Gravesande, Willem Jacob 's
,
An essay on perspective
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on PERSPECTIVE.
"/>
and conſequently to V P. </
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<
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xml:space
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preserve
">Therefore if the before-
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mentioned Plane be ſuppoſed to revolve upon the Line
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V I, as an Axis, until it coincides with the Per-
<
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ſpective Plane, the Center of the Sphere will meet
<
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the Perſpective Plane in Q, and the Eye in F;
<
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</
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<
s
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xml:space
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">whence the Part G E of the Line I V is the tranſ-
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verſe Diameter of the Ellipſis.</
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</
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<
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xml:space
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">Again let G D E in Figure 30, and g e f, in
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xml:space
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">Fig. 30,
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31.</
note
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Figure 31 repreſent the Points denoted with the ſame
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Letters in the foregoing Figure. </
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<
s
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xml:space
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">Now if the Cone,
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whoſe Profile is denoted by the Lines f g and fe be ſup-
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poſed to be compleated, and to be cut by a Plane paſ-
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ſing through the Line g e perpendicular to the Plane
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of the Figure; </
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<
s
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xml:space
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">we ſhall have an Ellipſis g 4 e 3
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ſimilar to that which is the ſought Repreſentation
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of the Sphere. </
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<
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xml:space
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">Further if the ſaid Cone be conceived
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to be cut by a Plane 14 m 3 parallel to its Baſe,
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and biſecting g e in n, it is manifeſt, that 3 4, the
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common Section of the Circle 14 m 3, and the Ellip-
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ſis g 4 e 3, is the conjugate Axis of the Ellip-
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ſis. </
s
>
<
s
xml:id
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echoid-s1149
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xml:space
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">And therefore this conjugate Axis is equal
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to the Line 3 4, Perpendicular in the Point n to the
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Diameter 1 m of the Circle 14 m 3. </
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<
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xml:space
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">Now draw
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the Lines E O and G Y in Figure 30, parallel to
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L M, then the Triangles E G Y and E N M are
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ſimilar, whence</
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">EG: EN:: GY: NM.</
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<
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<
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xml:space
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">But E G is twice E N; </
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<
s
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xml:space
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">wherefore G Y is alſo the
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double of N M, and ſo N M equal to G Z. </
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<
s
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xml:space
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">After
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the ſame manner we demonſtrate, that L N is equal
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to X E; </
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<
s
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xml:space
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">whence it follows, that G D is equal to
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L M, and is ſo cut in z as L M is in N; </
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<
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xml:space
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">and there-
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fore R L or G T of Figure 29, is equal to 34 in
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Figure 31; </
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<
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xml:space
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">and conſequently equal to the conjugate
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Axis of the Ellipſis to be drawn. </
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<
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xml:space
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">On the other
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Hand, it is manifeſt by Conſtruction, that ſome one
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of the Perpendiculars m n, Figure 29, viz. </
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which paſſes through the Center of the </
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