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

Table of figures

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              <s>
                <pb xlink:href="040/01/875.jpg" pagenum="182"/>
                <emph type="italics"/>
              equal. </s>
              <s>And that two points at pleaſure D and E being taken, equally
                <lb/>
              remote from the Angle B, the Tranſition along D B is made in a Time
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              equal to the Time of the Reflection along B E, we may collect from hence:
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              Draw D F, which ſhall be Parallel to B C; for it is manifeſt that the
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              Deſcent along A D is reflected along D F: And if after D the Move­
                <lb/>
              able paſſe along the Horizontal Plane D E, the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in E ſhall be
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              the ſame as the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in D: Therefore it will aſcend from E to C:
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              And therefore the degree of Velocity in D is equal to the degree in E.
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              </s>
              <s>From theſe things, therefore, we may rationally affirm, that, if a de­
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              ſcent be made along any inclined Plane, after which a Reflection may
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              follow along an elevated Plane, the Moveable may by the conceived
                <emph.end type="italics"/>
                <lb/>
              Impetus
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              aſcend untill it attain the ſame beight, or Elevation from the
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              Horizon. </s>
              <s>As if a Deſcent be made along A B, the Moveable would
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              paſſe along the Reflected Plane B C, untill it arrive at the Horizon
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              A C D; and that not only when the Inclinations of the Planes are
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              equal, but alſo when they are unequal, as is the Plane B D: For it was
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              first ſuppoſed, that the degrees of Velocity are equal, which are acqui­
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              red upon Planes unequally inclined, ſo long as the Elevation of thoſe
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              Planes above the Horizon was the ſame: But, if there being the ſame
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              Inclination of the Planes E B and B D, the Deſcent along E B ſufficeth
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              to drive the Moveable along the Plane BD as far as D, ſeeing this Impulſe
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.875.1.jpg" xlink:href="040/01/875/1.jpg" number="121"/>
                <lb/>
                <emph type="italics"/>
              is made by the
                <emph.end type="italics"/>
              Impe­
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              tus
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              of Velocity in the
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              point B; and if the
                <emph.end type="italics"/>
                <lb/>
              Impetus
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              be the ſame
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              in B, whether the
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              Moveable deſcend a­
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              long A B, or along E B: It is manifeſt, that the Moveable ſhall be in
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              the ſame manner driven along B D, after the Deſcent along A B, and
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              after that along E B: But it will happen that the Time of the Aſcent
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              along B D ſhall be longer than along B C, like as the Deſcent along
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              E B is made in a longer time than along A B: But the Proportion of
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              thoſe Times was before demonſtrated to be the ſame as the Lengths of
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              thoſe Planes. </s>
              <s>Now it follows, that we ſeek the proportion of the Spaces
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              paſt in equal Times along Planes, whoſe Inclinations are different, but
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              their Elevations the ſame; that is, which are comprehended between
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              the ſame Horizontal Parallels. </s>
              <s>And this hapneth according to the fol­
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              lowing Propoſition.
                <emph.end type="italics"/>
              </s>
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