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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/822.jpg" pagenum="129"/>
            <p type="head">
              <s>THEOR. III. PROP. III.</s>
            </p>
            <p type="main">
              <s>The Times in which the ſame Space is paſt tho­
                <lb/>
              row by unequal Velocities, have the ſame pro­
                <lb/>
              portion to each other as their Velocities contra­
                <lb/>
              rily taken.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the two unequal Velocities be A the greater, and B the leſſe:
                <lb/>
              and according to both theſe let a Motion be made thorow the ſame
                <lb/>
              Space C D. </s>
              <s>I ſay the Time in which the Velocity A paſſeth the
                <lb/>
              Space C D, ſhall be to the Time in which the Velocity B paſſeth the
                <lb/>
              ſaid Space, as the Velocity B to the Velocity A. </s>
              <s>As A is to B, ſo let
                <lb/>
              C D be to C E: Then, by the
                <lb/>
              former Propoſition, the Time in
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.822.1.jpg" xlink:href="040/01/822/1.jpg" number="77"/>
                <lb/>
                <emph type="italics"/>
              which the Velocity A paſſeth
                <lb/>
              C D, ſhall be the ſame with
                <lb/>
              the Time in which B paſſeth
                <lb/>
              C E. </s>
              <s>But the Time in which
                <lb/>
              the Velocity B paſſeth C E, is
                <lb/>
              to the Time in which it paſſeth C D, as C E is to C D: Therefore
                <lb/>
              the Time in which the Velocity A paſſeth C D, is to the Time in which
                <lb/>
              the Velocity B paſſeth the ſame C D, as C E is to C D; that is, the Ve­
                <lb/>
              locity B is to the Velocity A: Which was to be proved.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. IV. PROP. IV.</s>
            </p>
            <p type="main">
              <s>If two Moveables move with an Equable Mo­
                <lb/>
              tion, but with unequal Velocities, the Spaces
                <lb/>
              which they paſſe in unequal Times, are to each
                <lb/>
              other in a proportion compounded of the pro­
                <lb/>
              portion of the Velocities, and of the propor­
                <lb/>
              tion of the Times.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the two Moveables moving with an Equable Motion, be E and
                <lb/>
              F: And let the proportion of the Velocity of the Moveable E be
                <lb/>
              to the Velocity of the Moveable F, as A is to B: And let the Time
                <lb/>
              in which E is moved, be unto the Time in which F is moved, as C is
                <lb/>
              to D. </s>
              <s>I ſay the Space paſſed by E, with the Velocity A in the Time C, is to
                <lb/>
              the Space paſſed by F, with the Velocity B in the Time D, in a proportion
                <lb/>
              compounded of the proportion of the Velocity A to the Velocity B, and of
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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