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

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          <head xml:id="echoid-head34" xml:space="preserve">THEOREMA IX. PROPOS. XVII.</head>
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            <s xml:id="echoid-s793" xml:space="preserve">SPhære eiuſdem generis inter ſe ſunt in grauitate, vt
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            diametrorum cubi in magnitudine.</s>
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            <s xml:id="echoid-s795" xml:space="preserve">SINT ſphæræ eiuſdem gene-
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            ris ABC, DEF, quarum diame
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            tri BC, EF. </s>
            <s xml:id="echoid-s796" xml:space="preserve">dico vt ſphęra ABC,
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            ſe habet in grauitate, ad ſphæram
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            DEF, ita ſe habere in maguitudi-
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            ne cubum ex BC, ad cubum ex
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            EF, ſit enim ſphæræ ABC, graui-
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            tas G, & </s>
            <s xml:id="echoid-s797" xml:space="preserve">ſphæræ DEF, grauitas H,
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            quoniam igitur eiuſdem generis
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            ponuntur ſphæræ ABC, DEF,
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            erit vt ſphæra ABC, ad ſphæram DEF, ita grauitas G, ad H,
              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">2. & 3.
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              huius.</note>
            tatem, ſed ſphæra ABC, ad ſphæram DEF, triplicatam habet
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">18. 12.
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            tionem eius, quam diameter BC, ad EF, diametrum, ergo & </s>
            <s xml:id="echoid-s798" xml:space="preserve">graui-
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            tas G, ad grauitatem H, triplicatam habebit rationem eius, quam
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            habet BC, ad EF, ſed & </s>
            <s xml:id="echoid-s799" xml:space="preserve">cubus ex BC, ad cubum ex EF,
              <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">33. 11.
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              Elem.</note>
            rationem habet eius, quam BC, ad EF, ergo vt grauitas G, ad graui-
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            tatem H, ita erit cubus ex BC, ad cubum ex EF. </s>
            <s xml:id="echoid-s800" xml:space="preserve">ſphæræ igitur eiuſ-
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            dem generis inter ſe ſunt in grauitate, vt diametrorum cubi in ma-
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            gnitudine, quod erat demonſtrandum.</s>
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