Part 6
Besides _Vignola_, _Palladio_ and _Scamozzi_ have also written excellently well of the Orders of Architecture; and each of ’em have deservedly their Followers and Admirers. That you might therefore be enabl’d to make Designs in Perspective, after the Proportions of the most celebrated Masters, I have in this Plate given you the Measures of all the Orders, as deliver’d by them in their Books.
Fig. Quinquages. tertia B.
Modus triplex delineandi columnas spirales.
_Columnæ figuræ superioris carent ea concinnitate, qua præditæ sunt columnæ spirales æneæ celeberrimi Equitis Bernini ad sepulcrum S. Petri in Vaticano. Itaque methodum triplicem exhibeo ad minuenda spatia totius altitudinis columnæ._
1. _Recta ~OA~ sit æqualis altitudini ~AB~ columnæ. Fiat autem recta ~OB~, & arcus ~AP~ ex centro ~O~, divisus in partes duodecim æquales, ducendo rectas, quæ per puncta divisionum desinant in columnam rectam; ac demum fiant parallelæ ad basim: Spatia inter has parallelas dabunt aperturam circini pro triangulis æquilateris & pro spiris, ut ostendit columna ~1~._
2. _Translatâ in ~C~ tertiâ parte altitudinis columnæ ab ejus imo scapo, habeat circinus aperturam ~CD~; ac posito uno ejus crure prius in ~D~, postea in ~C~, fiant duo parvi arcus ad ~E~: sectio illorum arcuum erit centrum arcûs ~DC~, quem oportet dividere in duodecim partes æquales, & ex punctis divisionum ducere parallelas ad basim. Tum spatiis inter parallelas divisis in quatuor partes æquales, tres ex illis partibus dabunt longitudinem crurum pro triangulis isoscelibus; vertices autem triangulorum erunt centra singularum spirarum, ut ostendit columna ~2~._
3. _Ductâ ex medio summitatis ~G~ rectâ ~GF~, spatium ~HF~ transferatur in ~I~, & fiat recta ~IL~ parallela ad basim ~HF~; spatium ~IL~ transferatur in ~N~, ac fiat ~NM~, & sic deinceps. In parvis columnis triangula sine sensibili errore duci possunt per diagonales: in columnis tamen grandioribus, alterutrum ex modis antea explicatis adhibere necesse est._
The Fifty-third Figure B.
_Three different Ways of delineating wreath’d Columns._
The wreath’d Columns describ’d in the Fifty-second Figure, being divided into Twenty-four equal Parts, want very much of that Elegancy of Contour, which is visible in those brass Pillars, made by the famous Cavalier _Bernino_, for S. _Peter_’s Sepulcher in the _Vatican_. Wherefore I here lay before you three several Ways of diminishing the Spaces through the whole Height of the Column.
1. Make the right Line OA equal to AB the Height of the Column; then draw the Line OB, and on the Center O describe at pleasure the Arch AP, which divide into twelve equal Parts, and by the Divisions draw streight Lines from the Center O to the Line of the Column; and lastly continue the same Parallels to the Base. The Spaces between these Parallels, shall be the Sides of equilateral Triangles, wherewith you are to describe the Wreath of the Column, as is seen in Column 1.
2. Having set the third Part of the Columns Height, from the Bottom of the Shaft to the Point C; with the Interval CD, from the Centers D and C, describe the Parts of Arches intersecting at E. On the Center E, with the same Interval, describe the Arch DC, which divide into twelve equal Parts; and from the Points of those Divisions, draw Parallels to the Base. Then dividing each Space between the Parallels into four equal Parts; three of those Parts shall be the Sides of the _Isosceles_ Triangle; whose _Vertex_ is the Center whereon to describe each Wreath of Column 2.
3. Having drawn from the midst of the Columns top G, the Line GF, make HI equal to HF, and draw IL parallel to the Base HF: Again, make IN equal to IL, and draw NM also parallel, and so on. In small Pillars, the Centers of the Diagonals of these Spaces may, without sensible Errour, serve for describing the Wreaths; but in greater Columns, either of the other two Methods is rather to be chosen.
