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.
[Illustration: FIG. XI.]
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.
[Illustration: FIG. XII.]
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.
[Illustration: FIG. XIII.]
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.
[Illustration: FIG. XIV.]
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.
[Illustration: FIG. XV.]
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.
[Illustration: FIG. XVI.]
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.
[Illustration: FIG. XVII.]
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.
[Illustration: FIG. XVIII.]
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.
[Illustration: FIG. XIX.]
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.
[Illustration: FIG. XX.]
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.
[Illustration: FIG. XXI.]
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.
[Illustration: FIG. XXII.]
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.
[Illustration: FIG. XXIII.]
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.
[Illustration: FIG. XXIV.]
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_.
Being to form the Plan E from the Plan B, you must, with occult Lines,
make the Squares necessary for bringing four, or at least three of the
Circles into Perspective; transferring into the Line D the Divisions
of the Line C, and the rest as usual. Then, with other occult Lines,
contract the Plans of the Leaves, and finish what’s farther requisite in
the Plan E.
To make the Optick Elevation of the Length F, you must transfer into the
Perpendicular H all the Divisions of the Elevation A; and complete the
same, by Lines drawn toward the Point of Sight, till they meet their
respective Perpendiculars; which proceeding from all parts of the Circles
parallel to the Line D, intersect the Visual G; from whence they descend,
Parallels to the Perpendicular H.
In working the clean Capital, you should begin with the lowest Circle I,
which denotes the Compass of the Column. Then make the Leaves 1, 2, by
taking their Breadths from the Plan E, with the Compasses, and keeping
one Point of them upon the Line H; and their Heights from the Elevation
F, keeping one Point on the Line D. The same must be done, as well by the
Leaves 3, 3, 4, 4, as by the Leaf 5, and the others; and last of all, by
the _Abacus_ also; the Sinking of the Horns whereof answers that of the
visual Line L.
[Illustration: FIG. XXV.]
Figura Vigesimaquinta.
Optica descriptio capitelli Compositi.
_Ex iis quæ diximus de capitello Corinthio, didiceris modum faciendi
capitellum Compositum. Velim autem tibi persuadeas, cum lectione harum
regularum quæ sunt magistri inanimes, circini usum perpetuò conjungi
oportere. Hic enim vivi magistri defectum unicè supplere potest._
The Twenty-fifth Figure.
_The ~Composite~ Capital in Perspective._
From what has been said of the _Corinthian_ Capital, may be learnt the
Manner of putting the _Composite_ also into Perspective. I wish I could
prevail with you, that to the Reading of the Rules, which in themselves
are but lifeless Masters, you would constantly add a diligent Practice of
the Figures by the Compasses; this being the only way to supply the Want
of a living Master.
[Illustration: FIG. XXVI.]
Figura Vigesimasexta.
Deformatio coronicis Etruscæ.
_Post capitella sequuntur coronices, quæ utpote quadratæ, minimam habent
arduitatem. Inter coronices verò, nulla est Etruscâ simplicior ac
facilior. Ex elevatione geometricâ, more solito, formatur vestigium
geometricum; ex eoque opticè contracto eruitur similis elevatio
longitudinis. Demùm ex elevatione & vestigio componitur coronix nitida.
Memineris autem duas esse lineas, quæ hinc inde terminant latitudinem
elevationis opticæ. Linea quæ altior est, dat altitudinem anterioris
faciei coronicis, alia quæ est depressior, dat altitudinem faciei
posterioris. Et ita erit in posterum._
Twenty-sixth Figure.
_The ~Tuscan~ Entablature in Perspective._
After Capitals we proceed to _Entablatures_, which because they are
square, are less difficult than the former. And of all Entablatures,
that of the _Tuscan_ Order is the most simple and easie to be put
in execution. From the Geometrical Upright is drawn, as usual, the
Geometrical Plan; from the Plan put in Perspective is describ’d the
Optick Elevation of the Length; and from both the latter is wrought the
clean Entablature requir’d. You may observe, here are two Lines that
terminate the Breadth of the Perspective on one side and the other. The
Line which proceeds from the higher Corner of the Visual, gives the
Height of the most advanc’d Part; that from the lower determines the
Height of the Back-part. And so for the future.
[Illustration: FIG. XXVII.]
Figura Vigesimaseptima.
