Deformatio elevationis figuræ sexagesimæoctavæ, & præparatio quarta ad
figuram septuagesimamprimam.
_Quæ dicta sunt de projectione vestigii nostri ædificii, habent locum
in elevatione. Nimirum, ut parallelæ invicem notabiliter distarent, usi
sumus industriâ quam declaravimus figurâ quadragesimasecundâ._
The Seventieth FIGURE.
_The Perspective of the Elevation of the Sixty-eighth Figure, and the
fourth Preparation to the Seventy-first Figure._
What has been said of the Perspective-Plan of this Structure, is also
here practis’d in the Elevation; namely, that the Parallels might be
sufficiently distinct, the Perpendiculars are drawn more remote from the
Point of Sight, as was shewn in the Forty-second Figure.
[Illustration: FIG. LXXI.]
FIGURA Septuagesimaprima.
Theatrum repræsentans Nuptias Canæ Galilææ, constructum Romæ, anno 1685.
in expositione Ven. Sacramenti in Templo Farnesiano Societatis JESU.
_Ex antecedentibus præparationibus eruimus projectionem nobilis hujus
Architecturæ, quæ oculos implebat tum ad lucem solis diurnam, tum
præcipuè ad lumen candelarum; ex quibus multæ palam erant expositæ,
aliæ omnino latebant, ut illuminarent sex diversos ordines telariorum
quibus tota machina constabat, non computando in hoc numero telaria,
quæ in medio arcûs maximi exprimebant nubes refertas Angelis adorantibus
Venerabile Sacramentum. Nubes istas omisimus, ne absconderentur
partes interiorum ædificiorum. In disponendis autem ordinibus
telariorum, servatus est modus quem declaravi figurâ sexagesimaprima
& sexagesimasecunda; ac præterea in eligenda eorum distantia curatum
fuit, ut candelæ in parte postica telariorum collocatæ, illuminarent
faciem telariorum interiorum. Porrò quot membra præcipua in duabus
faciebus majoribus, totidem distincta telaria numerabantur, quorum
proinde connexiones discerni vix poterant; eorumque aliquot paria ferreis
hamulis copulata erant, ut explicari ac replicari possent, ad faciliorem
tractationem diuturnioremque conservationem._
_Qui hucusque sequuti me fuerint, nihil dubito quin suum iter felicissimè
sint prosequuturi; atque Opera his nostris majora melioraque inventuri._
The Seventy-first FIGURE.
_A Theater representing the Marriage of ~Cana~ in ~Galilee~, erected in
the ~Jesuits~ Church at ~Rome~, in the Year ~1685~; for the Solemnity of
exposing the Holy Sacrament._
From the foregoing Preparations, is drawn the Perspective of this noble
Piece of Architecture; which struck the Eye when seen by Day-light, but
was more especially surprizing by Candle-light; many of the Candles being
expos’d to Sight, and others altogether hidden, to illuminate the six
different Ranges of Scenes, of which the whole Work consisted, without
reckoning that in the midst of the great Arch, representing Clouds fill’d
with Angels adoring the blessed Sacrament. Those Clouds are here omitted,
that the inner Parts of the Work might be the better seen. In disposing
the several Ranges of Scenes, the same Method was observ’d, which was
deliver’d in the Sixty-first and Sixty-second Figures; and great Care was
also taken in their Distances, that the Candles plac’d on the Back of one
of them might illuminate the Face of the other behind it. Moreover, each
Scene consisted of as many parts, as there were principal Members in the
two greater Façades; so that the Joints were scarcely discernible: and
some Pairs of them being coupl’d with Hinges, folded and unfolded, for
the more easy managing and preserving them.
I doubt not but those who have follow’d me thus far, will be encourag’d
so to prosecute their Studies, as to be able to design even greater and
more noble Works, than these of mine.
[Illustration: FIG. LXXII.]
FIGURA Septuagesimasecunda.
De theatris scenicis.
