Approbation of this Edition.

At the Request of the Engraver, We have perus’d this Volume of PERSPECTIVE; and judge it a WORK that deserves Encouragement, and very proper for Instruction in that ART.

_Chr. Wren_,
_J. Vanbrugh_,
_N. Hawksmoor_.

POZZO’s

ARCHITECTURE IN PERSPECTIVE.

FIGURA PRIMA.

Explicatio linearum Plani & Horizontis, ac Punctorum Oculi & Distantiæ.

_Ut principia Perspectivæ faciliùs intelligas, pono tibi ob oculos Templum, in cujus interiori facie, præter cætera, pingendum sit aliquid ad Perspectivam pertinens. Templi hujus vestigium geometricum est ~A~, elevatio geometrica in longum est ~B~, in latum est ~C~. In ~A~ est locus Hominis aspicientis lineam ~DE~, cui paries pingendus incumbit. In ~B~ idem Homo ex eâdem distantiâ intuetur lineam ~FG~, quæ refert elevationem parietis. In figura ~C~ supponimus Hominem consistere è regione ipsius parietis: easdemque proportiones mensuratum translatas esse ex vero pariete in figuram ~C~, quæ ipsum in parvo repræsentat._

_Prima ergo linea ~HI~ dicitur linea terræ vel plani, ex quâ incipit, eidemque incumbit ædificium. Secunda linea ~NON~ priori parallela, dicitur horizontalis, in quâ ponitur ~O~ punctum oculi, & ~N~ punctum distantiæ. Duo autem puncta distantiæ à nobis posita sunt, ut unum adhibeas ex quâ parte volueris; nam ad figuras opticè contrahendas sufficit unum punctum distantiæ: nec fieri potest ulla optica delineatio, quin primo loco designentur duæ parallelæ, una plani seu terræ, altera horizontis, notando in lineâ horizontis, punctum oculi, seu opticum, & punctum distantiæ. Porrò unam eandemque rem triplici Schemate repræsentare oportuit, ut videas, locum ex quo aspicienda est figura ~C~ esse punctum ~N~ unius ex rectis ~NO~, quam concipere debemus veluti normaliter infixam in ~O~; ac distantiam inter ~O~ & ~N~ eandem esse debere cum distantiâ inter ~A~ & ~DE~, inter ~B~ & ~GF~._

_In picturis multum spatii occupantibus, punctum oculi poni solet in medio lineæ horizontalis: atque ubi altitudo picturæ sit major latitudine, distantia ~NO~ fiet æqualis altitudini. Si latitudo picturæ sit major altitudine, distantia ~NO~ fiet æqualis latitudini; ita enim unico intuitu totum picturæ spatium comprehendi poterit. Porrò quamvis eadem distantia diverso modo adhibeatur in vestigio ~A~, & in elevationibus ~B~ & ~C~; nihilominus sectiones visualium cum pariete vestigii ~A~, & elevationis ~B~, omninò conspirant cum sectionibus visualium figuræ ~C~._

_Jam si velimus ut spectatori in ~A~ & ~B~ paries depictus videatur distare à lineis ~DE~ & ~GF~, quanta est longitudo quadrati ~P~, cujus elevatio est ~Q~; ex punctis ~A~ & ~B~ fiant visuales ad puncta extrema quadrati, notando sectiones visualium cum pariete ~DE~ & ~GF~, qui ab aliis vocatur velum, vitrum diaphanum, sectio, tela, vel tabula. Invenies autem, lineas ~RS~ ac ~TV~ esse æquales, ac similiter lineas ~XZ~ & ~YK~; & sic de aliis._

The First Figure.

_Explication of the Lines of the Plan and Horizon, and of the Points of the Eye and of the Distance._

That you may the better understand the Principles of Perspective, here is presented to your View a Temple, on the inner Wall of which, amongst other things, one would paint something in Perspective. The Geometrical Plan of this Church is A, the Geometrical Elevation, or Upright, lengthwise is B, breadthwise is C. In A is the Place from whence a Man beholds the Line DE, which is the Plan of the Wall that is to be painted: In B the same Man, from the same Distance, looks upon the Line FG, that represents the Elevation of the Wall. In Fig. C, the Man is supposed to stand opposite to the said Wall; and this Figure contains, in Little, the very same Proportions of Measures transferr’d from the real Wall.

