Gravesande, Willem Jacob 's
,
An essay on perspective
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on PERSPECTIVE.
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<
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.</
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<
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xml:space
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">If a Plane be conceiv’d to paſs thro’ the Eye,
<
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perpendicular to the Geometrical Plane, and paral-
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lel to the given Lines; </
s
>
<
s
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xml:space
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preserve
">it is evident, that the ſaid
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Plane will cut the Horizontal Plane in the Line
<
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O D, and the perſpective Plane in D F. </
s
>
<
s
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xml:space
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">It is,
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moreover, manifeſt, that a Line drawn thro’ the
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Eye, parallel to the given Line, is in the ſaid
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Plane, and (with the Line O D) makes an An-
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gle, equal to the Angle E C P, below the Hori-
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zontal Plane, if the Lines be inclin’d towards
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the perſpective Plane, and above it, if they in-
<
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/>
cline to the oppoſite ſide; </
s
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<
s
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xml:space
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">whence this laſt Line
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makes a right-angled Triangle with O D and
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D F, whoſe Angle at the Point O, is equal to
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the Angle C E P. </
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<
s
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xml:space
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">But D G F is likewiſe a
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right-angled Triangle, as having the Angle at the
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Point G, equal to ECP; </
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<
s
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xml:space
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">therefore theſe two
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Triangles are ſimilar. </
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<
s
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xml:space
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preserve
">And ſince the Side D G
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is equal to the Side D O, the Triangles are alſo
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equal: </
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<
s
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xml:space
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">Therefore the Line D F, being common
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to theſe two Triangles; </
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<
s
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xml:space
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">the Point F, is the
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Point wherein the Line, paſſing thro’ the Eye
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parallel to the given Line, meets the Per-
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ſpective Plane: </
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>
<
s
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xml:space
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</
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<
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<
s
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">Note, This Demonſtration as well regards
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note
>
inclin’d Lines entirely ſeparate from the Geo-
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metrical Plane, as thoſe that meet it in one of
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their Extremes only.</
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<
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X.</
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<
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">To find the Repreſentation of one or more
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Lines, inclin’d to the Geometrical Plane.
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</
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<
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xlink:label
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xml:space
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">Fig. 36.</
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>
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<
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<
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Plane; </
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<
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xml:space
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">whereon ſtands a Line, whoſe Length,
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Direction, and Angle of Inclination is known.</
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