Optica delineatio coronicis Doricæ.
_In faciendâ coronice Doricâ, quæ majorem operam poscit, ob denticulos
& triglyphos; communis regula servanda est. Si autem libeat coronicem
nitidam describere in papyro separatâ ab ejus præparationibus, id
profectò licet, tum in hoc, tum in quocunque alio schemate._
Twenty-seventh Figure.
_The ~Dorick~ Entablature in Perspective._
In making the _Dorick_ Entablature, which has something more Work in it
than the former, on account of its Dentels and Triglyphs; the common Rule
is to be observ’d. And if you would delineate the finish’d Entablature in
a Paper distinct from that of its Preparations, you are at liberty so to
do, either in this or any other Figure.
[Illustration: FIG. XXVIII.]
Figura Vigesimaoctava.
Præparatio figuræ sequentis.
_In figurâ vigesimaoctavâ, quæ continet vestigium & elevationes
geometricas figuræ vigesimænonæ, oportuit latus ~C~ delineare seorsim à
facie ~B~; quia facies exhibet latitudinem ædificii, latus verò exhibet
longitudinem; atque una non est alteri æqualis. In vestigio geometrico
solidus paries est ~A~: circuli referunt summum scapum columnarum. Cætera
dant projecturas coronicis, cum suis mutulis._
Twenty-eighth Figure,
_Preparatory to the following Figure._
In this Twenty-eighth Figure, which contains the Plan and Geometrical
Elevations of the Twenty-ninth Figure, it was requisite to delineate the
Side C separately from the Front B; because the Front, which signifies
the Breadth of the Building, and the Side, which shews its Length, are
not equal one to the other. In the Geometrical Plan the solid Wall is A:
the Circles express the Nakeds of the Pillars Shafts at top. The rest is
the Projecture of the Cornice, with its Mutules.
[Illustration: FIG. XXIX.]
Figura Vigesimanona.
Optica projectio ædificii Dorici.
_Habes in hac figura vigesimanona, opticam delineationem vestigii, &
unius ex elevationibus figuræ vigesimæoctavæ; nimirum, elevationis
longitudinis; ex quibus eruitur imago nitida ædificii Ordinis Dorici, cum
summitatibus & capitellis trium columnarum; ejusque epistylium, zophorus,
& corona._
BO _est linea horizontis; ~AC~ est linea plani; in quam, ex lineis
~D~ & ~C~ figuræ vigesimæoctavæ, transferuntur puncta latitudinis &
longitudinis duarum elevationum; prolongando versus ~C~ ipsam lineam
plani, ut oportet. Operaberis autem, ut diximus figurâ vigesimatertia;
nimirum, in puncto ~V~ desinet latitudo vestigii, incipiet longitudo;
& ex punctis latitudinis lineæ tendent ad punctum oculi; ex punctis
longitudinis lineæ occultæ tendent ad punctum distantiæ. Ubi verò hæ
lineæ secant visualem ~VO~, fient parallelæ ad lineam ~AC~, cum cæteris
quæ necessaria sunt ad complendam delineationem opticam vestigii._
_Elevatio ~C~ figuræ vigesimæoctavæ opticè contrahetur more consueto,
translatis in lineam ~AB~ divisionibus lineæ ~E~ vel ~F~, ex quibus
fient visuales ad punctum oculi; ac demissis ex linea visuali ~AO~
perpendicularibus ad lineam ~AC~, ita ut lineæ parallelæ ad lineam plani
~AC~ continuentur cum aliis lineis parallelis ad lineam ~AB~._
_Hic quoque locum habet observatio illa, cujus meminimus figura
vigesimasexta, de lineis quæ deorsum excurrunt, & hinc inde terminant
membra elevationis opticæ. Ex iis autem desumuntur projecturæ omnes
coronicis & capitellorum._
Twenty-ninth Figure.
_A Projection of the ~Dorick~ Order in Perspective._
In this Twenty-ninth Figure, you have in Perspective the Plan, and one
of the Uprights of the Twenty-eighth Figure; namely, that of the Length;
from whence is drawn this finish’d Piece of the _Dorick_ Order, which has
the upper Part and Caps of three Pillars, with their Architrave, Freeze,
and Cornice.