FIGURA Quinquagesimaquarta.
Vestigia ædificii Ordinis Corinthii.
_Descripturi ædificium Corinthium octangulare, ponimus hic vestigia unius ex quatuor partibus pilarum, quibus imponetur fornix in modum tholi, ut constabit in figurâ quinquagesimaoctava. Ad faciliorem descriptionem, in parte inferiori paginæ posui vestigium geometricum stylobatæ, in superiori vestigium geometricum coronicis, cum latitudinibus & longitudinibus membrorum singulorum; ut eas transferendo in lineam plani more consueto, utrumque vestigium opticè deformetur. Ad vitandam confusionem, prius notare oportebit puncta quæ spectant ad membra propinquiora solido parieti, deinde alia._
The Fifty-fourth FIGURE.
_The Plan of a Design of the ~Corinthian~ Order._
Being to describe an Octangular _Corinthian_ Work, I have here inserted the Plan of one Quarter of the Composition; which is vaulted in Form of a _Cupola_, as is seen in the Fifty-eighth Figure. To render the Plan less confus’d, I have, in the lower part of the Plate, given the Geometrical Plan of the Pedestal; and in the upper part, that of the Cornice; with the Breadths and Lengths of each Member: so that by transferring the same into the Ground-line, after the usual Manner; you delineate each Plan in Perspective. For avoiding Confusion, ’twill be requisite first, to transfer the Points of those Members that are next the Solidity of the Wall; and then proceed to the others.
FIGURA Quinquagesimaquinta.
Elevatio ædificii Ordinis Corinthii.
_Elevatio geometrica ædificii octangularis congruit cum duobus ejus vestigiis figuræ antecedentis. Quia verò elevatio parietis abscondit secundam ex quatuor columnis, eademque in ædificio deformato conspicua futura est; iccircò eam lineis occultis designare oportuit._
The Fifty-fifth FIGURE.
_The Geometrical Elevation of a ~Corinthian~ Work._
The Geometrical Elevation of this Octangular Design, is wholly correspondent to the two Plans of the foregoing Figure: But because the Wall in this Upright takes off the Sight from the second of the four Columns, which is notwithstanding visible in the finish’d Perspective that follows; ’tis requisite to delineate the same with occult Lines, as in the Figure.
FIGURA Quinquagesimasexta.
Deformatio vestigiorum & elevationis ædificii Corinthii.
_In hac figurâ, lineam plani coincidere volui cum linea horizontis. Itaque videri non posset vestigium inferius, nisi ut alias deorsum protraxi lineam plani, hic è converso sursum promovissem lineam horizontis, quam constitui mediam inter lineas plani utriusque vestigii, ut ambæ projectiones essent æquè distinctæ. In elevatione, columna secunda, quam, ut dixi, paries abscondit, lineis occultis designanda est._
The Fifty-sixth FIGURE.
_The Perspective Plans and Upright of the ~Corinthian~ Design foregoing._
In this Figure, I have made the Ground-line coincident with that of the Horizon, in which case the lower Plan can’t be seen, unless the Ground-line be sunk lower, as before intimated; or contrariwise, the Point of Sight rais’d higher, as I have here done, keeping it in the midst between the Ground-lines of the two Plans, that the Perspective of both might be equally distinct. In the Elevation, the second Column, which I mention’d to be hidden by the Wall, should be design’d with occult Lines.
FIGURA Quinquagesimaseptima.
Adumbratio figuræ sequentis.
_Figuram hanc seorsim delineavi, ut videas quomodo facienda sit operis totius adumbratio, accipiendo altitudines membrorum singulorum ex elevatione; latitudines & longitudines ex vestigiis. Quæ omnia ex diagrammatis inspectione clarissimè apparent._
The Fifty-seventh FIGURE.
_The rough Draught of the following Figure._
I have drawn this Figure apart, that you may see the Manner of describing the Out-line of the whole Work, by taking the Heights of the several Members from the Elevation, and their Breadths and Lengths from the Plans; all which is very plain, upon Inspection of the Figure.