The first Line therefore HI is call’d the Ground-line, or Line of the Plan, at which the Edifice begins, and on which it stands. The second Line NON, parallel to the former, is call’d the Horizontal Line, wherein is plac’d O the Point of the Eye, and N the Point of the Distance. Two Points of Distance are here laid down, that you may make use of which you please; for that on one Side only is sufficient for the fore-short’ning Figures in Perspective: Neither can any Optick Delineation, or Perspective, be described, without first making two Parallels; one of the Plan, or Ground-line, the other of the Horizon; marking, in the Line of the Horizon, the Point of the Eye, or Sight, and the Point of Distance. It was thought besides expedient to put one and the same Thing into three Schemes or Designs, to let you see, that the Place, from which the Figure C is to be look’d upon, is the Point N, one of the right Lines NO, which must be conceived as fixt at right Angles into O; the Distance ON being the same as that between A and DE in the Plan, or between B and GF in the Upright.

In Pictures taking up a great deal of Room, the Point of Sight ought to be made in the middle of the Horizontal Line; and where the Height of the Picture happens to be greater than the Breadth, the Distance NO must be made equal to the Height. If the Breadth of the Picture exceed the Height, the Distance NO must be made equal to the Breadth: For so will the Extent of the Picture be the better comprehended, or receiv’d, at one View. And altho’ the same Distance may seem to be used in a different manner in the Plan A, and in the Elevation B, from what it is in C; nevertheless the Sections of the visual Rays, with the Wall of the Plan A, and of the Elevation B, have a perfect Correspondence with the Sections of those of the Figure C.

Now, if to the Spectator in A and B, we would have the farthest Part of the Work seem to recede from the Lines DE and GF, as much as the Square P does, whose Elevation is Q; draw from the Points A and B, the visual Rays to the extreme Points of the Square P and Q; noting the Sections they make with the Walls DE and GF; which by some is call’d the Veil, Transparent Medium, Section, Cloth, or Table: and you’ll find RS equal to TV, XZ equal to YK; and so of the rest.

FIGURA Secunda.

Modus delineandi opticè Quadratum.

_Ante descriptionem opticam quadrati ~A~, quod fingimus delineatum esse in papyro separatâ, ducendæ sunt duæ lineæ parallelæ; altera plani, altera horizontis, ut jam docuimus; notando in linea horizontis punctum oculi ~O~, & punctum distantiæ ~E~. Tum translatâ in lineam plani latitudine ac longitudine ipsius quadrati ~A~, ita ut linea ~CB~ sit æqualis latitudini, & ~DC~ sit æqualis longitudini. Ex punctis ~B~ & ~C~ fiunt visuales ~BO~, ~CO~ ad punctum oculi; ex puncto ~D~ fit recta ~DE~ ad punctum distantiæ. Demum ubi visualem ~CO~ secat recta ~DE~, fit ~GF~ parallela ad ~CB~; habesque quadratum opticè contractum._

_Compendium temporis & laboris facies, præsertim in schematibus quæ abundant lineis, si chartulam in medio complicaveris, eademque utaris, ut latitudinem ac longitudinem quadrati transferas in lineam plani._

The Second Figure.

_Manner of delineating a ~Square~ in Perspective._

Before the _Square_ A, which is supposed to be drawn on a separate Paper, can be laid down in Perspective, two parallel Lines must be drawn; one of the Plan, the other of the Horizon, as is already intimated; noting in the Horizontal Line the Point of Sight O, and the Point of Distance E. Then, when the Length and Breadth of the Square A shall be transferr’d into the Line of the Plan, so that the Line CB be equal to the Breadth, and DC be equal to the Length, let the visual Lines BO, CO be drawn from the Points B and C to the Point of Sight O, and the right Line DE from the Point D to the Point of Distance. Lastly, where the Line DE cuts the Visual CO, make GF parallel to CB: and you have the _Square_ Optically contracted, or fore-shorten’d in Perspective.

To spare Time and Pains, especially in Figures that abound in Lines, fold your Paper in the middle, and make use of it to transfer the Breadth and Length of the Square, into the Line of the Plan.

