Explicatio linearum Plani & Horizontis, ac Punctorum Oculi & Distantiæ.
_Ut principia Perspectivæ faciliùs intelligas, pono tibi ob oculos
Templum, in cujus interiori facie, præter cætera, pingendum sit aliquid
ad Perspectivam pertinens. Templi hujus vestigium geometricum est ~A~,
elevatio geometrica in longum est ~B~, in latum est ~C~. In ~A~ est locus
Hominis aspicientis lineam ~DE~, cui paries pingendus incumbit. In ~B~
idem Homo ex eâdem distantiâ intuetur lineam ~FG~, quæ refert elevationem
parietis. In figura ~C~ supponimus Hominem consistere è regione ipsius
parietis: easdemque proportiones mensuratum translatas esse ex vero
pariete in figuram ~C~, quæ ipsum in parvo repræsentat._
_Prima ergo linea ~HI~ dicitur linea terræ vel plani, ex quâ incipit,
eidemque incumbit ædificium. Secunda linea ~NON~ priori parallela,
dicitur horizontalis, in quâ ponitur ~O~ punctum oculi, & ~N~ punctum
distantiæ. Duo autem puncta distantiæ à nobis posita sunt, ut unum
adhibeas ex quâ parte volueris; nam ad figuras opticè contrahendas
sufficit unum punctum distantiæ: nec fieri potest ulla optica delineatio,
quin primo loco designentur duæ parallelæ, una plani seu terræ, altera
horizontis, notando in lineâ horizontis, punctum oculi, seu opticum,
& punctum distantiæ. Porrò unam eandemque rem triplici Schemate
repræsentare oportuit, ut videas, locum ex quo aspicienda est figura ~C~
esse punctum ~N~ unius ex rectis ~NO~, quam concipere debemus veluti
normaliter infixam in ~O~; ac distantiam inter ~O~ & ~N~ eandem esse
debere cum distantiâ inter ~A~ & ~DE~, inter ~B~ & ~GF~._
_In picturis multum spatii occupantibus, punctum oculi poni solet
in medio lineæ horizontalis: atque ubi altitudo picturæ sit major
latitudine, distantia ~NO~ fiet æqualis altitudini. Si latitudo picturæ
sit major altitudine, distantia ~NO~ fiet æqualis latitudini; ita
enim unico intuitu totum picturæ spatium comprehendi poterit. Porrò
quamvis eadem distantia diverso modo adhibeatur in vestigio ~A~, & in
elevationibus ~B~ & ~C~; nihilominus sectiones visualium cum pariete
vestigii ~A~, & elevationis ~B~, omninò conspirant cum sectionibus
visualium figuræ ~C~._
_Jam si velimus ut spectatori in ~A~ & ~B~ paries depictus videatur
distare à lineis ~DE~ & ~GF~, quanta est longitudo quadrati ~P~, cujus
elevatio est ~Q~; ex punctis ~A~ & ~B~ fiant visuales ad puncta extrema
quadrati, notando sectiones visualium cum pariete ~DE~ & ~GF~, qui ab
aliis vocatur velum, vitrum diaphanum, sectio, tela, vel tabula. Invenies
autem, lineas ~RS~ ac ~TV~ esse æquales, ac similiter lineas ~XZ~ & ~YK~;
& sic de aliis._
The First Figure.
_Explication of the Lines of the Plan and Horizon, and of the Points of
the Eye and of the Distance._
That you may the better understand the Principles of Perspective, here
is presented to your View a Temple, on the inner Wall of which, amongst
other things, one would paint something in Perspective. The Geometrical
Plan of this Church is A, the Geometrical Elevation, or Upright,
lengthwise is B, breadthwise is C. In A is the Place from whence a Man
beholds the Line DE, which is the Plan of the Wall that is to be painted:
In B the same Man, from the same Distance, looks upon the Line FG, that
represents the Elevation of the Wall. In Fig. C, the Man is supposed to
stand opposite to the said Wall; and this Figure contains, in Little, the
very same Proportions of Measures transferr’d from the real Wall.