FIGURA Quinquagesimaoctava.
Ædificium Ordinis Corinthii octangulare.
_Hucusque descripsimus pilas anticas sinistras ædificii Corinthii. En hoc loco medietatem dexteram totius Operis. Integrum verò ædificium habebis figurâ sexagesimâ._
The Fifty-eighth FIGURE.
_Part of an Octangular Work of the ~Corinthian~ Order._
Hitherto the nearest left-hand Quarter of this _Corinthian_ Design has been describ’d. In this Plate you have the right-hand Half of the whole Work; and in the Sixtieth Figure, the entire Perspective compleat.
FIGURA Quinquagesimanona.
Vestigia tabernaculi octangularis.
_Projectiones rerum octangularium sunt quadratis difficiliores: ideò in eis explicandis diligentiæ non peperci. Moles cujus vestigia vides in ~A~ & ~B~, convenit in multis cum eâ quam ereximus figurâ quinquagesimaoctavâ. Visualis ~CD~ recipit sectiones perpendicularium, quæ deserviunt pro elevatione figuræ sequentis, ut sæpius dictum est. Si facies interior delineanda sit seorsim à facie anteriori, illam perficies ope linearum ~CE~, istam ope linearum ~FD~._
The Fifty-ninth FIGURE.
_The Plans of an Octangular Tabernacle._
Octangular Figures being more difficult to be put in Perspective, than the Square; I shall use my best Endeavours to render the Method as plain as possible. The Composition whose Plans you see in A and B, has much Affinity with that describ’d in the Fifty-eighth Figure. The Visual CD receives the Sections, from which Perpendiculars are rais’d for the Elevation and Profile of the following Figure, as has been often said. If you would delineate the Back-part separate from the Fore-part, you may do the former by means of the Line CE, and the latter by that of FD.
FIGURA SEXAGESIMA.
Tabernaculum octangulare.
_Hoc tabernaculo aliquoties usus fui pro expositione quadraginta horarum. Si colores scitè inducti fuerint in duos ordines telariorum, resectis omnibus quæ ad molem ipsam non pertinent, spectatoribus imponet, & solida videbitur. Oportebit autem exemplar externæ faciei eruere ex parte ~DF~ vestigii & elevationis; exemplar interioris faciei eruere ex parte ~EC~, servando in omnibus regulas quas hucusque tradidimus._
The SIXTIETH FIGURE.
_An Octangular Tabernacle in Perspective._
I have sometimes made use of this Tabernacle for the Exposition of the _Forty Hours_. If the Colours are laid by a skilful Hand, on two Ranges of Cloth, and the Frame cut away according to the Out-line of the Work, they will wonderfully deceive the Eye, and appear as solid; but then the outer Range must be drawn after the Plan and Elevation of the Part DF in the foregoing Figure; and the inner Range after that of EC; in all things observing the Rules hitherto deliver’d.
FIGURA Sexagesimaprima.
Modus erigendi machinas, quæ constant pluribus ordinibus telariorum.