BO is the Horizontal-line; AC that of the Plan; into which, from the
Lines D and C of the Twenty-eighth Figure, are transferr’d the Points
of Breadth and Length of the two Elevations; first prolonging the Line
itself, as much as is needful, through C. The Work is then perform’d,
as was shewn in the Twenty-third Figure; namely, the Divisions of the
Breadth of the Plan end in the Point V, at which those of Length begin.
From the first, Lines are drawn to the Point of Sight; and from the
latter, occult Lines are directed to the Point of Distance: And where
these cut the Visual VO, Lines are drawn parallel to AC; with those that
are farther necessary for completing the Plan in Perspective.
The Elevation C of the Twenty-eighth Figure is put in Perspective, as
usual, by transferring the Divisions of the Line E, or F, into that of AB
in this Plate; from whence drawing Visuals to the Point of Sight, they
are intersected by Perpendiculars let fall from those Divisions of AO
made by the Parallels to the Ground-line AC, and again continu’d parallel
to the Perpendicular AB.
The Observation, mention’d in the Twenty-sixth Figure, is also pertinent
in this place; That the Lines, which, in the Perspective-Elevation, tend
downward, give the Advance and Recess of the several Members of the
Work; and from them are taken all the Projectures of the Entablature and
Capitals.
[Illustration: FIG. XXX.]
FIGURA Trigesima.
Optica projectio ædificii Ionici; ubi de modo jungendi fictum cum vero.
_Si tibi Pictor quum sis, occasione apparatûs quadraginta horarum, vel
sepulcri Domini, mutare ad tempus libeat formam architecturæ alicujus
Ecclesiæ jungendo fictum cum vero, ut mihi sæpius contigit Mediolani ac
Romæ, cum ingenti spectatorum delectatione & admiratione; paucis ostendam
tibi modum quem servare debeas in operando._
_Sectio coronicis veræ, quæ, ut suppono, videri debet continua esse
cum coronice picta in telario, est ~A~; elevatio geometrica coronicis,
& reliquorum quæ delineanda sunt, est ~B~; vestigium geometricum est
~C~. Porrò, tum vestigium tum elevatio longitudinis opticè contrahentur
more consueto, ut vides in ~C~ & ~B~: ex iisque formabitur in telario
coronix nitida cum columna & anta; ipsumque telarium depictum, normaliter
coagmentandum erit veræ coronici._
_Ut fiat ea pars longitudinis, quæ coronicem pictam continuare videatur
cum vera, & erui non potest ex elevatione deformata; oportet sectionem
~A~ transferre in ~D~, ducendo visuales ex punctis terminativis membrorum
sectionis ~D~, usque dum occurrant lineis latitudinis eorundem membrorum.
Quod si colores in telarium scitè inducantur, angulus in ~E~, quamvis
merè depictus, videbitur verus; & ex adverso, anguli quos telarium ipsum
depictum facit cum diversis adeò crepidinibus coronicis veræ, nusquam
apparebunt, præterquàm in quadra simæ dumtaxat; & unio architecturæ veræ
cum ficta dignosci non poterit._
The Thirtieth Figure.
_An ~Ionick~ Work in Perspective; with the Manner of reconciling the
fictitious to the solid Architecture._
If, being a Painter, you were requir’d, against the Solemnity of the
Holy-Week, to alter for a while the Architecture of some Altar-piece, by
joining Painting to the real Work; as I have often done, both at _Rome_
and _Milan_, to the great Satisfaction and Surprize of the Beholders: I
shall briefly shew the Method to be observ’d in performing the same.
The Dissection of the solid Cornice, which I here suppose shall appear
continu’d in that painted on the Canvass, is A; the Geometrical Elevation
of the Cornice, and other Parts to be drawn, is B; the Geometrical Plan
is C. The Plan and Elevation of the Length are put in Perspective after
the usual manner, in C and B; from those the finish’d Cornice, with the
Pillar and Pilaster, are delineated on the Canvass; and the Picture is
then conjoin’d, at right Angles, to the true Cornice.
For adjusting the Members so, that the painted Cornice may seem to be the
real one continu’d, (which can’t be done by the Perspective Upright) you
must transfer the Section A to D; and from the terminating Points of the
several Members thereof, draw visual Lines, till they meet those of their
respective Members in the Perspective. And if the Colours are laid by a
skilful Hand, the Angle at E, tho’ painted only, will appear as real;
and on the contrary, the Angles which the Members of the painted Cornice
make with the different Projectures of those of the true, will never be
discern’d, unless in the very uppermost Fillet; but the Conjunction of
the real with the painted Architecture, will be altogether imperceptible.
