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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/823.jpg" pagenum="130"/>
                <emph type="italics"/>
              the proportion of the Time C to the Time D. </s>
              <s>Let the Space paſſed by the
                <lb/>
              Moveable E, with the Velocity A in the Time C, be G: And as the
                <lb/>
              Velocity A is to the Velocity B,
                <lb/>
                <figure id="id.040.01.823.1.jpg" xlink:href="040/01/823/1.jpg" number="78"/>
                <lb/>
              ſo let G be to I: And as the
                <lb/>
              Time C is to the Time D, ſo
                <lb/>
              let I be to L: It is manifeſt,
                <lb/>
              that I is the Space paſſed by F
                <lb/>
              in the ſame Time in which E
                <lb/>
              paſſeth thorow G; ſeeing that
                <lb/>
              the Spaces G and I are as the
                <lb/>
              Velocities A and B; and ſeeing that as the Time C is to the Time D, ſo
                <lb/>
              is I unto L; and ſince that I is the Space paſſed by the Moveable F in the
                <lb/>
              Time C: Therefore L ſhall be the Space that F paſſeth in the Time D,
                <lb/>
              with the Velocity B: But the proportion of G to L, is compounded of the
                <lb/>
              proportions of G to I, and of I to L; that is, of the proportions of the
                <lb/>
              Velocity A to the Velocity B, and of the Time C to the Time D:
                <lb/>
              Therefore the Propoſition is demonſtrated.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. V. PROP. V.</s>
            </p>
            <p type="main">
              <s>If two Moveables move with an Equable Motion,
                <lb/>
              but with unequal Velocities, and if the Spaces
                <lb/>
              paſſed be alſo unequal, the Times ſhall be to
                <lb/>
              each other in a proportion compounded of the
                <lb/>
              proportion of the Spaces, and of the proporti­
                <lb/>
              on of the Velocities contrarily taken.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let A and B be the two Moveables, and let the Velocity of A be to
                <lb/>
              the Velocity of B, as V to T, and let the Spaces paſſed, be as S to
                <lb/>
              R. </s>
              <s>I ſay the proportion of the Time in which A is moved to the
                <lb/>
              Time in which B is moved, ſhall be compounded of the proportions of the
                <lb/>
              Velocity T to the Velocity V, and of the Space S to the Space R. </s>
              <s>Let C be
                <lb/>
              the Time of the Motion A;
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.823.2.jpg" xlink:href="040/01/823/2.jpg" number="79"/>
                <lb/>
                <emph type="italics"/>
              and as the Velocity T is to
                <lb/>
              the Velocity V, ſo let the
                <lb/>
              Time C be to the Time E:
                <lb/>
              And for aſmuch as C is the
                <lb/>
              Time in which A with
                <lb/>
              the Velocity V paſſeth the
                <lb/>
              Space S; and that the
                <lb/>
              Time C is to the Time E, as the Velocity T of the Moveable B is to the
                <lb/>
              Velocity V, E ſhall be the Time in which the Moveable B would paſſe
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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