_Ex figuræ inspectione addisces modum erigendi machinas quæ constant pluribus ordinibus telariorum. Tabernaculum hoc nostrum indiget duobus tantum ordinibus; nam telaria propinquiora oculo exprimunt faciem externam, remotiora exhibent faciem internam. Ne autem lateant stipites quibus telaria sustinentur, medietatem telariorum adumbrare omisimus. Recta ~LS~ est linea plani, recta ~DG~ est linea horizontalis; ac punctum distantiæ quod cadit extra paginam in recta ~CG~ prolongatâ, debet esse remotum à puncto ~C~, quantum in superiori parte figuræ quinquagesimænonæ, punctum distantiæ est remotum à puncto oculi. Eadem horizontalis ~DG~ secatur normaliter in ~C~ à recta ~EF~, quæ est sectio externæ faciei tabernaculi, & ex ~C~ incipiunt divisiones in partes æquales pro reticulatione anterioris faciei telariorum, ut dicemus figurâ sexagesimasecunda. Recta ~IL~ quæ est sectio internæ faciei tabernaculi, distat ad libitum à recta ~EF~ cui est parallela. Porrò, per divisiones rectæ ~EF~ (ut vides in ~M~, ~N~, ~O~) ex puncto distantiæ ducendæ sunt visuales ad rectam ~IL~ pro reticulatione aliorum telariorum: distantia enim ~DC~ facit ut augere oporteat ea quæ in telariis pinguntur, alioquin justo minora viderentur. Atque hinc dignosces, cur arcus qui in telariis anterioribus pertingeret solum ad ~B~, in posterioribus elevetur usque ad ~H~._
_Figura sequenti proponemus modum delineandi faciem internam telariorum, adhibita reticulatione externæ faciei: ad intelligentiam verò illius methodi, fiat in hac figurâ recta ~HP~ parallela ad ~DC~, ac recta ~BC~ dividatur in totidem partes æquales, in quot partes divisa fuerit recta ~PC~._
The Sixty-first FIGURE.
_The Manner of erecting Machines, that consist of several Ranges of Frames._
By casting your Eye on the Figure, you’ll readily apprehend the Manner of erecting the several Ranges of Frames. This Tabernacle last describ’d needs only two of them; the Frame next the Eye represents the outer Face, and the hinder Frame the inner Face thereof. I have here describ’d but the Half-Breadth of the said Frames, that you might have a Sight of the Poles and Braces which support them. The Line LS is the Line of the Plan, or Ground-line; the Line DG is that of the Horizon; and the Point of Distance, which falls without the Page CG prolong’d, is as far from the Point C, as the Point of Distance is from the Point of Sight in the upper Part of the Fifty-ninth Figure. The Horizontal DG is cut perpendicularly in C by the Line EF, which is the Section of the outer Face of the Tabernacle; and from the Point C begin the equal Divisions for the Net-work of the foremost Frame, as is shewn in the Sixty-second Figure. The Line IL, which is the Section of the inner Face of the Tabernacle, may at pleasure be set nearer or farther from the Line EF, to which it is parallel. By the Divisions of the Line EF (as M, N, O) Lines are drawn from the Point of Distance to the Perpendicular IL, for the Net-work of that Frame; for the Distance DC obliges the Parts of D to be painted larger, otherwise they will appear less than they really ought. And from hence you may discern, why the Arch, which in the foremost Frame would reach only to B, does in the hindmost rise up to H.
In the following Figure is shewn the Manner of delineating the inner Frame, from the Net-work of the outer Face; for the better understanding of which, make the Line HP in this Figure parallel to DC, and let the Line BC be divided into as many equal Parts, as the Line PC was.
FIGURA Sexagesimasecunda.
De reticulandis telariis, quæ repræsentent ædificia solida.