_Theatris quæ jam delineavimus affinia sunt theatra scenica: in his tamen
non adeò facilè reperitur punctum oculi seu perspectivæ. Præterea, quia
ex obliquitate canalium intra quos moventur scenæ, oritur ut lineæ rectæ
quæ videri debent parallelæ ad lineam plani, non debeant esse parallelæ
sed obliquæ, harum delineatio difficultate non caret. Incommodum istud
vitari posset adhibendo canales parallelos ad poscenium, ut alicubi
fieri solet, præsertim in Germaniâ. Nihilominus usus Italicus affert
hoc adjumentum, ut illi quibus incumbit suggerere actoribus, vel scenas
movere, aliisque similibus præesse, facilius lateant & liberius fungantur
munere suo._
_Ut brevem summam habeas eorum quæ deinde latius declaraturi sumus,
hanc figuram contemplare. ~1~, ~2~, ~3~, ~4~, est vestigium aulæ quæ
habet in longitudine centumviginti palmos Romanos, in latitudine
sexaginta palmos; ut ostendit scala ~S~ triginta palmorum. Medietatem
loci occupat theatrum, medietatem obtinent podia & loca spectatorum.
~O~ punctum in quo uniuntur lineæ visuales, ~D~ locus pro apparentiis
rerum magis ac magis distantium. ~BC~ locus poscenii. ~HH~ sunt canales
obliqui, quorum latitudo est dupla latitudinis scenarum. ~FG~ frons
& facies theatri. ~AO~ ejus profunditas aut longitudo. ~E~ locus pro
psaltibus, tibicinibus, & fistulatoribus. ~K~ spatium pro spectatoribus.
~I~ vestigium podiorum. ~L~ scalæ podiorum. ~N~ ipsorum elevatio. ~M~
declivitas tabulati, cum sectione & elevatione theatri, & scenis ex
latere inspectis, quæ cum suis canalibus congruunt, ut demonstrant lineæ
occultæ. ~OO~ linea normalis ad lineam horizontalem. ~P~ & ~Q~ elevatio
scenarum coram inspectarum, quæ introrsum flectuntur; & in latitudine
congruunt cum canalibus vestigii ~B~, in altitudine cum sectionibus
elevationis ~M~; ut constat ex lineis occultis. In eâdem elevatione ~M~
pars altitudinis tribuenda est scenis, pars laquearibus ~R~, per quæ
jungitur unumquodque par telariorum. ~VV~ lineæ ad explorandum an detur
vacuum inter scenas & laquearia, vel inter scenas, vel inter laquearia.
In quibusdam autem scenis, loco laquearium pinguntur nubes & aer._
The Seventy-second FIGURE.
_Of Scenes for the Stage._
Scenes for the Stage have very much Affinity with those lately describ’d,
but the Point of Sight is not so easily found in these; and from the
Obliquity of the Grooves in which the Scenes run, it comes to pass, that
the right Lines which ought to appear parallel to the Line of the Plan,
must not be drawn parallel thereto, but oblique; which is a Work of some
Difficulty. This indeed may be avoided, by fixing the Grooves parallel
to the Poscene; as is usual in some Places, especially in _Germany_.
Nevertheless, the _Italian_ Manner has this Advantage; That those who
are employ’d to prompt the Actors, and shift the Scenes, _&c._ are less
expos’d to Sight, in the Performance of their Business.
In this Figure I have given you an Abridgment of those things, which
shall hereafter be more enlarg’d on. The Numbers 1, 2, 3, 4, denote the
Area of a Hall an hundred and twenty _Roman_ Palms in Length, and sixty
in Breadth; as is manifest from the Scale of thirty Palms mark’d S. Half
this Space is taken up by the Stage, the other half by the Spectators. O
is the Point in which the visual Lines concenter. D is the Place of those
things that are to appear most remote. BC is the Place of the Poscene.
HH are the oblique Grooves, whose Lengths are double the Breadth of
the Scenes. FG is the Front of the Stage. AO is its Depth or Length.
