Part 10
_Postquam descripseris in papyro separata quadratum geometricum A, facies duas lineas parallelas inter se distantes altitudine, quam dederis puncto oculi; linea inferior erit linea plani, linea superior erit linea horizontalis, super quam ponuntur puncta oculi ~O~, & distantiæ ~E~, quod sit ex parte quam mavis: linea distantiæ non debet esse brevior magnitudine rerum describendarum. Transfer posteà circino latitudinem quadrati ~A~ in ~CB~, unà cum visualibus ad punctum ~O~; & similiter transfer longitudinem ipsius quadrati in ~DC~, ducens lineam à puncto ~D~ ad punctum distantiæ ~E~, transeuntem per visualem ~CO~, & ubi illa secat, habebis terminum quadrati optici ~GFCB~, ducens parallelam ad lineam plani in ~F~._
_Ut autem hoc idem citiùs absolverem, sæpius chartam complicavi, ut habes in ~A~._
SECOND FIGURE.
_A Square in Perspective._
After you have drawn, on a separate Paper, the Geometrical Square A, make two parallel Lines as much distant one from the other, as you would have the Height of the Eye. The under Line is the Plan or Ground-line; the upper Line is that of the Horizon, on which are plac’d the Points of Sight O, and of Distance E, on which side you please. The Line of Distance should not be shorter than the Extent of the thing to be describ’d in Perspective. Then with your Compasses set the Breadth of the Square A on CB, and draw Visuals to the Point O; and from the Length of the Square transferr’d into DC, draw a Line from the Point D to the Distance E; and where that cuts the Visual CO, by drawing a Line parallel to GF, you describe the Square in Perspective GFCB.
For the more quick Dispatch of this, I commonly fold the Paper, as you see in A.
FIGURA TERTIA.
Rectangulus altera parte oblongior opticé.
_Quidquid in proximo quadrato vidisti, facies in præsenti. Transferres latitudinem ~BC~ in ~BC~, & longitudinem in ~CD~, ducens latitudinem ~BC~ ad punctum oculi ~O~, & longitudinem ~CD~ ad punctum distantiæ ~E~. Ubi vero hæc linea secat visualem ~CO~, erit terminus rectanguli supradicti ~FG, BC,~ ducens parallelam, ut supra._
THIRD FIGURE.
_An Oblong Square in Perspective._
What was done in the preceding, repeat in this Third Figure. Transfer the Breadth BC into BC, and the Length into CD, drawing the Breadth BC to the Point of Sight O, and the Length CD to the Point of Distance E. Where this cuts the Visual CO, you terminate the Square FG, BC, by drawing the Parallel, as before.
FIGURA QUARTA.
Quadratum duplex opticé.
_Eodem modo construes quadratum duplex ~A~, transferens circino, aut duplicando chartulam, latitudinem cujuscumque lineæ, ut vides in punctis ~1~, ~2~, ~3~, ~4~, ~5~, ~6~, super lineam plani in iisdem numeris, & ab istis transferes visuales ad punctum ~O~. Postea transfer longitudinem ~7~, ~8~, ~9~, ~10~, super lineam plani in iisdem pariter numeris, & ab istis duc lineas ad punctum distantiæ ~E~. Ubi hæ lineæ secant lineam ~6, 7, O,~ fiunt lineæ parallelæ ad lineam plani, & quadratum conficitur; parem constructionem facies de quadrato secundo, & tertio, facilè ex dictis._
FOURTH FIGURE.
_A double Square in Perspective._
The double Square A is made after the same manner as the former, by transporting, either with the Compasses, or folded Paper, the Breadth of every Line, as you see the Points 1, 2, 3, 4, 5, 6, on the Ground-line mark’d with the same Numbers; and from these draw Visuals to the Point of Sight. Then transfer the Points of Length 7, 8, 9, 10, into the Ground-line, as you see also in the same Numbers; and direct their Lines to the Point of Distance E. Where these intersect the Visual 6, 7, O, make Parallels to the Ground-line, and the Square is complete. The same is done in describing the middle Square, and that on the other Side.
