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

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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/858.jpg" pagenum="165"/>
                <emph type="italics"/>
              is D A to C G, or B E. </s>
              <s>The proportion therefore of the Elevations
                <lb/>
              of the Planes equal to C D and C E, is the ſame with the proportion
                <lb/>
              of the Longitudes D C and C E: Therefore, by the firſt Corollary of
                <lb/>
              the precedent Sixth Propoſition, the Times of the Dcſcent along the
                <lb/>
              ſame ſhall be equal: Which mas to be proved.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Take the ſame another way: Draw F S perpendicular to the
                <lb/>
              Horizontal Parallel A S. </s>
              <s>Becauſe the Triangle C S F is like to
                <lb/>
              the Triangle D G C, it ſhall be, that as S F is to F C, ſo is G C
                <lb/>
              to C D. </s>
              <s>And becauſe the Triangle C F G is like to the Triangle
                <lb/>
              D C A, it ſhall be, that as F C is to C G, ſo is C D to D A:
                <lb/>
              Therefore,
                <emph.end type="italics"/>
              ex æquali,
                <emph type="italics"/>
              as
                <lb/>
              S F is to C G, ſo is C G to
                <lb/>
              D A: Thorefore C G is a
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.858.1.jpg" xlink:href="040/01/858/1.jpg" number="100"/>
                <lb/>
                <emph type="italics"/>
              Mean-proportional between
                <lb/>
              S F and D A: And as DA
                <lb/>
              is to S F, ſo is the Square
                <lb/>
              D A unto the Square C G
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              Again, the Triangle A C D
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              being like to the Triangle
                <lb/>
              C G F, it ſhall be, that as
                <lb/>
              D A is to D C, ſo is G C
                <lb/>
              to C F: and, Alternately,
                <lb/>
              as D A is to G C, ſo is D C to C F; and as the Square of D A
                <lb/>
              is to the Square of C G, ſo is the Square of D C to the Square of
                <lb/>
              C F. </s>
              <s>But it hath been proved that the Square D A is to the
                <lb/>
              Square C G as the Line D A is to the Line F S: Therefore, as the
                <lb/>
              Square D C is to the Square C F, ſo is the Line D E to F S: There­
                <lb/>
              fore, by the ſeventh fore-going, in regard that the Elevations D A
                <lb/>
              and F S, of the Planes C D, and C F are in double proportion to
                <lb/>
              their Planes; the Times of the Motions along the ſame ſhall be
                <lb/>
              equal.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. X. PROP. X.</s>
            </p>
            <p type="main">
              <s>The Times of the Motions along ſeveral Inclina­
                <lb/>
              tions of Planes whoſe Elevations are equal,
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              are unto one another as the Lengths of thoſe
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              Planes, whether the Motions be made from
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              Reſt, or there hath proceeded a Motion from
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              the ſame height.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Motions be made along A B C, and along A B D, until
                <lb/>
              they come to the Horizon D C, in ſuch ſort as that the Motion
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              along A B precedeth the Motions along B D and B C. </s>
              <s>I ſay,
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              that the Time of the Motion along B D, is to the Time along B C, as
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
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