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="040/01/869.jpg" pagenum="176"/>
                <emph type="italics"/>
              the given part C D. </s>
              <s>Take a Mean-proportional betwixt B C and C D,
                <lb/>
              to which ſuppoſe B A equal; and let C E be a third proportional be-
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.869.1.jpg" xlink:href="040/01/869/1.jpg" number="114"/>
                <lb/>
                <emph type="italics"/>
              tween B C and C A. </s>
              <s>I ſay, that E B is the Space that after
                <lb/>
              the Fall out of C ſhall be past in the ſame Time as the ſaid
                <lb/>
              C D is paſſed. </s>
              <s>For if we ſuppoſe the Time along C B
                <lb/>
              to be as C B; B A (that is the Mean-proportional betwixt
                <lb/>
              B C and C D) ſhall be the Time along C D. </s>
              <s>And becauſe
                <lb/>
              C A is the Mean proportional betwixt B C and C E, C A
                <lb/>
              ſhall be the Time along C E: But the whole B C is the
                <lb/>
              Time along the Whole C B: Therefore the part B A ſhall be
                <lb/>
              the Time along the part E B, after the Fall out of C: But
                <lb/>
              the ſaid B A was the Time along C D: Therefore C D and
                <lb/>
              E B ſhall be paſt in equal Times out of Reſt in C: Which
                <lb/>
              was to be done.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. XIV. PROP. XXI.</s>
            </p>
            <p type="main">
              <s>If along the Perpendicular a Fall be made
                <emph type="italics"/>
              ex quie­
                <lb/>
              te,
                <emph.end type="italics"/>
              in which from the begining of the Motion
                <lb/>
              a part is taken at pleaſure, paſſed in any Time,
                <lb/>
              after which an Inflex Motion followeth along
                <lb/>
              any Plane however Inclined, the Space which
                <lb/>
              along that Plane is paſſed in a Time equal to
                <lb/>
              the Time of the Fall already made along the
                <lb/>
              Perpendicular ſhall be to the Space then paſ­
                <lb/>
              ſed along the Perpendicular more than double,
                <lb/>
              and leſſe than triple.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              From the Horizon A E let fall a Perpendicular A B, along which
                <lb/>
              from the begining A let a Fall be made, of which let a part A C
                <lb/>
              be taken at pleaſure; then out of C let any Plane G be inclined at
                <lb/>
              pleaſure: along which after the Fall along A C let the Motion be con­
                <lb/>
              tinued. </s>
              <s>I ſay, the Space paſſed by that Motion along C G in a Time
                <lb/>
              equall to the Time of the Fall along A C, is more than double, and leſs
                <lb/>
              than triple that ſame Space A C. </s>
              <s>For ſuppoſe C F equal to A C, and
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              extending out the Plane G C as far as the Horizon in E, and as C E
                <lb/>
              is to E F, ſo let F E be to E G. </s>
              <s>If therefore we ſuppoſe the Time of
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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