FIGURA QUINTA.
Quadratorum vestigia cum elevationibus.
_Figuram hanc in duas partes divisi; in superiori parte vides tria quadrata optica aliquantulum adumbrata, eaque tam inter se distantia, quanta est distributio super lineam plani. ~BC~ erit quadratum primum. Secundum erit in ~EF~. Si ergo posueris longitudinem quadrati in ~BC~, eamque duxeris ad distantiam, secabit in ~DD~ visualem ~AO~. Si pariter posueris alterum spatium longitudinis ejusdem quadrati in ~EF~, & duxeris ad lineam distantiæ, habebis secundum quadratum opticé. Idem facies de tertio, & de aliis, quæ distribuenda sunt._
_In secunda parte. Si desideres supra totidem vestigia formare elevationes cuborum, & stylobatarum, ut in inferiori figuræ parte vides, satis erit ex omni vestigiorum angulo elevare lineas occultas, & apparentes, determinando altitudinem faciei ~L~ primo cubo, & anguli ejusdem faciei dabunt altitudinem omnium aliorum._
_Immò etiam totidem cubos formare potes sine lineis occultis, ducendo solùm apparentes, ut vides in tribus expositis adumbratis, & nitidis, quorum perpendiculares sumuntur ab angulis vestigiorum, ut in superiori figura habes in ~H~, & lineæ plani translatæ sunt ab angulis elevationis, ut videtur in ~F~._
FIFTH FIGURE.
_Several Plans of Squares, with their Elevations._
I have divided this Figure into two Parts; In the uppermost you have three Squares in Perspective a little shadow’d, distant one from another, according to their Distribution on the Ground-line. BC is the first Square; EF the second. If you then set the Length of a Square on BC, and draw Lines to the Point of Distance, they will intersect the Visual AO in DD. In like manner, if you set another Length of the said Square on EF, and draw to the Point of Distance, you’ll have the second Square in Perspective. The same you may do in the third, and as many as you have occasion for.
In the second Part you see, that if upon the fore-mention’d Plans the Elevations of Cubes or Pedestals were requir’d, it would suffice to elevate the occult and visible Lines from every Angle of the Plan; and determining the Height of the Face L of the first Cube, the Angles of that Face drawn to the Point of Sight, give the Height of all the others.
You may form the same Cubes without occult Lines, drawing only those that are apparent, as you see in the three Cubes that are finish’d and shadow’d; the Perpendiculars of which are taken with the Compasses from the Angles of the Plan, as is shewn in HI of the upper Figure; and the level Lines are transferr’d from the Angles of the Elevation, as in FG of the same Figure.
FIGURA SEXTA.
Modus delineandi opticè sine lineis occultis.
_Desiderans facili methodo figuram hanc exponere, dabo rationem elevandi corpora sine lineis occultis, ut in superiori tetigi; ostendam igitur hic, quomodo quinque cubi adumbrati desumantur ab eorum vestigiis, & elevationibus._
_Duas debes facere præparationes, si libeat, in chartis etiam separatis. Prima erit formare geometricè vestigium, & elevationem, ut vides in ~B~ & ~A~. Secunda erit distribuere super lineam plani latitudinem vestigii ~B~, puta in ~NM~, & in duabus proximis: Illius longitudo ~MX~ ducta ad distantiam ~D~, secat visualem ~MO~ in ~R~. Spatium autem obliquatum ~E~ utile etiam est aliis duobus quadratis positis super eamdem lineam plani; anguli quorum translati ad distantiam ~B~, totidem angulos dabunt inter visuales ~NO~, ~MO~. Hoc posito, duces perpendicularem ad angulum ~N~, quæ in elevationibus geometricis semper necessaria est, eaque tertia linea est, quam supra dixi. Transfer postea altitudinem ~A~ in ~NF~, cum visualibus ~FO, NO,~ & invenies altitudinem ~ST~. Hoc pariter de cæteris eveniet._
_Sciendum superest quonam modo supradicta præparatione uti possis ad construendos stylobatas adumbratos, & inornatos._
_Super aliam igitur chartam dispone situm cum duabus lineis, plani scilicet, & horizontis, una cum puncto oculi ~O~, & perpendiculari ~V~, ejusdem mensuræ cum supradicta præparatione, & faciens uti me fecisse vides. Experire postea circino ~NF~ æqualia esse ~1, 5,~ & ~2, 6~. Metire pariter ~ST~, & invenies æqualia ~7~ & ~3~; facies postea lineas planas, & visuales ad punctum oculi, & habebis planum superius cubi in ~1~, ~2~, ~3~, ~4~. Hoc idem faciendum est de aliis. Uno verbo: anguli vestigiorum dabunt tibi lineas perpendiculares, & anguli elevationis dabunt lineas planas; atque hoc semper erit._
SIXTH FIGURE.