E is the Place for the Musick. K is the Room for Spectators. I is the
Plan of the Galleries. L the Stairs to the same. N is the Elevation of
the Galleries. M shews the Declivity of the Floor, with the Section
and Elevation of the Stage and Scenes view’d on the Side; answering
their respective Grooves, as the occult Lines demonstrate. OO is a Line
perpendicular to that of the Horizon. P and Q are the Elevation of the
Scenes view’d in Front, turning inwards, in Breadth agreeing with the
Length of the Grooves of the Plan B; and in Height answering that of the
Sections of the Elevation M; as is evident from the occult Lines. In this
Profile M, part of the Height belongs to the Scenes, and part to their
Soffites, or Ceilings, R; where each Pair of these Frames are join’d. VV
are the Lines by which is espy’d what Vacancy there is either between
the Scenes and their Ceilings, between the Scenes themselves, or between
their respective Ceilings; though in some Scenes the Place of these last
is supply’d by painting therein the Air with Clouds, _&c._
[Illustration: Fig. lxxiii.]
FIGURA Septuagesimatertia.
Aliud vestigium theatri, ubi de modo inveniendi ejus punctum.
_Si pingendæ sint scenæ theatri alicujus antea constructi, delineare
oportebit vestigium geometricum ex ipso erutum, (ad formam vestigii quod
cernis in hac paginâ) ut inveniatur longitudo theatri, seu distantia quam
ejus punctum habet à puncto ~A~: id autem nullo negotio fiet, accipiendo
distantias ~BC~ inter primos canales, & ~DE~ inter ultimos, ac ducendo
visuales ~MO, NO~: nam theatrum habebit longitudinem ~AO~, ac punctum
perspectivæ in vestigio theatri erit ~O~. Præterea scire oportebit
longitudinem & latitudinem canalium, eorumque numerum, distantias, &
flexus; ac præcipuè curandum est, ut licet sint obliqui ad lineam ~MN~,
sint invicem paralleli in unoquoque latere, ac singuli tangant lineas
~MO, NO~. Jam si rectæ ~AO~ fiat æqualis recta ~FA~, in ~F~ erit punctum
distantiæ: adeoque si theatrum juxta methodum à nobis tradendam depictum
fuerit, spectatori qui consistat in ~F~ apparebit veluti tabula picta
juxta leges perspectivæ, posita in ~A~._
The Seventy-third FIGURE.
_Another Plan of a Theater, with the Method of finding the Point of Sight
therein._
If it be requir’d to paint the Scenes of some Theater already built, the
Geometrical Plan thereof must first be carefully drawn, (as you see, for
Example, in this Plate) that the Length of the Theater may be found; or
the Distance of its Point from that of A; which is easily done, by taking
the Interval BC of the first Grooves, and DE of the latter; and drawing
the Visuals MO, NO: for AO is the Length of the Theater, and the Point
of Sight, or Perspective, therein, is O. Moreover the Length and Breadth
of the Grooves must be known, as also their Numbers, Distance, and
Obliquity; and especial Care must be taken, that though they be oblique
to the Line MN, that on each Side they be Parallels between themselves,
and that they all touch the Lines MO, NO. If you then make AO equal to
FA, the Point of Distance will be F; and if the Theater be painted
according to the Rules hereafter given, it will appear to him that views
it from F, as a regular Piece of Perspective plac’d in A.
[Illustration: FIG. LXXIV.]
Figura Septuages. quarta.
Sectio Scenarum Theatri.