The first Line therefore HI is call’d the Ground-line, or Line of the
Plan, at which the Edifice begins, and on which it stands. The second
Line NON, parallel to the former, is call’d the Horizontal Line, wherein
is plac’d O the Point of the Eye, and N the Point of the Distance. Two
Points of Distance are here laid down, that you may make use of which you
please; for that on one Side only is sufficient for the fore-short’ning
Figures in Perspective: Neither can any Optick Delineation, or
Perspective, be described, without first making two Parallels; one of the
Plan, or Ground-line, the other of the Horizon; marking, in the Line of
the Horizon, the Point of the Eye, or Sight, and the Point of Distance.
It was thought besides expedient to put one and the same Thing into three
Schemes or Designs, to let you see, that the Place, from which the Figure
C is to be look’d upon, is the Point N, one of the right Lines NO, which
must be conceived as fixt at right Angles into O; the Distance ON being
the same as that between A and DE in the Plan, or between B and GF in the
Upright.
In Pictures taking up a great deal of Room, the Point of Sight ought to
be made in the middle of the Horizontal Line; and where the Height of
the Picture happens to be greater than the Breadth, the Distance NO
must be made equal to the Height. If the Breadth of the Picture exceed
the Height, the Distance NO must be made equal to the Breadth: For so
will the Extent of the Picture be the better comprehended, or receiv’d,
at one View. And altho’ the same Distance may seem to be used in a
different manner in the Plan A, and in the Elevation B, from what it is
in C; nevertheless the Sections of the visual Rays, with the Wall of the
Plan A, and of the Elevation B, have a perfect Correspondence with the
Sections of those of the Figure C.
Now, if to the Spectator in A and B, we would have the farthest Part of
the Work seem to recede from the Lines DE and GF, as much as the Square
P does, whose Elevation is Q; draw from the Points A and B, the visual
Rays to the extreme Points of the Square P and Q; noting the Sections
they make with the Walls DE and GF; which by some is call’d the Veil,
Transparent Medium, Section, Cloth, or Table: and you’ll find RS equal to
TV, XZ equal to YK; and so of the rest.
[Illustration: FIG. II.]
FIGURA Secunda.
Modus delineandi opticè Quadratum.
_Ante descriptionem opticam quadrati ~A~, quod fingimus delineatum esse in
papyro separatâ, ducendæ sunt duæ lineæ parallelæ; altera plani, altera
horizontis, ut jam docuimus; notando in linea horizontis punctum oculi
~O~, & punctum distantiæ ~E~. Tum translatâ in lineam plani latitudine
ac longitudine ipsius quadrati ~A~, ita ut linea ~CB~ sit æqualis
latitudini, & ~DC~ sit æqualis longitudini. Ex punctis ~B~ & ~C~ fiunt
visuales ~BO~, ~CO~ ad punctum oculi; ex puncto ~D~ fit recta ~DE~ ad
punctum distantiæ. Demum ubi visualem ~CO~ secat recta ~DE~, fit ~GF~
parallela ad ~CB~; habesque quadratum opticè contractum._
_Compendium temporis & laboris facies, præsertim in schematibus quæ
abundant lineis, si chartulam in medio complicaveris, eademque utaris, ut
latitudinem ac longitudinem quadrati transferas in lineam plani._
The Second Figure.
_Manner of delineating a ~Square~ in Perspective._
Before the _Square_ A, which is supposed to be drawn on a separate Paper,
can be laid down in Perspective, two parallel Lines must be drawn; one of
the Plan, the other of the Horizon, as is already intimated; noting in
the Horizontal Line the Point of Sight O, and the Point of Distance E.
Then, when the Length and Breadth of the Square A shall be transferr’d
into the Line of the Plan, so that the Line CB be equal to the Breadth,
and DC be equal to the Length, let the visual Lines BO, CO be drawn from
the Points B and C to the Point of Sight O, and the right Line DE from
the Point D to the Point of Distance. Lastly, where the Line DE cuts the
Visual CO, make GF parallel to CB: and you have the _Square_ Optically
contracted, or fore-shorten’d in Perspective.
To spare Time and Pains, especially in Figures that abound in Lines, fold
your Paper in the middle, and make use of it to transfer the Breadth and
Length of the Square, into the Line of the Plan.
[Illustration: FIG. III.]