[Illustration: FIG. XXXI.]
Figura Trigesimaprima.
Optica projectio coronicis Corinthiæ, cum capitello & summitate columnæ.
_In hoc schemate linea plani est ~CIE~, horizontis est ~DFO~; punctum
oculi est ~O~, distantiæ est ~D~. Elevatio geometrica capitelli Corinthii
cum sua coronice est ~A~, quorum divisiones cernuntur in perpendiculari
~CD~. Vestigium geometricum ~B~ habet longitudinem æqualem latitudini:
opticè autem contrahitur methodo consueta. Nimirum, translatis
divisionibus latitudinis & longitudinis in lineam plani ~CIE~; ex punctis
latitudinis fiunt visuales ad punctum oculi; ex punctis verò longitudinis
fiunt occultæ ad punctum distantiæ: hoc modo habes quicquid necessarium
est ad contractionem opticam vestigii. Nam lineæ longitudinum sunt partes
visualium, ut patet in ~GN~, ~HL~: lineæ latitudinum, parallelæ ad lineam
plani fiunt ex punctis in quibus lineæ tendentes ad punctum distantiæ
secant visualem ~HO~, ut vides in ~NL~. Porro, si tantundem prolongaretur
horizontalis ~DO~, ita ut haberet duo puncta distantiæ remota æqualiter
ab ~O~, medietas diagonalium, quæ sunt in quadrato majori ~GNLH~ opticè
deformato, & in quadratis ejus minoribus, tendent ad unum punctum
distantiæ; altera medietas ad aliud punctum distantiæ._
_Elevatio longitudinis opticè contrahitur ductis parallelis ad ~CE~,
quæ ubi pervenerint ad visualem ~IO~, continuentur cum aliis parallelis
ad ~IK~. Præterea, translatis in lineam ~IK~ divisionibus lineæ
perpendicularis ~CD~, ex punctis divisionum fiunt visuales ad punctum
oculi, ac ducuntur singula membra ipsius elevationis, cujus latitudines
sunt partes visualium, altitudines verò sunt partes linearum parallelarum
ad ~IK~. Demùm ex vestigio & ex elevatione longitudinis, formatur coronix
nitida cum capitello. Ut autem faciliùs delineentur mutuli, primùm fient
quadratâ formâ, ut in ~M~; deinde congruus flexus in singulos inducetur._
The Thirty-first Figure.
_The Optick Projection of a ~Corinthian~ Cornice, with the Capital and
PART of the Column._
In this Figure the Line of the Plan is CIE, that of the Horizon is
DFO; the Point of Sight is O, the Point of Distance D; the Geometrical
Elevation of the _Corinthian_ Capital, with its Entablature, is A; whose
Divisions are seen in the Perpendicular CD. The Length and Breadth of the
Geometrical Plan B are equal, and the Plan is put into Perspective after
the usual Method; to wit, by transferring the Divisions of Breadth and
Length into the Line CIE; from the Points of Breadth drawing Visuals to
the Point of Sight; and from those of Length occult Lines to the Point
of Distance: by which Intersections you have all that’s necessary for
putting the Plan into Perspective. For the Lines of Length are Parts of
visual Rays, as is manifest by GN, HL; and the Lines of Breadth are made
Parallels to the Ground-line, from the Intersections before-mention’d,
as is seen in NL. Moreover, if the Horizontal-line DO were so prolong’d,
as to receive another Point of Distance equidistant from O; half the
diagonal Lines of the great Square GNLH, and of the lesser Squares
contain’d therein, would tend to one Point of Distance, and the other
half to the other.
The Elevation of the Length is put in Perspective, by continuing the
Parallels to CE, till they cut the Visual IO; and from thence dropping
Lines parallel to IK: Then transferring into IK the Divisions of the
Perpendicular CD, from them make visual Lines to the Point of Sight, and
draw the several Members of the Upright; whose Breadths are Parts of
Visuals, and their Heights Parts of Perpendiculars, or Lines parallel
to IK. Lastly, from the Plan and Elevation of the Length, you delineate
the finish’d Cornice and Capital: But that you may more easily draw the
Modillions, first make them in a square Form, as in M; and that will very
much assist you to give the Scroll of each a more agreeable Turn.