_Præter vestigium Theatri delineanda est sectio scenarum. Itaque si
acceptis mensuris altitudinis, quam punctum ~A~ unde incipit tabulatum,
ac punctum ~D~ poscenii, habent supra planum horizontale ~FV~, fiant ex
perpendiculo ~NV~ tum recta ~ADO~ ex qua innotescit declivitas tabulati,
tum recta ~NO~, quæ sit parallela ad ~FV~ & æqualis rectæ ~AO~ figuræ
septuagesimætertiæ; punctum theatri in elevatione est ~O~; in poscenio
verò punctum theatri est ~Q~. Si maxima scenarum altitudo sit ~EB~, recta
~OE~ dat altitudinem omnium reliquarum. Vera tamen altitudo cujuslibet
scenæ est illa quam habet linea major, ex minori autem dignoscitur
quantum obliquitas cujusque scenæ apparenter minuat altitudinem extremæ
illius lineæ. Porro excessus quo linea major superat minorem tum in summo
tum in imo, diligenter notandus est, hinc enim pendet intelligentia
figuræ septuagesimæquintæ. Punctum ~M~ quod est remotum ab ~N~ quantum in
figura septuagesimatertia punctum ~F~ est remotum ab ~A~, designat locum
unde Theatrum spectari oporteat, ut ibidem notavimus._
_In construendo tabulato solet servari hæc regula, ut altitudo puncti ~O~
sit æqualis altitudini oculi, & elevatio ex ~A~ usque ad ~D~ sit nona
circiter vel decima pars ipsius longitudinis ~AD~. Expediret autem ad
scenas facilius movendas, pavimentum ~F~ esse profundius pavimento ~G~,
ut erecto corpore sub tabulato ambulari possit._
Seventy-fourth Figure.
_The Section or Profile of Scenes for Theaters._
Besides the Plan of the Theater, the Section of the Scenes is also to
be delineated, for finding the Point of the Theater in the Elevation.
Wherefore, setting the Measures of the Heights which the Point A, where
the Floor of the Stage begins, and the Point D of the Poscene, have above
the Level of the Horizontal FV; from the Perpendicular NV draw the right
Line ADO, which gives the Declivity of the Stage; then make NO parallel
to FV, and equal to AO of the Seventy-third Figure: The Point of the
Theater in Elevation is O; the Point of the same on the Poscene is Q. If
EB be the greatest Height of the first Scene, the Line OE determines the
Height of all the others. The longest of the two Lines gives the true
Height of each Scene; and the shorter discovers how much of that Height
the Sight loses on the Out-line, by the oblique Position of the Scenes.
Moreover, the Excess of the longer Line above the shorter, as well at
top as at bottom, is to be well observ’d; for on this depends the right
Understanding of the Seventy-fifth Figure. The Point M, which is as far
distant from N, as that of F is from A in the Seventy-third Figure,
denotes the Place from whence the Stage ought to be view’d; as is there
mention’d.
In laying the Floor of the Stage, this Rule is commonly observ’d, That
the Height of the Point O be made equal to the Height of the Eye, and
that the Rise of the Floor from A to D, be about a Ninth or Tenth Part of
the Length AD. ’Tis also requisite, for the better shifting the Scenes,
that the Pavement F be sunk lower than that of G, that a Man may walk
upright under the Floor thereof.
[Illustration: FIG. LXXV.]
FIGURA Septuagesimaquinta.
Elevatio scenarum coram inspectarum: ubi docetur artificium ut scenæ
obliquæ appareant rectæ.
_Scenæ quas vides in ~S~, habent suam latitudinem à vestigio figuræ
septuagesimætertiæ, altitudinem ab elevatione figuræ septuagesimæquartæ,
ac censentur erectæ & canalibus insertæ, quæ omnia repræsentantur etiam
figurâ septuagesimasecunda in ~P~ & ~Q~. Velim observes quantum elevetur
tabulatum in principio ~A~, in poscenio ~D~, & in puncto theatri ~O~.