FIGURA TERTIA.

Optica delineatio rectanguli, alterâ parte longioris.

_Latitudo ~BC~ rectanguli ~A~ ponatur in linea plani, adhibito circino, vel chartulâ complicatâ; & ex punctis ~B~ & ~C~ fiant visuales ad ~O~, punctum perspectivæ. Tum papyro ex altera parte iterum complicatâ, notetur longitudo ~CD~ rectanguli; ducendo tum rectam ~DE~ ad punctum distantiæ, tum rectam ~FG~ parallelam ad ~BC~, quæ complebit opticam delineationem rectanguli._

_Altera figura ostendit complicationem cruciformem papyri, quæ adhiberi potest in delineandis rectangulis, seu latitudo eorum sit major longitudine, aut vice versâ; seu latitudo & longitudo sint æquales._

The Third Figure.

_The Delineation of an Oblong ~Square~ in ~Perspective~._

Let the Breadth BC of the Square A, be plac’d in the Line of the Plan, by the Compass, or a folded Paper, and from the Points B and C, make the Visuals to the Point of Sight O. Then fold your Paper cross-wise, and mark CD the Length of the Square, drawing the Line DE to the Point of Distance, and the Line FG parallel to BC, which will complete the Optick Delineation of the oblong Square.

The other Figure shews the Folding of the Paper cross-wise, which is of ready use in delineating Squares, whose Breadth exceeds their Length, or _vice versâ_; or whose Length and Breadth are equal.

FIGURA QUARTA.

Optica descriptio quadrati duplicis.

_Iam incipies frui compendio papyri complicatæ. Nam eam admovendo lineæ plani, nullo negotio notare poteris puncta ~1~, ~2~, ~3~, ~4~, ~5~, ~6~, linearum visualium, quæ ducentur ad ~O~ punctum perspectivæ. Exinde complicatâ rursum chartulâ in crucem ad ~P~, notabuntur hæc puncta; ~7~, coincidens cum puncto ~6~, nisi quadratum distet à linea plani; ~8~, ~9~, ~10~. Ductis autem rectis ex ~8~, ~9~, ~10~, ad punctum ~E~, ubi secant visualem ~6~, ~7~, ~O~ fient parallelæ, eritque completa delineatio._

_In medio quadrati ~B~, aliud quadratum facilè describetur, ducendo diagonales seu diametros ab angulo ad angulum, ut in figura._

The Fourth Figure.

_The Optical Delineation of a double Square._

Here you’ll find the Advantage of your folded Paper; for, applying it to the Line of the Plan, you readily mark the Points 1, 2, 3, 4, 5, 6, of the visual Lines, which must be drawn to the Point of Sight O. Then folding the Paper cross-wise, as in P, you mark the Points 7, 8, 9, 10, placing the Point 7 on that of 6, unless you would have the Square removed within the Line of the Plan. Then from 8, 9, 10, drawing Lines to the Point of Distance E; where they intersect the Line 6, 7, O, draw Parallels to the Line of the Plan; and your Work is done.

Within the Square B, you may easily inscribe another Square, by help of the Diagonals; as may be seen in the Figure.

FIGURA QUINTA.

Vestigia quadratorum, cum elevationibus.

_Suppositis iis quæ jam diximus de Contractione optica Quadratorum, notandum est, vestigium primi Quadrati distare à linea plani spatio ~BA~ opticè contracto; quia linea ~BD~ habet à visuali ~AO~, distantiam ~BA~. Eodem modo Quadratum secundum distat à linea plani spatio ~EA~, & sic deinceps._

_Velim observes, in omnibus his Quadratis lineas longitudinis esse partes visualium, lineas vero latitudinis esse parallelas lineæ plani, & in primo Quadrato duci ex punctis, in quibus lineæ ~BD~, ~CD~, tendentes ad punctum distantiæ, secant visualem ~AO~._

_Sub singulis vestigiis Quadratorum, delineavimus alia omnino similia, per quæ parvo labore fient tres bases, erigendo ad libitum duas primas perpendiculares æquales; ac ducendo tum duas visuales ad punctum oculi ~O~, tum reliquas, ut in figura. Supponendum est autem, geometricam altitudinem cujuslibet rei desumi ex lineis normalibus ad lineam plani; quemadmodum latitudo & longitudo geometrica desumuntur ex eadem linea plani._

