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="040/01/862.jpg" pagenum="169"/>
                <emph type="italics"/>
              of A, ſhall be made in the ſame Time, as along A B from Reſt in A. </s>
              <s>Let
                <lb/>
              C D be equal to C B, and drawing B D, let B E be applied equal to both
                <lb/>
              B D and D C. </s>
              <s>I ſay B E is the Plane required. </s>
              <s>Continue out E B to
                <lb/>
              meet the Horizontal Line A G in G;
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.862.1.jpg" xlink:href="040/01/862/1.jpg" number="105"/>
                <lb/>
                <emph type="italics"/>
              and let G F be a Mean-Proportional be­
                <lb/>
              tween the ſaid E G and G B. </s>
              <s>E F ſhall
                <lb/>
              be to F B, as E G is to G F; and the
                <lb/>
              Square E F ſhall be to the Square F B, as
                <lb/>
              the Square E G is to the Square G F;
                <lb/>
              that is as the Line E G to G B: But
                <lb/>
              E G is double to G B: Therefore the
                <lb/>
              Square of E F is double to the Square of F B: But alſo the Square of
                <lb/>
              D B is double to the Square of B C: Therefore, as the Line E F is to
                <lb/>
              F B, ſo is D B to B C: And by Compoſition and Permutation, as E B is
                <lb/>
              to the two D B and B C, ſo is B F to B C: But B E is equal to the two
                <lb/>
              D B and B C: Therefore B F is equal to the ſaid B C, or B A. </s>
              <s>If there­
                <lb/>
              fore A B be underſtood to be the Time of the Fall along A B, G B ſhall
                <lb/>
              be the Time along G B, and G F the Time along the whole G E: There­
                <lb/>
              fore B F ſhall be the Time along the remainder B E, after the Fall from
                <lb/>
              G, or from A, which was the Propoſition.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROBL. II. PROP. XIV.</s>
            </p>
            <p type="main">
              <s>A
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular and a
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane inclined to it being
                <lb/>
              given, to find a part in the upper
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicu­
                <lb/>
              lar which ſhall be paſt
                <emph type="italics"/>
              ex quiete
                <emph.end type="italics"/>
              in a Time
                <lb/>
              equal to that in which the inclined
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane is
                <lb/>
              paſt after the Fall along the part found in the
                <lb/>
              Perpendicular.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Perpendicular be D B, and the Plane inclined to it A C. </s>
              <s>It is
                <lb/>
              required in the Perpendicular A D to find a part which ſhall be
                <lb/>
              paſt
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in a Time equal to that in which the Plane A C is
                <lb/>
              paſt after the Fall along the ſaid part. </s>
              <s>Draw the Horizontal Line C B;
                <lb/>
              and as B A more twice A C is to A C, ſo let E A be to A R; And from
                <lb/>
              R let fall the Perpendicular R X unto D B. </s>
              <s>I ſay X is the point requi­
                <lb/>
              red. </s>
              <s>And becauſe as B A more twice A C is to A C, ſo is C A to A E,
                <lb/>
              by Diviſion it ſhall be that as B A more A C is to A C, ſo is C E to E A:
                <lb/>
              And becauſe as B A is to A C, ſo is E A to A R, by Compoſition it ſhall
                <lb/>
              be that as B A more A C is to A C, ſo is E R to R A: But as B A more
                <lb/>
              A C is to A C, ſo is C E to E A: Therefore, as C E is to E A, ſo is E R,
                <lb/>
              to R A, and both the Antecedents to both the Conſequents, that is, C R
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
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