Similiter notare oportet elevationem singularum scenarum, quæ propter
obliquitatem canalium flectuntur introrsum: iccirco lineæ ~BL~, ~KI~,
partis ~C~, non videntur parallelæ ad lineam plani, ut reipsa sunt; ac
visualis ~LF~ non tendit ad punctum oculi ~O~, sed ad punctum ~F~. Si
autem excessus apparens, quem recta ~BK~ habet in summo & imo supra
rectam ~LI~ transferatur in partem ~E~ scenarum, (iidem excessus desumi
etiam possunt ex figura septuagesimaquarta) ac ducantur rectæ ~LG~, ~IH~,
habebuntur lineæ apparenter parallelæ ad lineam plani. Si fiat recta
~LO~, quæ cum ~LG~ faciat angulum ~GLO~ æqualem angulo ~BLF~, eadem ~LO~
tendet exactissimè ad punctum ~O~ oculi, eâque utendum erit ut visuali._
_In ~P~ supponimus scenas ~M~ & ~N~ jacere super pavimento unas super
aliis, ac duas lineas ~RT~ habere distantiam eandem cum duabus ~LI~, &
ita in reliquis scenis. Ubi notandum est, lineas ~RS~, ~TV~, easdem esse
cum lineis ~LG~, ~IH~, scenarum ~E~: nihilominus lineas ~RS~, ~TV~, non
esse parallelas, quum tamen ~LG~, ~IH~, videantur parallelæ. Proinde, si
fiat recta ~RL~, & anguli ~SRL~, ~GLO~, sint æquales, rectâ ~RL~ utendum
erit tanquam visuali, in ~L~ erit punctum accidentale oculi pro pingendis
scenis ~N~, ac lineæ ~RS~, ~TV~, habebuntur ut parallelæ: id autem quod
superest in telario ultra tales lineas, pro nihilo computabitur, ibique
pingetur aer aut aliquid aliud. Punctum accidentale oculi pro pingendis
scenis ~M~ erit in ~I~._
The Seventy-fifth FIGURE.
_The Elevation of Scenes in Front, and how the oblique Scenes are made
to appear direct._
The Scenes in S have their Breadth from the Plan of the Seventy-third
Figure, and their Height from the Elevation of the Seventy-fourth
Figure; and are suppos’d to stand perpendicularly in their Grooves; all
which is also represented in P and Q of the Seventy-second Figure. I
would have you observe, how much the Floor rises, from its Edge A, to
the Poscene D, and to the Point of the Theater O. You should also note
the Elevation of each Scene, which, by reason of the Obliquity of the
Grooves, turn inward: Wherefore the Lines BL, KI, of the Part C, do not
seem Parallels to the Ground-line, as they really are; and the Visual LF
tends not to the Point of Sight O, but to the Point F. But if the seeming
Excess, which the Line BK has at top and at bottom, above the Line LI, be
transferr’d on the Side of the Scenes E, (which Excess may also be taken
from the Seventy-fourth Figure) and you draw the Lines LG, IH; these
Lines will appear Parallels to the Line of the Plan. Then drawing the
Line LO, so as to make the Angle GLO equal to the Angle BLF, the said LO
shall tend directly to the Point of Sight O; and serve for a visual Line.
In P, I suppose the Scenes M and N to lie one upon another on the Floor,
and the two Lines RT to have the same Distance as the Lines LI; and so
of the others. Where you are to take Notice, that the Lines RS, TV, are
the same with the Lines LG, IH, of the Scenes E: and that the Lines RS,
TV, are not Parallels; altho’ LG, IH, seem to be so. Therefore, if you
draw the Line RL, so that the Angles SRL, and GLO, be equal; the Line RL
shall serve as a Visual, and L shall be the accidental Point of Sight,
for painting the Scenes of the Side N; and the Lines RS, TV, shall be
us’d as Parallels. What remains on the Frame, beyond those Lines, is to
be reckon’d as nothing; but you may paint there Air, or what you please.
The accidental Point of Sight for painting the Scenes of the Side M, is I.
[Illustration: FIG. LXXVI.]
FIGURA Septuagesimasexta.
Modus delineandi exemplar scenarum.
_Iterum delineavimus scenas erectas super tabulato; in ~B~ nudas, in
~A~ depictas, additis projecturis coronicum & aliorum ornamentorum.
Deformatio scenarum ~A~ eruitur methodo consuetâ ex vestigio ~C~, in quo
videbis lineam plani deorsum protractam. Vestigium autem geometricum est
in ~D~._
The Seventy-sixth FIGURE.