_The Manner of designing in Perspective without occult Lines._
Being desirous to make this Rule as easy as possible, I shall give a farther Account of raising Solids without the Help of occult Lines, which I only touch’d upon in the foregoing Figure. I therefore here shew you, how the five shadow’d Cubes of this Figure are taken from their Plans and Elevations.
Two things preparatory are to be done, and, if you please, on separate Papers. The first is, to describe the Geometrical Plan and Elevation, as you see in B and A. The second is, to dispose on the Ground-line the Breadth of the Plan B; as, for Example, in NM, and the two next to it. The Length thereof MX, drawn to the Point of Distance D, cuts the Visual MO in R; and the Foreshortning E serves also for the other two Squares plac’d upon the same Ground-line, whole Angles being directed to the Distance D, give as many Angles on the Visuals NO, MO. This done, erect a Perpendicular on the Angle N, which in Geometrical Elevations is always necessary, and is the third Line mention’d in the first Figure. Then carry the Height A on NF, drawing the Visuals FO, NO, which determine the Height ST, and that of the other Squares.
It remains to be known, how to make use of the foresaid Preparation for the Construction of the shadow’d Pedestals.
On another Paper therefore dispose the Horizontal and Ground-lines, together with the Point of Sight O, and the Perpendicular V, keeping the same Measures as in the aforesaid Preparation, and doing as I have done. You may prove by the Compasses, that NF is equal to 1, 5, and 2, 6, and measuring ST, you’ll find it equal to 7, 3, then drawing the level Lines, and the Visuals to the Point of Sight, you have the upper Face of the Cube C in 1, 2, 3, 4. The same must be done in the others. In a word, the Angles of the Plan give you the perpendicular Lines, and the Angles of the Elevation give the level Lines, or those parallel to the Ground-line; and this you are always to understand for the future.
FIGURA SEPTIMA.
Aliud exemplum construendi vestigium geometricum, cum elevatione longitudinis.
_Vides hic stylobatam ~P~ in quatuor partes divisum, & adumbratum. Si illum opticè delineare velis, construere debes supradictas præparationes, geometricam nempe, & opticam. Nomine geometricæ intelligo vestigium ~A~, & elevationem ~B~; nomine vero opticæ, totum id quod includitur in ~GCDEO~._
_Transfer igitur latitudinem geometricam ~CD~ vestigii ~A~ super lineam plani pariter ~CD~, & transfer longitudinem ~DE~ super lineam plani pariter ~DE~, operans more solito; & habebis vestigium opticé. Transfer posteà elevationem ~HX~ in ~CG~ perpendicularis; ducens visualem ~GO~, eleva ad lineam ~GO~ omnem angulum, quem planum facit in linea ~CO~, & habebis altitudinem necessariam etiam sectionis._
_Transferes denique circino in aliam chartam angulos vestigii, qui dabunt tibi lineas perpendiculares, & anguli sectionis dabunt lineas planas: Visuales vero duces ad punctum oculi._
SEVENTH FIGURE.
_Another Example of a Geometrical Plan, with the Elevation of its Length._
If you would delineate in Perspective the Pedestal P, which you here see divided into four Parts, and shadow’d; you must make the two foregoing Preparations; namely, the Geometrical and the Perspective. By the _Geometrical_, I mean the Plan A, and the Elevation B; By the _Perspective_, all that’s contain’d within G, C, D, E, O.