[Illustration: FIG. XXXII.]
Figura Trigesimasecunda.
Delineatio geometrica coronicis, Ordinis Compositi.
_Ut hoc schema grandius ac distinctius esset, ejus medietatem dumtaxat
suscepi delineandam. ~PN~ est vestigium geometricum. ~M~ est solidus
paries. ~OO~ spatia columnarum. In ~H~ sunt crepidines coronicis.
Elevatio geometrica latitudinis ædificii constat epistylio ~T~, zophoro
~L~, & coronâ ~V~, supra quam eminet fastigium ~S~._
_Jam ut inveniatur centrum arcuum, distantiæ ~AV~ fiat æqualis distantia
~AC~. Positaque una cuspide circini in ~C~, alia extendatur usque ad ~V~:
ita fient arcus, quorum ultimus est ~BD~, omnesque sunt concentrici.
Elevatio ~F~ ostendit longitudinem ædificii ex parte ~GI~; elevatio ~E~
ostendit longitudinem ipsius ex parte ~DR~._
Thirty-second Figure.
_The Geometrical Design of a Cornice, of the ~Composite~ Order._
That this Figure might be larger and more distinct, I have here describ’d
only the Half of it. PN is the Geometrical Plan. M is the solid Wall. OO
are the Places of the Columns. H shews the Projectures of the Cornice.
The Geometrical Elevation of the Breadth of the Frontispiece, consists of
the Architrave T, the Freeze L, and the Cornice V, over which is rais’d
the Pedament S.
For finding the Center of the arch’d Lines of the Pedament, make the
Distance AC equal to that of AV; and placing one Point of the Compasses
in C, extend the other to V, and describe the Arch. The other Arches, of
which BD is the utmost, have all the same Center. The Elevation F shews
the Length of the Work on the Side GI. The Upright E shews the Length of
the same on the Front DR.
[Illustration: FIG. XXXIII.]
Figura Trigesimatertia.
Deformatio coronicis Compositæ.
_Figura hæc trigesimatertia minus ardua tibi videbitur, si ex ea
delineandam primùm suscipias medietatem quæ respondet vestigio ~PN~ &
elevationi ~BR~ figuræ trigesimæsecundæ; rejecto in ultimum fastigio,
postquàm cætera compleveris. Linea ~BV~ est horizontalis. Punctum oculi
est ~V~, punctum distantiæ remotum est ab ~V~ spatio ~BV~, additis
modulis quatuordecim cum dimidio. Linea plani est ~AR~, in quam ex ~Q~
versus ~A~ transfertur latitudo ~P~; ex ~Q~ versus ~R~ transfertur
longitudo ~N~, cum omnibus earum divisionibus; ut ex punctis latitudinis
fiant visuales ad punctum oculi; & ex punctis longitudinis fiant
occultæ ad punctum distantiæ. Ex his habes quicquid necessarium est ad
projectionem opticam vestigii, ut ostendimus figurâ trigesimaprimâ.
Eademque methodo, quam ibi servavimus, contrahes elevationem ~P~
longitudinis coronicis: ac tum ex illa, tum ex vestigio, eruetur coronix
nitida more consueto._
_Ut delineetur fastigium, transferendæ sunt in lineam ~AB~ divisiones
ipsius ex elevatione ~F~ figuræ trigesimæsecundæ, ac ducendæ visuales
ad punctum oculi, additis lineis terminativis uniuscujusque membri,
quæ accipientur ex vestigio ~Q~ opticè deformato. Centrum ~O~ arcuum
fastigii nitidi, remotum est à summitate coronicis, medietate distantiæ,
quam habent ungues quadræ cui fastigium ipsum incumbit. Ac proinde, si
accipias ex elevatione ~P~ diversas altitudines membrorum fastigii;
latitudines verò accipias ex vestigio ~Q~; opus tuum feliciter absolves._
The Thirty-third Figure.
