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="040/01/1043.jpg" pagenum="348"/>
              tions of a Sphære, ſhall have its Axis in the Perpendicular, that is
                <lb/>
              drawn through the point K; and its Centre of Gravity, for the ſame
                <lb/>
              reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R:
                <lb/>
                <arrow.to.target n="marg1141"/>
                <lb/>
              But the Centre of Gravity of the whole Portion is in the Line F T,
                <lb/>
              betwixt the Point R and
                <lb/>
                <figure id="id.040.01.1043.1.jpg" xlink:href="040/01/1043/1.jpg" number="238"/>
                <lb/>
              the Point F; let us ſuppoſe
                <lb/>
              it to be the Point
                <emph type="italics"/>
              X
                <emph.end type="italics"/>
              : The re­
                <lb/>
              mainder, therefore, of that
                <lb/>
                <arrow.to.target n="marg1142"/>
                <lb/>
              Figure elivated above the
                <lb/>
              Surface of the Liquid, hath
                <lb/>
              its Centre of Gravity in
                <lb/>
              the Line R X produced or
                <lb/>
              continued right out in the
                <lb/>
              Part towards X, taken ſo,
                <lb/>
              that the part prolonged may
                <lb/>
              have the ſame proportion to
                <lb/>
              X R, that the Gravity of
                <lb/>
              that Portion that is demer­
                <lb/>
              ged in the Liquid hath to
                <lb/>
              the Gravity of that Figure which is above the Liquid; let us ſuppoſe
                <lb/>
                <arrow.to.target n="marg1143"/>
                <lb/>
              that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that
                <lb/>
                <arrow.to.target n="marg1144"/>
                <lb/>
              ſame Centre S draw the Perpendicular L S. </s>
              <s>Now the Gravity of the Fi­
                <lb/>
              gure that is above the Liquid ſhall preſſe from above downwards ac­
                <lb/>
              cording to the Perpendicular S L; & the Gravity of the Portion that
                <lb/>
              is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor­
                <lb/>
              ding to the Perpendicular R L. </s>
              <s>Therefore that Figure will not conti­
                <lb/>
              nue according to our Adverſaries Propoſall, but thoſe parts of the
                <lb/>
              ſaid Figure which are towards E, ſhall be born or drawn downwards,
                <lb/>
              & thoſe which are towards H ſhall be born or driven upwards, and
                <lb/>
              this ſhall be ſo long untill that the Axis F T comes to be according
                <lb/>
              to the Perpendicular.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1139"/>
              (a)
                <emph type="italics"/>
              Perpendicular
                <lb/>
              is taken kere, as
                <lb/>
              in all other places,
                <lb/>
              by this Author for
                <lb/>
              the Line K L
                <lb/>
              drawn thorow the
                <lb/>
              Centre and Cir­
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              cumference of the
                <lb/>
              Earth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1140"/>
              C</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1141"/>
              D</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1142"/>
              E</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1143"/>
              *
                <emph type="italics"/>
              i. </s>
              <s>e,
                <emph.end type="italics"/>
              The Center
                <lb/>
              of Gravity.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1144"/>
              F</s>
            </p>
            <p type="main">
              <s>And this ſame Demonſtration is in the ſame manner verified in
                <lb/>
              the other
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ortions. </s>
              <s>As, firſt, in the Hæmiſphere that lieth with its
                <lb/>
              whole Baſe above or without the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, the Centre of the Sphære
                <lb/>
              hath been ſuppoſed to be the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              oint T; and therefore, imagining T
                <lb/>
              to be in the place, in which, in the other above mentioned, the
                <lb/>
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              oint R was, arguing in all things elſe as you did in that, you ſhall
                <lb/>
              find that the Figure which is above the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid ſhall preſs from
                <lb/>
              above downwards according to the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular S
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ; and the
                <lb/>
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ortion that is ſubmerged in the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid ſhall preſs from below up­
                <lb/>
              wards according to the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular R
                <emph type="italics"/>
              L.
                <emph.end type="italics"/>
              And therefore it ſhall
                <lb/>
              follow, as in the other, namely, that the parts of the whole Figure
                <lb/>
              which are towards E, ſhall be born or preſſed downwards, and thoſe
                <lb/>
                <arrow.to.target n="marg1145"/>
                <lb/>
              that are towards H, ſhall be born or driven upwards: and this ſhall
                <lb/>
              be ſo long untill that the Axis F T come to ſtand ^{*}
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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