Gravesande, Willem Jacob 's
,
An essay on perspective
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An ESSAY
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cauſe the Triangles THX and a F X are ſimilar,
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TH — a F: </
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<
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<
s
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">Ta: </
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<
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<
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<
s
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xml:space
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">And becauſe the Triangles T I x and ax L, are
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alſo ſimilar, we have
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TI + a L : </
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<
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<
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">a L: </
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<
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<
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">ax.</
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s
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">Now let PM NR be the perſpective Plane,
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<
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">Fig. 54.</
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O the Eye, A Q the Perpendicular, whoſe
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Perſpective is requir’d, and O t a perpendicular
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let fall from the Eye upon the perſpective Plane,
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and ſo t will be the ſame, as the Point T in the
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aforegoing Figure, Now if the Lines O Q be
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drawn, it is manifeſt that A x, or A X, is the
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Perſpective of A Q, according as this Line is
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above or below the perſpective Plane in reſpect
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to the Eye. </
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<
s
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xml:space
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">Then becauſe the Triangles O t x
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and Q A x are ſimilar, we have
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O t — A Q: </
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<
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">Ax.</
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<
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</
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<
s
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xml:space
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">And ſince the Triangles O t X and X A Q are
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ſimilar,
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O t + A Q: </
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<
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<
s
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">Now Ot is equal to TH or TI of the afore-
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going Figure, and AQ to a F or a L of the
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ſame Figure; </
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<
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">as likewiſe At, Ta: </
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xml:space
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">Therefore
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if theſe two laſt Proportions be compared with
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the two precedent ones, we ſhall find A x = a X,
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and A X = a x; </
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<
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xml:space
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">which was to be demon-
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ſtrated.</
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<
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<
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">When the two Circles interſect each other,
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or fall within one another, and ſo this Way be-
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comes uſeleſs; </
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<
s
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xml:space
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">a Line muſt be drawn at Pleaſure,
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through the Point T, equal to the Diſtance of
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the Eye from the perſpective Plane; </
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<
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xml:space
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">and then a
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parallel equal to the given Perpendicular muſt be
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drawn to the ſaid Line through the Point a, ei-
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ther towards L or F, according as the </
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