_Tres aliæ bases inferiores formantur sine lineis occultis ex vestigio & ex elevatione longitudinis opticè deformatis, adhibendo solas altitudines ac latitudines angulorum. Nomine altitudinis intelligimus distantiam cujuslibet anguli à linea plani; nomine latitudinis intelligimus distantiam anguli ab una aliqua linea normali ad lineam plani; dummodo hæ normales eandem habeant positionem respectu basium, & respectu vestigiorum & elevationum. Quemadmodum autem per concursum altitudinis ~FG~, & latitudinis ~HI~, ope duorum circinorum invenitur unus angulus in una basi; ita inveniuntur cæteri tum in ea, tum in reliquis._

The Fifth Figure.

_Plans of Squares, with their Elevations._

Besides what has been already said of the fore-short’ning of Squares in Perspective, it is convenient to observe, That the Foot of the first Square is here set within the Line of the Plan, as much as the Space BA optically contracted; because the Line BD has the Distance BA from the Visual AO: And in like manner, the second Square is distant from the Line of the Plan the Space EA; and so for the rest.

I would have you observe in all these Squares, That by the _Length_ I always understand part of the visual Lines, and by the _Breadth_ those parallel to the Ground-line; which in the first Square are drawn from the Points in which the Lines BD, CD, tending to the Point of Distance, intersect the Visual AO.

Under the Plans of these Squares are described three others just like them, which are easily converted into three Bases, by erecting, at pleasure, the two first Perpendiculars of equal Height, and thence drawing two Visuals to the Point of Sight O, which also bound the rest, as in the Figure. Observe also, That the Geometrical Height of every thing is to be set perpendicularly from the Ground-line, or Line of the Plan, as the Geometrical Length and Breadth are also placed on the same Line.

The three other Bases below are form’d without the Help of Occult Lines, by making use only of the Heights and Breadths of the Angles, taken from the Perspective Plan and Upright. By _Height_ I understand the Distance of each Angle, or Corner, from the Ground-Line; By _Breadth_, the Distance of an Angle, or Corner, from any Line perpendicular to the Ground-line; provided these Lines have always the same Place in respect of the Bases, as they have in respect of the Perspective Plan and Upright. And as, by the Help of two Compasses, the Height FG, and the Breadth HI determine the Corner of the first Base; so, in like manner, are found the Corners of the other Bases.

FIGURA SEXTA.

Modus opticæ delineationis, absque lineis occultis.

_In hac figura sexta, vestigium geometricum ~B~ seorsim posui ab elevatione geometrica ~A~, ut deinceps faciemus. Vestigium ~B~ opticè contractum in ~E~ est ~NMRS~; elevatio contracta longitudinis vestigii est ~FTSN~. Posito autem quòd altitudines ~FN~, ~1, 5~, ~2, 6~, sint æquales; latitudines ~NM~, ~1, 2~, ~5, 6~, sint æquales; & rectæ ~NM~, ~5,6~, sint in linea ~X~ plani; rectæ ~FN~, ~1, 5~, sint in perpendiculo ~V~: anguli ~3~ & ~4~ basis ~C~ habent eandem elevationem seu distantiam à linea ~X~ plani, quam habet angulus ~T~: anguli ~1~ & ~2~ habent elevationem, quam angulus ~F~: anguli ~3~ & ~7~ habent eandem latitudinem seu distantiam à perpendiculo ~V~, quam habet angulus ~R~: anguli ~2~ & ~6~ habent eandem latitudinem, quam habet angulus ~M~._

The Sixth Figure.

_The Manner of designing in Perspective, without occult Lines._

In this 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.

FIGURA SEPTIMA.

Aliud exemplum vestigii geometrici, cum elevatione longitudinis.

_Si delineanda sit basis dissecta in quatuor partes, fiat vestigium ~A~ cum suis divisionibus longitudinis ~ED~ & latitudinis ~CD~. Easdem vero divisiones latitudinis habebit in ~EF~ elevatio ~B~ quæ pertingit usque ad ~X~. 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._

The Seventh Figure.

_Another Example of a Geometrical Plan and Upright, put in Perspective._

For drawing 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.

