Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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          <chap>
            <pb pagenum="413"/>
            <p type="head">
              <s>LEMMA I.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              The abſolute Gravities of Solids, have a proportion com-
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
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                <lb/>
                <emph type="italics"/>
              pounded of the proportions of their ſpecificall Gravities,
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              and of their Maſſes.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1415"/>
              The abſolute
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              Gravity of
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              lids, are in a
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              portion
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              pounded of their
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              Specifick
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              ties, and of their
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              Maſſes.</s>
            </p>
            <p type="main">
              <s>Let A and B be two Solids. </s>
              <s>I ſay, that the Abſolute Gravity
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              of A, hath to the Abſolute Gravity of B, a proportion
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              pounded of the proportions of the ſpecificall Gravity of A, to
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              the Specificall Gravity of B, and of the Maſs
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              A to the Maſs B. </s>
              <s>Let the Line D have the
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                <figure id="fig265" number="4"/>
                <lb/>
              ſame proportion to E, that the ſpecifick
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              Gravity of A, hath to the ſpecifick Gravity
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              of B; and let E be to F, as the Maſs A to the
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              Maſs B: It is manifeſt, that the proportion
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              of D to F, is compounded of the proportions
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              D and E; and E and F. </s>
              <s>It is requiſite,
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              therefore, to demonſtrate, that as D is to F, ſo the abſolute Gravity
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              of A, is to the abſolute Gravity of B. </s>
              <s>Take the Solid C, equall in
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              Maſs to the Solid A, and of the ſame Gravity
                <emph type="italics"/>
              in ſpecie
                <emph.end type="italics"/>
              with the Solid
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              B. Becauſe, therefore, A and C are equall in Maſs, the abſolute
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              Gravity of A, ſhall have to the abſolute Gravity of C, the ſame
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              portion, as the ſpecificall Gravity of A, hath to the ſpecificall Gravity
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              of C, or of B, which is the ſame
                <emph type="italics"/>
              in ſpecie
                <emph.end type="italics"/>
              ; that is, as D is to E. And,
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              cauſe, C and B are of the ſame Gravity
                <emph type="italics"/>
              in ſpecie,
                <emph.end type="italics"/>
              it ſhall be, that as
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              the abſolute weight of C, is to the abſolute weight of B, ſo the Maſs
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              C, or the Maſs A, is to the Maſs B; that is, as the Line E to the Line
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              F. </s>
              <s>As therefore, the abſolute Gravity of A, is to the abſolute
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              Gravity of C, ſo is the Line D to the Line E: and, as the abſolute
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              Gravity of C, is to the abſolute Gravity of B, ſo is the Line E to the
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              Line F: Therefore, by Equality of proportion, the abſolute
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              vity of A, is to the abſolute Gravity of B, as the Line D to the
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              Line F: which was to be demonſtrated. </s>
              <s>I proceed now to
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              ſtrate, how that,</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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