Gravesande, Willem Jacob 's
,
An essay on perspective
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on PERSPECTIVE.
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s i by x, and i h be y; </
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<
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">it is manifeſt, that i 4 = a 5
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being Algebraially Expreſſed, will be {ydy/dx}</
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<
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">Again, the ſimilar Triangles, s a 5 and s i g give
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s a (e): </
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<
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<
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">i g ({xydx/edx}) Alſo by
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the Conſtruction of Figure 32,
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A S (e): </
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<
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xml:space
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<
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">A I ({yy/e});
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</
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<
s
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xml:space
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">Whence it follows, ſince I G = i g, that A G =
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(I G - A I) = {xyd/cdx} - {yy/e}. </
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<
s
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xml:space
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">And conſequently, H
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and F are the Seats of the two Points whoſe Perſpe-
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ctive is required, and thoſe Points are both in a
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Plane parallel to the Geometrical Plane, which is the
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height of 21 above the Geometrical Plane.</
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<
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">If the precedent Calculation be apply’d to the Lower
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Part of the Torus, the Expreſſion {xydy/edx} - {yy/e}, will
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be chang’d into this, - {xydy/edx} - {yy/e;</
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<
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">} which ſhews that
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theſe two Quantities muſt be aſſumed on the ſame Side
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of A, viz. </
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<
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">Moreover 9 q, inthe Line
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9 m, is equal to {xydy/edx}; </
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<
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xml:space
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">for 98 ({ydy/e}) = i 4.
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</
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<
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xml:space
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">Which ſhews that M and L are alſo the Seats of two
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Points whoſe Perſpective muſt be found, and which are
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both in a Plane parallel to the Geometrical Plane, and
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above it the Height of 29.</
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">This Problem may be likewiſe ſolved in
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conſidering the Torus of a Column as made up of
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an infinite Number of Baſes of Cones, whoſe Al-
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titudes are determin’d by the concurrence of the
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Tangents of the Semicircular Concavity of the
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Axis of the Column; </
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xml:space
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