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

Table of figures

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/824.jpg" pagenum="131"/>
                <emph type="italics"/>
              the ſame Space S. </s>
              <s>Again as the Space S is to the Space R, ſo let the
                <lb/>
              Time E be to the Time G: Therefore G is the Time in which B would
                <lb/>
              paſſe the Space R. </s>
              <s>And becauſe the proportion of C to G is compounded
                <lb/>
              of the proportions of C to E, and of E to G; And ſince the proportion
                <lb/>
              of C to E is the ſame with that of the Velocities of the Moveables A and
                <lb/>
              B contrarily taken; that is, with that of T and V; And the proportion
                <lb/>
              of E to G is the ſame with the proportion of the Spaces S and R: There­
                <lb/>
              fore the Propoſition is demonſtrated.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. VI. PROP. VI.</s>
            </p>
            <p type="main">
              <s>If two Moveables move with an Equable Motion,
                <lb/>
              the proportion of their Velocities ſhall be com­
                <lb/>
              pounded of the proportion of the Spaces paſ­
                <lb/>
              ſed, and of the proportion of the Times con­
                <lb/>
              trarily taken.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let A and B be the two Moveables moving with an Equable
                <lb/>
              Motion; and let the Spaces by them paſſed, be as V to T; and
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              let the Times be as S to R. </s>
              <s>I ſay that the proportion of the Ve­
                <lb/>
              locity of the Moveable A, to that of the Velocity of B, ſhall be
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              compounded of the proportions of the Space V to the Space T, and
                <lb/>
              of the Time R to the Time S. </s>
              <s>Let C be the Velocity with which the
                <lb/>
              Moveable A paſſeth the Space V in the Time S: And let the Velocity C
                <lb/>
              be to the Velo-
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.824.1.jpg" xlink:href="040/01/824/1.jpg" number="80"/>
                <lb/>
                <emph type="italics"/>
              city E, as the
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              Space V is to
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              the Space T;
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              And E ſhall
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              be the Veloci­
                <lb/>
              ty with which
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              the Moveable
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              B paſſeth the Space T in the Time S: Again, let the Velocity E be to the
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              other Velocity G, as the Time R is to the Time S; And G ſhall be the
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              Velocity with which the Moveable B paſſeth the Space T in the Time R.
                <lb/>
              </s>
              <s>We have therefore the Velocity C, wherewith the Moveable A paſſeth
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              the Space V in the Time S; and the Velocity G, wherewith the Move­
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              able B paſſeth the Space T in the Time R: And the proportion of C to
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              G is compounded of the proportions of C to E and of E to G: But the
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              proportion of C to E, is ſuppoſed the ſame with that of the Space V to
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              the Space T; and the proportion of E to G, is the ſame with that of R
                <lb/>
              to S: Therefore the Propoſition is manifest.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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