Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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              And the ſame alſo hapneth if the precedent Motion be not made
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              along the Perpendicular, but along an Inclined Plane; and the Demon­
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              ſtration is the ſame, provided that the Reflex Plane be leſſe riſing, that is,
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              longer than the declining Plane.
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              <s>THEOR. XVI.
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              P
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              RO
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              P.
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              XXV.</s>
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              <s>If after the Deſcent along any Inclined Plane a
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              Motion follow along the Plane of the Hori­
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              zon, the Time of the Deſcent along the Incli­
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              ned Plane ſhall be to the Time of the Motion
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              along any Horizontal Line; as the double
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              Length of the Inclined Plane is to the Line ta­
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              ken in the Horizon.</s>
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              Let the Horizontal Line be C B, the inclined Plane A B, and after
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              the Deſcent along A B let a Motion follow along the Horizon, in
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              which take any Space B D. </s>
              <s>I ſay, that the Time of the Deſcent
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              along A B to the Time of the Motion along B D is as the double of A B
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              to B D. </s>
              <s>For B C being ſuppoſed
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              the double of A B, it is manifeſt by
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              what hath already been demonſtra­
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              ted that the Time of the Deſcent
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              along A B is equal to the Time of
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              the Motion along B C: But the
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              Time of the Motion along B C is to
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              the Time of the Motion along B D, as the Line C B is to the Line B D:
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              Therefore the Time of the Motion along A B is the Time along B D, as
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              the Double of A B is to B D: Which was to be proved.
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              <s>PROBL X. PROP. XXVI.</s>
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              <s>A Perpendicular between two Horizontal
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              P
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              aral­
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              lel Lines, as alſo a Space greater than the ſaid
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              P
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              erpendicular, but leſſe than double the ſame,
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              being given, to raiſe a
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              P
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              lane between the ſaid
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              P
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              arallels from the loweſt Term of the
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              P
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              er­
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              pendicular, along which the Moveable may
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              with a Reflex Motion after the Fall along the
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              P
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              erpendicular paſſe a Space equal to the Space
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              given, and in a Time equal to the Time of the
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              Fall along the
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              erpendicular.</s>
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