_A ~Composite~ Cornice in Perspective._
This Thirty-third Figure will be found the less difficult, if you
first attempt that Half which answers to PN in the Plan, and BR in the
Upright of the Thirty-second Figure; leaving the Pedament, till all
the rest be finish’d. The Line BV is the Horizontal. V is the Point of
Sight; the Point of Distance is fourteen Modules and a half without
the Point B, more than the Interval BV. The Line of the Plan is AR, in
which from Q toward A you have the Divisions of Breadth of the foregoing
Plan P; and from Q to R those of the Length thereof N: From the former,
Visuals are drawn to the Point of Sight; and from the latter, occult
Lines to the Point of Distance. And from these you have all that’s
necessary for putting the Plan in Perspective; as was shewn in the
Thirty-first Figure. By the Method there observ’d, you may also describe
the Perspective-Elevation of the Length P; and from this, and the Plan,
delineate the finish’d Cornice after the usual Manner.
For making the Pedament, the Divisions of the Elevation F in the
Thirty-second Figure, must be transferr’d into the Line AB, and Visuals
drawn from them to the Point of Sight; giving to each Member its proper
Out-line and Contour, as may be taken from the Perspective-Plan Q. The
Center O of the Arches in the finish’d Pedament, is plac’d below the
upper Member of the Cornice, as much as half the Extent of the upper
Fillet from whence the Pedament springs. And by taking the several
Heights of the Members thereof, from the Elevation P; and the Breadths
from the Plan Q; you will successfully finish and complete your Work.
[Illustration: FIG. XXXIV.]
Figura Trigesimaquarta.
Præparatio ad figuram trigesimamquintam.
_Si placuerit conferre figuram trigesimamtertiam cum præsenti figura
trigesimaquarta, dignosces vestigium & elevationem coronicis Compositæ
alio modo hic deformari, mutando scilicet longitudinem in latitudinem, &
latitudinem in longitudinem. Propterea hæc figura tantum spatii occupat,
ut eam seorsim à coronice nitida delineare oportuerit._
_Divisiones latitudinis in vestigio incipiunt ex ~V~ versus ~R~, & sunt
eædem cum divisionibus rectæ ~IG~ figuræ trigesimæsecundæ. Divisiones
longitudinis incipiunt ex ~V~ versus ~S~, & sunt eædem cum divisionibus
rectæ ~IP~ duplicatis. Ex divisionibus latitudinis fiunt visuales ad
punctum oculi; ex divisionibus longitudinis fiunt rectæ ad punctum
distantiæ; cum reliquis quæ necessaria sunt ad complendum vestigium
~AVDC~._
_Elevatio longitudinis coronicis & fastigii, opticè contrahitur per
lineas parallelas ad lineam plani ~AS~; quæ ubi pervenerint ad visualem
~AC~, continuentur cum aliis parallelis ad perpendiculum ~P~, ut diximus
figurâ trigesimaprimâ. In idem perpendiculum ~P~ transferuntur ex figurâ
trigesimasecundâ divisiones rectæ ~DR~; & insuper altitudines, quas
puncta ~KXZ~ habent supra rectam ~VA~; fientque visuales ad punctum
oculi: sectiones autem visualium cum parallelis ad perpendiculum ~P~,
dabunt sex puncta simæ fastigii, respondentia punctis ~KXZ~ duplicatis,
figuræ trigesimæsecundæ; earumque ductu formandus est supremus arcus.
Eodem artificio fient reliqui omnes._
_Faciliùs delineabitur coronix, cujus maximam partem occupant lineæ
visuales ad punctum oculi: porrò, membra omnia, exceptâ simâ, communia
sunt coronæ & fastigio. Adeoque puncta similia in lineis terminativis
membrorum singulorum, ex quibus desumuntur crepidines & ungues figuræ
nitidæ, sunt parallela ad perpendiculum ~P~._
The Thirty-fourth Figure,
_Preparatory to the Thirty-fifth._
If you please to compare the Thirty-third Figure with this Thirty-fourth
Figure, you will perceive the Plan and Elevation of this _Composite_
Cornice to be delineated differently from that; to wit, by making the
Length of that the Breadth of this, and the Breadth of that the Length of
this: On which account, this Figure takes up so much Room, that there was
a necessity of drawing the finish’d Cornice on a separate Paper.
The Divisions of Breadth in the Plan begin from V toward R; and are the
same with those of the Line IG in the Thirty-second Figure. The Divisions
of Length are set from V toward S; and are the same with those of the
Line IP in the Thirty-second Figure; which being the Half, is here
doubl’d. From the Divisions of Breadth, Lines are drawn to the Point of
Sight; and from those of the Length, Lines to the Point of Distance; with
the farther Requisites for completing the Plan AVDC in Perspective.