FIGURA OCTAVA.

Optica projectio stylobatæ.

_Si libitum fuerit delineare stylobatam, cum projecturis in summo & imo, incipies ab elevatione geometrica ~A~, ducendo occultas ad id necessarias, tum versus perpendicularem ~L~, tum deorsum pro vestigio geometrico ~B~, cujus distantiæ transferentur in spatium ~G~. Si mensuræ longitudinis distent spatio ~C~ à mensuris latitudinis, vestigium deformatum videbitur distare à linea ~K~ plani, quantum est idem spatium ~C~. In construenda optica elevatione ~D~, visuales ex punctis lineæ ~L~ dabunt lineas latitudinis; lineas vero altitudinis accipies ex lineis vestigii contracti, ut in figura. In formando stylobata nitido ~EF~, locum anguli ~H~ dabit concursus latitudinis ex linea ~L~ usque ad ~M~, & altitudinis ex linea ~K~ usque ad ~I~. Concursus tum ejusdem altitudinis, tum latitudinis ex ~L~ usque ad ~O~, dabit angulum ~N~. Demum altitudinem anguli ~P~ accipies ex ~K~ usque ad ~Q~; latitudinem ex ~L~ usque ad ~R~._

The Eighth Figure.

_The Projection of a Pedestal in Perspective._

If you 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.

FIGURA NONA.

Optica delineatio Architecturæ Jacobi Barozzii; & primum, de Stylobata Ordinis Etrusci.

_Perspectiva nusquam clariùs emicat, quàm in Architectura. Iccirco tibi ob oculos pono Architecturam Jacobi Barozzii, quem à patria nuncupant ~Il 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 geometricam ~A~ delineare oportet vestigium geometricum ~B~; ex ambobus autem opticè contractis formatur stylobata nitidus ~D~, 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 Ninth Figure.

_The Architecture of ~Vignola~ in Perspective; and first, of his Pedestal of the ~Tuscan~ Order._

Perspective never appears more graceful, than in Architecture; for which Reason I present you with that of _James Barozzi_, from his Country generally call’d _Vignola_; which perhaps is more in use than any other; and contains the Geometrical Upright of each of the five Orders, _viz._ the _Tuscan_, _Dorick_, _Ionick_, _Corinthian_, and the _Roman_, or _Composite_; 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 square _Tuscan_ Pedestal, 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 the ~Tuscan~ and ~Dorick~ Module into twelve Parts, and that of the other Orders into eighteen._

FIGURA DECIMA.

Optica deformatio stylobatæ Dorici; ubi de modo vitandi confusionem, in vestigiis delineandis.

_Elevatio geometrica ~B~ stylobatæ Dorici continet eandem symmetriam partium quæ habetur apud Barozzium; ex eaque eruitur vestigium geometricum ~A~ per 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 vestigium ~E~ distinctiùs vestigio ~D~. Singula hæc vestigia fiunt notando in linea cujuslibet plani mensuras latitudinis & longitudinis vestigii ~A~, & ducendo lineas ad eadem puncta oculi ac distantiæ._

_Stylobatam nitidum descripsimus ex parte ~G~, tum ex necessitate, tum ut videas, pro distantia ~FO~, usurpandam esse distantiam ~GO~ penitus æqualem._

The Tenth Figure.

_A ~Dorick~ Pedestal in Perspective; with the Manner of avoiding Confusion, in designing the Plans._

The Geometrical Elevation B has the same Members and Proportions, as the _Dorick_ Pedestal of _Vignola_; 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.

FIGURA Undecima.

Stylobatæ Ionici deformatio; ubi de vitanda confusione in elevationibus.

_Tum in figura præcedenti, tum rursus in hac, ostendimus quid agendum sit ubi vestigia ~AA~ nimium 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 elevationis ~B~ adhibebitur elevatio ~C~, quæ distinctior est, tum illâ, tum duabus intermediis ~D~ & ~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 literæ ~O~: altitudines accipientur ex elevatione ~C~, ponendo unam cuspidem circini in linea plani, ut in præcedentibus ostensum est._

The Eleventh Figure.

_The ~Ionick~ Pedestal in Perspective; with the Manner of avoiding Confusion, in Elevations._

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_.