Ghetaldi, Marino, Marini Ghetaldi Promotvs Archimedis sev de varijs corporum generibus grauitate & magnitudine comparatis

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          <p>
            <s xml:id="echoid-s137" xml:space="preserve">
              <pb o="2" file="0014" n="14" rhead="PROMOTVS"/>
            grauitatem æqualem ipſi H. </s>
            <s xml:id="echoid-s138" xml:space="preserve">Si duorum igitur grauium corporum
              <lb/>
            eiuldem generis, & </s>
            <s xml:id="echoid-s139" xml:space="preserve">c. </s>
            <s xml:id="echoid-s140" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s141" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div8" type="section" level="1" n="7">
          <head xml:id="echoid-head10" xml:space="preserve">THEOREMA II. PROPOS. II.</head>
          <p>
            <s xml:id="echoid-s142" xml:space="preserve">COrpora grauia eiuſdem generis magnitudine com
              <lb/>
            menſurabilia, eandem in grauitate rationem ha-
              <lb/>
            bent, quam in magnitudine.</s>
            <s xml:id="echoid-s143" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s144" xml:space="preserve">SINT corpora commenſurabilia eiuſdem generis A, B, quorum
              <lb/>
            grauitates C, ipſius A, & </s>
            <s xml:id="echoid-s145" xml:space="preserve">D, ipſius B, Dico eſſe vt A, ad B, ita C, ad D,
              <lb/>
            quoniam enim, A, B, commenſura-
              <lb/>
              <figure xlink:label="fig-0014-01" xlink:href="fig-0014-01a" number="3">
                <image file="0014-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0014-01"/>
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            bilia ſunt, metietur ipſa aliquod
              <lb/>
            corpus, metiatur, & </s>
            <s xml:id="echoid-s146" xml:space="preserve">ſit E, cuius
              <lb/>
            grauitas F, ſitque corpus E, eiuſdĕ
              <lb/>
              <note position="left" xlink:label="note-0014-01" xlink:href="note-0014-01a" xml:space="preserve">Ex an-
                <lb/>
              teced.</note>
            generis cum corporibus A, B, ergo quotuplex eſt corpus A, ipſius E,
              <lb/>
            totuplex erit grauitas C, grauitatis
              <lb/>
              <note position="left" xlink:label="note-0014-02" xlink:href="note-0014-02a" xml:space="preserve">Ex an-
                <lb/>
              teced.</note>
            F, & </s>
            <s xml:id="echoid-s147" xml:space="preserve">quotuplex B, ipſius E, totuplex D, ipſius F, ſi igitur diuidantur cor-
              <lb/>
            pora A, B, in partes æquales ipſi E,
              <lb/>
            & </s>
            <s xml:id="echoid-s148" xml:space="preserve">grauitates quoque C, D, in partes æquales ipſi F, erit vt corporis
              <lb/>
            A, pars vna, ad corpus E, ita pars vna grauitatis C, ad grauitatem F,
              <lb/>
            æquale videlicet ad æquale, & </s>
            <s xml:id="echoid-s149" xml:space="preserve">æque multiplicatis antecedentibus
              <lb/>
            erit vt A, ad E, ita C, ad F, ſunt enim antecedentium, hoc eſt, illarum
              <lb/>
            partium æque multiplicia A, C, eadem ratione, vt B, ad E, ita erit D,
              <lb/>
            ad F, & </s>
            <s xml:id="echoid-s150" xml:space="preserve">conuertendo vt E, ad B, ita F, ad D. </s>
            <s xml:id="echoid-s151" xml:space="preserve">quoniam igitur vt A, ad
              <lb/>
            E, ita eſt C, ad F, & </s>
            <s xml:id="echoid-s152" xml:space="preserve">vt E, ad B, ita F, ad D, erit ex æquali vt A,
              <note position="left" xlink:label="note-0014-03" xlink:href="note-0014-03a" xml:space="preserve">22. 5.
                <lb/>
              Elem.</note>
            B, ita C, ad D. </s>
            <s xml:id="echoid-s153" xml:space="preserve">corpora igitur commenſurabilia eiuſdem generis ean-
              <lb/>
            dem in grauitate rationem habent, quam in magnitudine, quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s154" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div10" type="section" level="1" n="8">
          <head xml:id="echoid-head11" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s155" xml:space="preserve">ET incommenſurabilia corpora eiuſdem generis
              <lb/>
            eandem in grauitate rationem habent, quam in
              <lb/>
            magnitudìne.</s>
            <s xml:id="echoid-s156" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s157" xml:space="preserve">SINT incommenſurabilia corpora A, BC, quorum grauitates
              <lb/>
            D, ipſius A, & </s>
            <s xml:id="echoid-s158" xml:space="preserve">EF, ipſius BC. </s>
            <s xml:id="echoid-s159" xml:space="preserve">Dico eſſe vt A, ad BC, ita D, ad EF, </s>
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