Then transfer the Geometrical Breadth CD of the Plan A, into CD of the Ground-line; and the Length DE of the said Plan into DE of the Ground-line working after the usual manner; and you will have the Plan in Perspective. Again, set the Elevation HX on CG of the Perpendicular, and drawing the Visual GO, elevate thereto every Angle made by the Plan on the Line CO, and you have all the Heights necessary for the Profile.
Lastly, by the Compasses you transport on a clean Paper the Angles of the Plan, which give the perpendicular Lines; and those of the Profile, which give the level Lines. The Visuals you draw to the Point of Sight.
FIGURA OCTAVA.
Stylobata opticé.
_Hic etiam postquam feceris supradictas præparationes, geometricam scilicet, & opticam; facies præsentem stylobatam adumbratum, transferens circino angulos vestigii, ut construas perpendiculares; & angulos sectionis, ut formes lineas planas, ut supra. Nam sic duo anguli vestigii ~MO~ dabunt lineas perpendiculares ~EF~; angulus vestigii ~R~ dabit perpendicularem ~P~, & sic reliqui anguli dabunt reliquas lineas perpendiculares. Similiter à sectione angulus ~I~ dabit lineam planam ~HN~. Breviter, primus terminus sectionis ~ID~ dabit altitudinem linearum planarum in facie stylobatæ adumbrati ~EFHN~. Secundus terminus ~Q~ dabit altitudinem faciei oppositæ, & occultæ ~P~._
_Duo tamen moneo; primum, ut faciens vestigia geometrica, ducas ab elevatione ~A~ totidem lineas ad latera vestigii ~B~, quot angulos invenies in prominentiis supradictæ elevationis ~A~, ut manifestè vides in lineis quas ex punctis composui, illæ enim à stylobata ~A~ cadunt super vestigium ~B~; quare prominentia major in elevatione ~L~ facit lineam majorem ~L~ in vestigio._
_Secundum quod moneo sit, ut volens elongare vestigium opticè delineatum ~MOR~ à linea plani ~K~, quantum erit spatium ~C~ in eadem linea plani, tantumdem elongabitur spatium ~G~ à linea ejusdem plani._
EIGHTH FIGURE.
_A Pedestal in Perspective._
Here also, after you have made the two foregoing Preparations, the Geometrical and the Perspective; this shadow’d Pedestal is made by taking with the Compasses the Angles of the Plan, for drawing the Perpendiculars, and the Angles of the Profile for the level Lines, as before. Thus the two Angles of the Plan MO, give the perpendicular Lines EF. The Angle of the Plan R, gives the Perpendicular P; and the other Angles give their respective Perpendiculars. So likewise in the Profile, the Angle I gives the level Line HN. In short, the first Out-line of the Profile ID gives the Height of the level Lines on the Front of the shadow’d Pedestal. The other Out-line Q gives the Height of the occult and back part thereof.
Nevertheless, two things are to be observ’d; first, that in making the Geometrical Plan, you draw from the Elevation A, as many Lines to the Side of the Plan B, as you have Angles in the Projectures of the said Elevation; as is manifest in the pointed Lines, which fall, from the Upright A, on the Plan B, where that of the greatest Projecture L in the Elevation makes the outer Line L of the Plan.
The second thing to be observ’d, is, That if you would have the Perspective-Plan MOR as far within the Ground-line K, as the Breadth of the Space C on the same Line, the Space G will then be the Distance thereof from the said Ground-line.
FIGURA NONA.
Optica delineatio Architecturæ Jacobi Barozzii: & primum, de stylobata Ordinis Etrusci.