The Upright of the Length of the Cornice and Pedament, is made by
producing Parallels to the Ground-line AS; till they intersect the Visual
AC; and thence continuing Lines parallel to the Perpendicular P, as was
directed in the Thirty-first Figure. Into the same Perpendicular P are
transferr’d the Divisions of the Line DR in the Thirty-second Figure;
and also the Heights which the Points KXZ have above VA in the same
Figure. From all which, Visuals are drawn to the Point of Sight; which
being intersected by the Perpendiculars, give six Points on the _Cima_ of
the Pedament, which answer to the said Points KXZ of the Thirty-second
Figure, doubl’d: By these the outward Arch is form’d. And by the same
Rule, you find Points for all the others.
You will more easily draw the Cornice, the greatest Part of it consisting
of visual Lines to the Point of Sight: Moreover, all the Members, except
the upper _Cima_, are common both to the Cornice of the Entablature,
and to the Pedament; so that the corresponding Points, in the Out-lines
of their several Members, from whence the Breaks and Contours of the
finish’d Piece are taken, are found in the same Parallels to the
Perpendicular P.
[Illustration: FIG. XXXV.]
Figura Trigesimaquinta.
Deformatio coronicis Compositæ, ad latus inspectæ.
_Artificium nitidæ coronicis, ex vestigio & elevatione figuræ
trigesimæquartæ eruendæ, non differt ab eo quod sæpè traditum est. Itaque
supposito, quòd linea plani & horizontis, ac puncta oculi ac distantiæ,
habeant in hoc schemate situm omnino eundem, quem habent in præcedenti;
ope duorum circinorum, invenientur distantiæ, quas anguli necessarii ad
integram delineationem coronicis, habent à linea plani, & à linea normali
ad ipsam lineam plani. Nam ducendo lineas visuales, aliasque lineas
parallelas ad ipsum perpendiculum, cum terminis & flexibus qui conveniunt
singulis membris, complebitur delineatio._
_In fastigio visuales sunt penitus occultæ: puncta autem similia ~H~
& ~L~, ex quibus fastigium incipit introrsum flecti, incidunt in unam
eandemque visualem. Idipsum dico de aliis punctis similibus. Nam
lineæ rectæ omnes, quæ in figura trigesimatertia sunt parallelæ ad
lineam plani, in figuris trigesimaquarta & trigesimaquinta sunt partes
linearum visualium._
The Thirty-fifth Figure.
_A Side-View of the ~Composite~ Cornice, in Perspective._
The Manner of drawing this finish’d Cornice, from the preceding Plan and
Elevation, is the same with that so often shewn you. Admitting therefore,
that the Lines of the Plan and Horizon, and the Points of Sight and
Distance, have the very same Position in this, that they had in the
preceding Scheme; all the Angles necessary for delineating the entire
Cornice, are readily found by the help of two pair of Compasses; taking
their Distances one way from the Ground-line; and the other way from a
Line perpendicular to the same: Then drawing the visual and perpendicular
Lines, and keeping the Place and Contour of the several Mouldings, you
complete your Design.
In the Pedament the visual Lines are wholly occult; and the Points H
and L, where the Pedament begins to break back, being of like Height,
are found in one and the same Visual: And the same may be said of all
Points that are of equal Height from the Plan; for all the right Lines,
which in the Thirty-third Figure are Parallels to the Ground-line, in the
Thirty-fourth and Thirty-fifth Figures are Parts of the visual Lines.
[Illustration: FIG. XXXVI.]
FIGURA Trigesimasexta.
Præparatio ad figuram trigesimamseptimam.