_The Manner of delineating the Designs of Scenes._
In this Plate you have another Design of Scenes erected on the Floor; the
naked Scenes are B; the painted ones A; with the additional Projectures
of Cornices and other Ornaments. The Draught of the Scenes A is produc’d
from the Plan C, after the usual Manner; in which you may observe the
Ground-line to be lower than its true place, for the greater Distinction
of the Parallels. The Geometrical Plan is D.
[Illustration: FIG. LXXVII.]
FIGURA Septuagesimaseptima.
Modus reticulandi & pingendi scenas theatri.
_Postquam in pavimento exactissimè disposueris tum poscenium, tum
ex ordine scenas reliquas, unam alteri incumbentem, ut figurâ
septuagesimaquintâ declaravimus, fiet linea horizontalis, in qua notanda
sunt tria puncta perspectivæ, unum in ~O~ usui futurum in pingendo
poscenio, ac duo reliqua hinc inde, singula videlicet pro scenis partis
oppositæ. Jam supponendo quòd in parvo exemplari ~A~ primæ scenæ facta
fuerit reticulatio per quadrata perfecta; proportionalis divisio
fiet tum in recta ~HI~ primæ scenæ ~B~, tum in recta ~CD~. Postea ex
puncto ~E~, per singula puncta divisionum rectæ ~HI~, fient visuales,
adhibendo funiculum colore nigro imbutum; earumque ope, ut figura
ostendit, reticulare oportebit scenam ~B~, tum remotâ ea scenam illi
subjectam, & eodem modo aliam & aliam; ac demum per divisiones quas
in recta ~LM~ faciunt visuales ex puncto ~E~, absolvetur reticulatio
poscenii, cujus quadrata esse debent perfecta, secus quadrata scenarum.
In parte inferiori paginæ, duæ scenæ ~G~ & ~F~ ostendunt ornamenta quæ in
scenis depingi possunt. Velim autem observes, tum lineas transversas
coronicum, quæ non sunt invicem parallelæ, tum visuales, quæ tendunt
ad puncta opposita. Nam ejusmodi lineæ continent duas peculiares
difficultates projectionum theatralium; easque ut superes, exactè
servandæ sunt regulæ quas declaravimus._
The Seventy-seventh FIGURE.
_The Manner of making the Net-work or Squares, and painting the Scenes of
Theaters._
After you have with great Exactness dispos’d the Poscene on the Pavement,
and the others in order one upon another, as was mention’d in the
Seventy-fifth Figure; draw the horizontal Line, and mark therein three
Points of Sight: That in O, for the Use of the Poscene; and the Points
on the Sides, for the Service of the opposite Scenes respectively. Then,
supposing that the Net-work of the small Draught of the first Scene A,
consists of perfect Squares; transport the same Divisions both on the
Lines HI and CD of the first Scene B; and with a black Line strike the
Visuals from the Point E, by the Points of the Divisions of HI; and
by the Help of those Visuals make the Net-work of the Scene B, as is
done in the Figure. When that’s done, lay it aside; and do the next in
the same manner; and so of the others. Lastly, by the Divisions, which
the Visuals from the Point E make on the Perpendicular LM, finish the
Net-work on the Poscene, which consists of perfect Squares, though that
of the Scenes does not. The two Scenes of the lower part of the Plate, G
and F, shew what Diversity of Ornament the Painter may introduce. I would
have you also take particular Notice, both of the transverse Lines of the
Cornice, which are not Parallels to each other; and of the Visuals which
are directed to their opposite Points: because in these two Particulars
lies the greatest Difficulty of describing Theatrical Designs; for the
surmounting which, it’s absolutely necessary, that you carefully regard
the Rules hitherto deliver’d.
[Illustration: FIG. LXXVIII.]
FIGURA Septuagesimaoctava.
De projectionibus horizontalibus.