_Quandoquidem omnibus nota est Architectura Barozzii, eam hic penitus immutatam cum suis regulis particularibus, & generalibus expono; Metieris autem illam modulis ut fieri solet; qui igitur illam desiderat, in sequentibus figuris inveniet totam, simulque discet opticè reddere. Cum autem non minus Opticæ studioso quam Architecturæ necesse sit, efficere delineamenta rei construendæ, ab hoc verè, ab illo fictè, id est, cum uterque facere debeat vestigium, elevationem, sectionem, & faciem, ob id delineavi hic stylobatam Ordinis Etrusci cum suo vestigio, quem vides in ~AB~, ut faciliùs percipias quod in proxima figura dixi, à totidem scilicet angulis prominentiarum elevationis, totidem ducendas esse lineas super lineam vestigii; cum hoc necesse sit ad inveniendum illorum angulorum cum istis lineis concursum in suis degradationibus. Nota, longitudinem, quam voco ~F~ ductam in ~G~ esse illam, à qua non solùm nascitur vestigii obliquitas, verùm etiam ab illa nascitur obliquitas illius quam voco sectionem ~E~. Ob id in altero hujus ejusdem figuræ stylobata totum id è contrario videbis._
_Non ampliùs repetam quonam modo eruatur nitida delineatio, de qua superiùs pluries; dicam tamen angulos primi termini sectionis ~E~ daturos lineas planas faciei ~D~, & angulos vestigii daturos omnes perpendiculares._
NINTH FIGURE.
_The Architecture of ~Vignola~ put in Perspective; and first, the Pedestal of the ~Tuscan~ Order._
Since every one is acquainted with _Vignola_’s Architecture, I determine not to alter it, but to explain it, with its general and particular Rules; measuring the same with Modules, after the usual manner. He therefore that has it not, may find it in the following Figures, and at the same time learn the Method of putting it in Perspective. And whereas the Drawing the Plan, Elevation and Profile of what’s to be built, is no less necessary for him that studies Perspective, than for the Architect, the first performing in Appearance, what the latter does in Reality; I have therefore here delineated the _Tuscan_ Pedestal, with its Plan, as you see in AB, that you may the better apprehend what I said in the foregoing Figure, That from all the Angles of Projecture in the Elevation, Lines must be let fall on the Plan; this being of absolute necessity for finding the Correspondence of the Angles with the Lines in the Perspective Projection. Observe, that what I always call Length, as from F to G, is that from which proceeds not only the Foreshortning of the Plan; but also that which I call the Profile E. Wherefore, in the opposite Pedestal of the same Figure, you’ll see a contrary Disposition of the Whole.
I shall not here repeat, how the finish’d Pedestal is taken from these; having so largely spoken of that before; but briefly tell you, that the Angles of the first Out-line of the Profile E give the level Lines of the Face D, and the Angles of the Plan give all the Perpendiculars.
FIGURA DECIMA.
Stylobata Doricus, & ratio vitandi difficultatem quamdam, quæ occurrit inter illum opticè delineandum.
_Hic oritur difficultas hæc. Vestigium ~A~ opticè translatum in ~C~ adeò contrahitur, ut distinctè videri nequeat ubi collocetur circini pes, ut transferri possint perpendiculares stylobatæ adumbrati; totaque hæc difficultas oritur à propinquitate quam habet linea horizontalis, seu punctum oculi cum linea plani. Ut igitur illam vincas: Duces lineam plani inferiùs quantum libuerit, & super illam feres denuò latitudinem, & longitudinem more solito, retinendo puncta oculi, & distantiæ ~OF~, & sic videbis vestigia magis minusve distincta; Vestigium enim ~E~ distinctius est vestigio ~D~, & ~D~ distinctius est vestigio ~C~._
TENTH FIGURE.
_A ~Dorick~ Pedestal, with the Manner of shunning a Difficulty, which occurs in putting the same in Perspective._
In this Figure a Difficulty arises, which is this; That the Plan A put in Perspective in C, is so foreshorten’d, that one can’t see distinctly, where to place the Compasses, for transferring the Perpendiculars on the shadow’d Pedestal; which is caus’d by the too near Approach of the horizontal Line to the Ground-line. For avoiding this Difficulty, draw another Ground-line as much below the first as you please, and carry the Breadth and Length thereon, after the usual manner, still keeping the same Points of Sight and Distance O and F: And according to the Removal of the Ground-line, the Plans will be more or less distinct; as you see the Plan E is more distinct than D, and D is more so than C.