_Duo exemplaria tabernaculi quæ seorsim delineanda sunt, conjunctim habes in ~A~. Utrisque deservit eadem reticulatio, quam suis numeris insignivimus. Postquam ergo designaveris amplitudinem totius ædificii, cum proportione ad ipsam reticulabis pavimentum ~B~ aulæ cujuspiam quod capiat rem totam, ascriptis eisdem numeris quos habet exemplar: ejusque retis ope, ducentur in pavimento lineæ terminativæ totidem membrorum, quot futura sunt telaria exprimentia faciem externam tabernaculi. Ubi hæc parata fuerint, singula disponentur exactè suis locis in ipsomet pavimento; ac funiculis colore nigro imbutis, repetetur in telariis eadem reticulatio, additis ad libitum pluribus visualibus; quarum adjumento dum seorsim pinguntur telaria, duci queant rectæ tendentes ad punctum oculi seu perspectivæ. Alia quoque reticulatio super pavimento necessaria est pro internâ facie tabernaculi: ac duæ reticulationes pavimenti eam inter se proportionem habebunt, quam habent divisiones rectarum ~IL~, ~EF~, figuræ sexagesimæprimæ. Hujus retis ductu fient lineæ terminativæ telariorum cum reliquis, ut jam indicavimus._
_Juxta hanc methodum nequeunt duci lineæ terminativæ interioris faciei, nisi fiat in pavimento aliud rete deleto priori, quod esset valdè laboriosum. Postquam ergo ex vestigio figuræ quinquagesimænonæ eruta sint duo exemplaria, in exemplar faciei externæ transferatur recta ~PC~ figuræ sexagesimæprimæ, in exemplar faciei internæ transferatur recta ~BC~. Si autem recta ~PC~ divisa fuerit in quindecim partes æquales, dividetur ~BC~ in quindecim partes æquales, atque ope harum divisionum reticulare oportebit utrumque exemplar. Porrò licet quadrata in reti exemplaris faciei externæ sint majora quadratis exemplaris internæ faciei, nihilominus idem rete pavimenti deserviet pro ducendis lineis terminativis utriusque faciei. Quæ dicta sunt de duobus exemplaribus, valent de aliis quotcunque. Exempli gratiâ; si construere placeat quinque ordines telariorum, fient quinque exemplaria in papyro. Si in omnibus exemplaribus usurpetur eadem reticulatio, in pavimento facere oportet quinque diversas reticulationes. Si autem in exemplaribus fiant quinque diversæ reticulationes, in pavimento sufficit una reticulatio._
_Curandum est ut singula retis quadrata in telariis sint exacta, omnesque illorum anguli sint recti. Modus expeditissimus faciendi angulos rectos est hujusmodi. Posito uno crure circini in puncto ~F~ lineæ rectæ ~EF~, alioque crure posito ubilibet in ~O~, fiet circulus ~GFI~, & ex puncto ~G~ diameter ~GI~. Si recta ~HF~ transeat per puncta ~I~ & ~F~, est normalis ad ~EF~._
The Sixty-second FIGURE.
_Of making the Net-work on Frames, for representing the Architecture as solid._
You have jointly in A, the two Designs of a Tabernacle, which are to be drawn separately; the same Net-work serving for both, which is also mark’d with Numbers. When you have therefore resolv’d on the Size of your Work, on the Pavement of some Room capacious enough make a Net-work answerable, and affix thereto the Numbers, as in your Copy: By the Help of which, you may on the Pavement describe the Out-line of all those Members that are requisite to the outer Frame of the Tabernacle. This being done, let the Frame be laid exactly in its place on the said Pavement, and with a black Line strike thereon the same Net-work; adding as many visual Lines as you please, which will be of Use for drawing Lines to the Point of Sight, when you come to paint the Frames asunder. Another Net-work on the Pavement is also necessary for the inner Face of the Tabernacle, which should bear such Proportion to this, as the Divisions of the Line IL do to those of EF in the Sixty-first Figure; and by this means the Out-lines of the inner Frame, _&c._ may be drawn, as has been shewn already.
Thus the Out-line of the inner Face can’t be describ’d, without rubbing out the first Net-work, and making a second on the Pavement; which would be very troublesom. Wherefore, from the Plan of the Fifty-ninth Figure, take the two Designs, and transfer the Line PC of the Sixty-first Figure on the outer Face, and the Line BC on the inner Face. Then if PC were divided into fifteen equal Parts, BC shall be divided in the same manner, and by these Divisions make the Net-work on each Design. And although the Squares of the outer Face be larger than those of the inner one, the same Net-work may nevertheless serve for giving the Out-line of both. What has been said of these two Designs, may be understood of many. For Instance; if five Ranges of Frames were requir’d, five Designs must be made in Paper. If in all the Designs the same Net-work be us’d, then five several Net-works must be made on the Pavement; but if the Designs have five different, then one Net-work on the Pavement will suffice.
You must be very careful that all the Squares of the Net-work be exactly divided, and at right Angles. The ready way of making a right Angle is thus: Placing one Foot of the Compasses in the Point F of the Line EF, and the other at pleasure in O, describe the Circle GFI; and from the Point G draw the Diameter GI. The Line FH drawn by the Points FI, shall be perpendicular to FE.
