Full text: Gravesande, Willem Jacob: An essay on perspective

on PERSPECTIVE. ved backwards or forwards, or elſe the Looking-
glaſs raiſed or lower’d, until the Rays proceed-
ing from the Statue may be reflected by the Mir-
rour upon the Convex Glaſs. When theſe Alte-
rations of the Box, or Mirrour, are not ſufficient to
throw the Rays upon the Convex Glafs, the whole
Machine muſt be removed backwards or for-
wards.

203. Demonstration .
Concerning the before-mention’d Inclination of the
Mirrours.

19. In order to demonſtrate, that the Mirrour
L hath been conveniently inclin’d, we need on-
ly prove, that the reflected Rays fall upon the
Table A under the ſame Angle, as the direct
Rays do upon a Plane, having the ſame Situation
as one would give to the Picture.

Now let A B be a Ray falling from a Point of
ſome Object upon the Mirrour G H, and from
thence is reflected in the Point a upon the Table
of the Machine: We are to demonſtrate, that if
the Line D I be drawn, making an Angle with
FE equal to the Inclination of the Picture; that
is, if the Angle DIE be the double of the Angle D F I; I ſay, we are to demonſtrate, that the
Angle B a f is equal to the Angle BCD.

203.1.

Fig. 71.
15, 16.

The Angle DIE, by Conſtruction, is the double
of the Angle DFI; and conſequently this laſt Angle
is equal to the Angle I D F; and ſince the Angle
of Incidence C B D is equal to the Angle of Re-
flection a B F, the Triangle BCD is ſimilar to
the Triangle F a B: Whence it follows, that the
Angle Ba F is equal to the Angle BCD. Which
was to be demonſtrated.

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