FIGURA UNDECIMA.
Stylobata Ionicus, & ratio vitandi aliam difficultatem in elevationibus.
_In elevationibus etiam sectionis opticè potest accidere, ut si visualis ~LK~ nimis recta sit, sectio ~B~ restringatur. Elongando lineam plani ab ~L~ ad ~M~, visualis ~MN~ erit inclinatior, & consequenter sectio ~C~ erit latior, & distinctior._
_Nota, difficultatem hanc sæpe sæpiùs te habiturum in figuris præcipuè, quæ multas lineas habent, ut in figura quadragesimasecunda, ubi pariter rationem vitandi confusionem reddam._
_Neque tibi molestiæ sim, quod in hac figura lineam horizontalem infra lineam plani collocaverim, id enim feci, ut illarum diversos effectus videas, utque tu in tuis studiis mutes, & discas._
ELEVENTH FIGURE.
_The ~Ionick~ Pedestal, and the Way to shun another Difficulty in the Elevations._
In Elevations of the Profile in Perspective, it may sometimes happen, that the Visual LK may be so direct, as to render the Profile B too close and narrow; wherefore prolonging the Ground-line from L to M, make the Visual MN, which being much more oblique, does consequently render the Profile C more broad and distinct.
And observe, that this Difficulty will very often occur; especially in Figures that have many Lines, as the Forty-second Figure has, where I speak also of the manner of avoiding the same.
Nor let it trouble you, that in this Figure I have plac’d the horizontal Line below the Ground-line; which I have done, that you might see their different Effects, and by changing the Disposition of your Designs, improve and learn.
FIGURA DUODECIMA.
Stylobata Corinthius cum suis pilis.
_Fecisse septimam figuram magno tibi documento erit ad construendum, & dividendum stylobatam ~A~, & vestigium ~B~; cum nihil addere debeas præter pilas ~C~ cum coronice, quæ duo latera ambit. Opticè hoc vestigium delineabis in ~D~, quæ delineatio distinctior est, quia inferiùs duxi lineam plani; & distinctior etiam est sectio ~E~, cum elongaverim visualem ~FG~. Sic semper agam, ut detur locus figuræ adumbratæ, & ut etiam videas perpendiculares stylobatæ adumbrati cadere super angulos vestigii, & lineas planas incidere è diametro super angulos sectionis ~E~. Iterùm libenter moneo, ut facias supradictas præparationes in chartulis separatis, ut initio assuescas transferendis figuris nitidis circino; facile enim tibi postea erit integras machinas Perspectivæ jucundioris delineare, ut videbis: in hoc enim tota regulæ hujusce, & totius operis facilitas sita est._
TWELFTH FIGURE.
_A ~Corinthian~ Pedestal, with its Pilasters._
The Performance of the Seventh Figure will be a great Assistance to you, in the Construction and Division of this Pedestal A, and the Plan B; since you have nothing more to add here, but the Pilasters C, and the Mouldings which surround the two Sides. This Plan is put in Perspective in D, and becomes more distinct by my sinking the Ground-line lower; and the Profile E is also more distinct by the Removal of the Visual FG, as mention’d in the foregoing Chapter. This I shall always do, that there may remain Room for the shadow’d Figure, and that you may also see that the Perpendiculars of the shaded Pedestal fall directly upon the Angles of the Plan, and that the level Lines directly answer the Angles of the Profile E. I repeat my Advice, that you would make the foresaid Preparations on several Papers, and accustom yourself at the beginning to take off the finish’d Figures with the Compasses; for it will become very easy to you afterward, to design entire Machines of delightful Perspectives, as you’ll see hereafter. And indeed in this Practice, the Facility of this Rule, and of all that follows in this Work, does chiefly consist.
_Respondetur objectioni factæ circa punctum oculi opticum._
Non omnium sensus est, uni optico operi unicum tantùm punctum assignare, _e. g._ toti spatio fornicis, tholi, & tribunæ, quam vocant, expressæ in figura nonagesimatertia, nolunt concedi unicum punctum, volunt concedi plura.