_Quemadmodum facilior est deformatio columnarum jacentium, quàm
columnarum erectarum; (nam lineæ quæ in istis sunt perpendiculares,
in illis sunt visuales, ac nullus circulus amittit suam formam) ita
projectiones horizontales, quas in laquearibus delineare necesse est,
contra quàm Pictores imaginantur, expeditiores & faciliores sunt
verticalibus, quas hucusque tractavimus. Nam ut stylobatæ & columnæ
appareant erectæ, pingendæ sunt veluti jacentes._
_Deformationes horizontales auspicamur à mutulis, quia columnæ ac
stylobatæ identidem iis imponuntur, ut magis in prospectu sint. Ob
diversitatem verò quam habet latus mutuli à sua facie, utriusque
delineationem geometricam seorsim in hac figura exhibemus._
The Seventy-eighth FIGURE.
_Of horizontal Perspective._
As it is easier to describe in Perspective Columns lying on the ground,
than those that are erect, (the Lines in these last being Perpendiculars,
which in the former are Visuals, wherein no Circle loses its Form) so
the horizontal Projections of Perspective, proper for Ceilings, contrary
to the Judgment Painters usually make, are perform’d with more Ease
and Expedition, than the vertical, which we have hitherto treated of;
forasmuch as the Pedestals and Columns that must appear erect, are
painted as if lying on the ground.
I have usher’d in these horizontal Designs with those of Corbels,
because, for setting the Pedestals and Columns more in View, they
generally seem to be supported by them. And the Side of this Corbel being
different from its Face, I have here inserted a Geometrical Description
of each distinct.
[Illustration: FIG. LXXIX.]
FIGURA Septuagesimanona.
Projectiones vestigii & elevationis mutuli.
_Facies mutuli quam delineavimus figurâ septuagesimaoctavâ, gerit
hic munus vestigii; latus verò gerit munus elevationis; ut ostendunt
lineæ occultæ, quæ ex divisionibus faciei tendunt ad punctum oculi,
ex divisionibus lateris tendunt ad punctum distantiæ (puncta oculi
ac distantiæ in hac & sequentibus figuris cadunt extra paginam.) Per
sectiones harum linearum ducuntur lineæ quæ terminant singulas partes
vestigii deformati; hujusque adjumento ducitur elevatio lateris, ac
methodo consuetâ latitudines & longitudines mutuli solidi eruuntur ex
vestigio, altitudines ex elevatione. Hic & deinceps nomina longitudinis
& altitudinis usurpamus, veluti planum cujuslibet perspectivæ esset
verticale; in quâ suppositione, ~IL~ esset latitudo mutuli, ~SR~
altitudo, ~RL~ longitudo: quum ~SR~ reverà sit longitudo, ~RL~ altitudo.
Ad faciliorem descriptionem hujus figuræ observandum est, rectis ~IL,
LM, GH,~ hujus paginæ inesse divisiones rectarum ~DC, FE, AB,~ figuræ
septuagesimæoctavæ._
The Seventy-ninth FIGURE.
_The Plan and Elevation of a Corbel in Perspective._
The Face of the Corbel describ’d in the Seventy-eighth Figure, in this
does the Office of a Plan; and the Side serves here for the Elevation;
as is plain from the occult Lines, which from the Divisions of the Face
tend to the Point of Sight, and from those of the Side tend to the Point
of Distance; both which Points, in this and the succeeding Figure, fall
without the Plate. From the Intersections of these Lines are drawn
others, that determine each Part of the Perspective-Plan; by means of
which, the Elevation of the Side being also form’d, the Breadths and
Lengths of the solid Corbel are taken, as usual, from the Plan, and the
Heights from the Elevation. Here and henceforward, the Terms of Length
and Height are made use of, as though the Plan of each Perspective were
vertical; according to which Supposition, IL is the Breadth of the
Corbel, SR the Height, and RL the Length; whereas in reality SR is the
Length, and RL the Height. For the more ready Description of this Figure
you will do well to observe, that the Lines IL, LM, GH, of this Plate,
bear the same Divisions as DC, FE, AB, of the Seventy-eighth Figure.
[Illustration: FIG. LXXX.]