FIGURA Sexagesimatertia.
Vestigia ædificii quadrati.
_Vestigium geometricum ~A~ hujus ædificii habet in ~B~ suam deformationem. Discrimen inter pilas ~C~ & ~D~ oritur ex eo, quòd in ~C~ posita sint vestigia stylobatarum, in ~D~ autem posita sint vestigia coronicum._
The Sixty-third FIGURE.
_The Plan of a square Design._
The Geometrical Plan of this Design A, is brought into Perspective in B. The Difference between the Parts C and D arises from hence, that the Plan of the Pedestals is plac’d in C, and that of the Cornice in D.
FIGURA Sexagesimaquarta.
Ædificium quadratum.
_Ex deformatione vestigii & elevationis, methodo consuetâ eruitur imago totius ædificii, quæ potest esse exemplar aræ maximæ alicujus Ecclesiæ. Hanc machinam, non sine communi approbatione, aliquoties adhibui, in apparatu quadraginta horarum; locum in medio vacuum occupantibus Angelis cum nubibus, additâ figurarum aliquot copiâ in parte inferiori. Modus faciendi in telariis remotioribus ab oculo partem tholi rotundi quam hic vides, deducitur ex iis quæ tradidimus in projectione circulorum._
The Sixty-fourth FIGURE.
_A square Design in Perspective._
From the Plan and Upright in Perspective, this finish’d Piece of the whole Work is delineated after the usual Manner, and may serve for the Design of a great Altar in a Church. I have sometimes, for the Solemnity of the _Forty Hours_, expos’d this painted on a Machine, with an universal Satisfaction; Angels with Clouds possessing the higher part of the Hemisphere within, and Groups of Figures the lower part. The Manner of designing on the inner Frame, that part of the said _Cupola_ which you here see, is deduc’d from what has been before said of putting Circles into Perspective.
FIGURA Sexagesimaquinta.
Vestigium ædificii rotundi opticè imminutum.
_Qui sedulam operam in circulis deformandis non posuerint, eosque minimo negotio ex usu describere nequiverint, frustra conabuntur projicere vestigia ædificiorum rotundorum. Ad vitandam confusionem, proderit in vestigio notare primùm lineas occultas membrorum præcipuorum; iisque translatis in elevationem, addere sensim reliquas. Hac industriâ ego ipse in hoc schemate usus sum. Quum autem experimento didicerim summam arduitatem harum descriptionum, aliam regulam adhibere jamdiu cœpi, quam, ut suprà diximus, in aliud Opus reservamus._
The Sixty-fifth FIGURE.
_The Plan of a Circular Work in Perspective._
They that have not diligently apply’d themselves to the putting Circles into Perspective, and, by a constant Practice, render’d the Work familiar to them, will in vain attempt that of the Plans of round Buildings. To prevent Confusion, you’ll do well, first to mark the occult Lines of the principal Members; and after those are transferr’d into the Upright, then proceed to the rest, as I myself did in this Figure. But having found by Experience, the great Difficulty of describing these round things, I have long since made use of another Method, which, as I said before, is reserv’d for another Volume.
FIGURA Sexagesimasexta.
Projectio ædificii rotundi.
_Mirifice oculis imponunt imagines rerum rotundarum, si omnibus resectis quæ ad eas non pertinent, exactè delineatæ ac depictæ fuerint. Hanc figuram ex vestigio eruere oportebit methodo consuetâ, eamque in Templo S. Ignatii Collegii Romani construxi pro feriâ V & VI Hebdomadæ sanctioris. Intra arcum, super altari, locus erat urnæ sepulcrali, cum Venerabili Sacramento. Sub altari visebatur simulacrum Christi Domini è Cruce depositi: in medio columnarum, imago Beatæ Virginis dolentis; super balaustiis Angeli lugentes, cum instrumentis cruciatuum Salvatoris._
The Sixty-sixth FIGURE.
_A Circular Design in Perspective._