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

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            enim non eſt vt A, adBC, ita D, ad EF, erit vt A, ad BC, ita D, vel ad
              <lb/>
            minorem quam EF,
              <lb/>
              <figure xlink:label="fig-0015-01" xlink:href="fig-0015-01a" number="4">
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            vel ad maiorem, ſit
              <lb/>
            primum ad minorĕ,
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            nempe ad EG, & </s>
            <s xml:id="echoid-s160" xml:space="preserve">ex-
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            ponatur aliquod cor
              <lb/>
            pus K, eiuſdem gene-
              <lb/>
            ris cum corporibus
              <lb/>
            A, B C, cuius graui-
              <lb/>
            tas ſit æqualis ipſi
              <lb/>
            GF, & </s>
            <s xml:id="echoid-s161" xml:space="preserve">à corpore BC,
              <lb/>
            auferatur aliqua
              <lb/>
            pars HC, quæ ſit mi-
              <lb/>
            nor corpore K, ita vt reliqua pars BL, ſit commenſurabilis ipſi A. </s>
            <s xml:id="echoid-s162" xml:space="preserve">& </s>
            <s xml:id="echoid-s163" xml:space="preserve">
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            ſit partis HC, grauitas IF, ergo reliquæ partis BL, grauitas erit EI.
              <lb/>
            </s>
            <s xml:id="echoid-s164" xml:space="preserve">Quoniam igitur corpus A, commenſurabile eſt ipſi BL, erit vt A,
              <note position="right" xlink:label="note-0015-01" xlink:href="note-0015-01a" xml:space="preserve">Ex an-
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              tecedĕ-
                <lb/>
              te.</note>
            BL, ita D, ad EI, ſed vt A, ad BC, ita eſt D, ad EG, atque A, primus,
              <lb/>
            proportionalium terminus in ſerie prima, maiorem habet ratio nem ad BL, ſecundum terminum, quam A, primus terminus in ſerie
              <lb/>
              <note position="right" xlink:label="note-0015-02" xlink:href="note-0015-02a" xml:space="preserve">8. 5.
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              Elem.</note>
            ſecunda ad BC, ſecundum; </s>
            <s xml:id="echoid-s165" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s166" xml:space="preserve">D, tertius terminus in ſerie prima
              <lb/>
            ad EI, quartum, maiorem habebit rationem quam D, tertius termi-
              <lb/>
            nus in ſerie ſecunda ad I G, quartum, quoniam igitur D, maiorem
              <lb/>
            habet rationem ad EI, quam ad EG, erit EI, minor quam EG,
              <note position="right" xlink:label="note-0015-03" xlink:href="note-0015-03a" xml:space="preserve">10. 5.
                <lb/>
              Elem.</note>
            eſt abſurdum. </s>
            <s xml:id="echoid-s167" xml:space="preserve">non igitur eſt vt A, ad BC, ita D, ad minorem quam E F.</s>
            <s xml:id="echoid-s168" xml:space="preserve"/>
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            <s xml:id="echoid-s169" xml:space="preserve">Deinde ſit vt A, ad BC, ita D, ad maiorem quam EF, nempe ad
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            EG, & </s>
            <s xml:id="echoid-s170" xml:space="preserve">expoſito cor-
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            pore K, vt dictum
              <lb/>
            eſt, cuius grauitas,
              <lb/>
            ſit æqualis grauita-
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            ti FG, addatur cor-
              <lb/>
            pori BC, aliquod
              <lb/>
            corpus CH, quod ſit
              <lb/>
            minus corpore K, & </s>
            <s xml:id="echoid-s171" xml:space="preserve">
              <lb/>
            eiuſdem generis cũ
              <lb/>
            corporibus A, BC,
              <lb/>
            ita vt totum corpus
              <lb/>
            BL, ſit commenſurabile ipſi A, & </s>
            <s xml:id="echoid-s172" xml:space="preserve">ſit ipſius CH, grauitas FI, ergo to
              <lb/>
            tius corporis BL, grauitas erit EI; </s>
            <s xml:id="echoid-s173" xml:space="preserve">Quoniam igitur corpori A, com-
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            menſurabile eſt corpus BL, erit vt A, ad BL, ita D, ad EI, ſed vt A,
              <note position="right" xlink:label="note-0015-04" xlink:href="note-0015-04a" xml:space="preserve">Ex an
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              teced.</note>
            BC, ita eſt D, ad EG, atque A, primus proportionalium terminus in
              <lb/>
            ſerie prima, minorem habet rationem ad BL, ſecundum
              <note position="right" xlink:label="note-0015-05" xlink:href="note-0015-05a" xml:space="preserve">8. 5. Ele</note>
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