_In vestigio geometrico ~C~, & in ejus elevatione ~AB~, præcipuas tantùm
lineas adnotavi, ne figuram confunderem, & ut studiosorum industriæ
aliquid relinquerem. Linea plani ~EG~ habet divisiones latitudinis ~P~,
& longitudinis ~Q~, vestigii geometrici ~C~. Ex punctis latitudinis
ducentur more solito visuales ad ~O~ punctum oculi; ex punctis
longitudinis fient occultæ ad punctum distantiæ, quod extra lineam
~AB~ protenditur modulis quatuordecim: & ubi occultæ ex divisionibus
longitudinis secant visualem ~FO~ fiunt parallelæ ad lineam plani ~EF~,
adhibitis sectionibus talium parallelarum cum visualibus, ad complendam
deformationem vestigii._
_Eædem lineæ quæ in vestigio deformato sunt parallelæ ad ~EF~,
prolongantur usque ad visualem ~EO~, & continuantur cum aliis parallelis
ad perpendiculum ~DE~. Fiunt quoque visuales ad punctum oculi ex
divisionibus elevationis ~AB~ translatis in perpendiculum ~DE~;
adhibitis sectionibus talium parallelarum cum visualibus, ad complendam
deformationem longitudinis elevationis._
The Six and thirtieth Figure,
_Preparatory to the Thirty-seventh._
In the Geometrical Plan C, and in the Elevation thereof AB, I have only
mark’d the principal Lines, as well for avoiding Confusion in the
Figure, as that something might be left to the Industry of the Studious.
The Line of the Plan EG has the Divisions of Breadth P, and of Length
Q, of the Geometrical Plan C. From the Points of Breadth are drawn, as
usual, Visuals to the Point of Sight O; From the Points of Length occult
Lines are produc’d to the Point of Distance, which lies fourteen Modules
without the Line AB: And where the occult Lines from the Divisions of
Length cut the Visual FO, Parallels are made to the Ground-Line EF; and
from the Intersections of those Parallels with the Visuals, you complete
the Delineation of the Plan in Perspective.
The Lines which in the Plan are parallel to EF, being prolong’d to the
Visual EO, are then continu’d parallel to the Perpendicular DE. And from
the Divisions of AB, produc’d to DE, visual Lines are drawn to the Point
of Sight; which intersecting the Perpendiculars aforesaid, you from
thence find the Length of the Elevation in Perspective.
[Illustration: FIG. XXXVII.]
FIGURA Trigesimaseptima.
Deformatio columnæ Etruscæ.
_Ex præparatione quam exhibuimus figurâ trigesimasextâ, eruitur columna
hæc nitida Ordinis Etrusci, opticè imminuta per latitudines & altitudines
partium singularum; quæ accipiuntur ope duorum circinorum, ut sæpiùs
dictum est._
The Thirty-seventh Figure.
_A ~Tuscan~ Column in Perspective._
From the Preparation exhibited in the Thirty-sixth Figure, is drawn this
complete Piece of the _Tuscan_ Order, brought into Perspective by means
of the Breadths and Heights of the several Parts, exactly taken off with
the Compasses, as has been often said.
[Illustration: FIG. XXXVIII.]
FIGURA Trigesimaoctava.
Præparatio ad figuram trigesimamnonam.
_Hæc figura est simillima figuræ trigesimæsextæ. In vestigio ~P~ limes
prominentiæ coronicis est ~R~; coronæ verò in stylobatâ est ~T~.
soliditas stylobatæ est ~V~. ambitus columnæ in imo est ~X~, in summo
~Z~._
The Thirty-eighth Figure.
_Preparatory to the Thirty-ninth._
This Figure is very much the same with the Thirty-sixth. In the Plan
P, the utmost Projecture of the Cornice is R; that of the Cap of the
Pedestal is T; the Trunk of the Pedestal is V; the naked Shaft of the
Column at bottom is X, at top is Z.
[Illustration: FIG. XXXIX.]
FIGURA Trigesimanona.
Deformatio ædificii Dorici.
_Habes hoc loco ædificium Doricum, addito statuæ unius ornamento. Velim
autem, ut si figuram aliquam ex his desumptam, delineandam assumas,
aliquid mutes saltem in loco punctorum oculi aut distantiæ. Hoc modo
majores in hac arte progressus facies; & si alicubi cælator aberraverit,
ex lapsu illius nullum senties detrimentum._
The Nine and thirtieth Figure.
_A Piece of ~Dorick~ Architecture in Perspective._
In this Plate you have a _Dorick_ Composition, with the additional
Ornament of a single Statue; but I would advise, when you undertake to
work after any of these Designs, you would at least place the Points
of Sight and Distance somewhat differing from those here given; which
Practice will both greatly further your Progress in this Art, and prevent
any Inconvenience, that may arise from a Mistake of the Engraver.
[Illustration: FIG. XL.]