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

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              <pb o="20" file="0032" n="32" rhead="PROMOTVS"/>
            ſunt quatuor corpora grauia E, D, B,
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              <figure xlink:label="fig-0032-01" xlink:href="fig-0032-01a" number="14">
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            A, quorum E, D, primum videlicet,
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            & </s>
            <s xml:id="echoid-s518" xml:space="preserve">ſecundum, ſunt æqualia magnitu-
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            dine, tertium vero B, & </s>
            <s xml:id="echoid-s519" xml:space="preserve">quartum A,
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            æquegrauia, & </s>
            <s xml:id="echoid-s520" xml:space="preserve">ſunt eiuſdem generis
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            corpora E, B, ſimiliter & </s>
            <s xml:id="echoid-s521" xml:space="preserve">corpora
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              <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">7. buius</note>
            D, A, erit vt grauitas H, ad graui- tatem G, ita magnitudo C, ad corpo-
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            ris B, magnitudinem, ſed vt grauitas
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            H, ad grauitatem G, ita eſt magnitu-
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            do C, ad F, magnitudinem, ergo ma-
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            gnitudo F, æqualis erit magnitudini
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            corporis B. </s>
            <s xml:id="echoid-s522" xml:space="preserve">inuenta igitur eſt corporis B, magnitudo F, quod facere
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            oportebat.</s>
            <s xml:id="echoid-s523" xml:space="preserve"/>
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            <s xml:id="echoid-s524" xml:space="preserve">Quod ſi propoſita duo corpora æque grauia A, B, fue
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            rint regularia, vtpote ſphærica, fuerit autem ſphæræ A,
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            data diameter C, & </s>
            <s xml:id="echoid-s525" xml:space="preserve">oporteat inuenire, quanta erit dia-
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            meter ſphærę B, ita faciendum erit.</s>
            <s xml:id="echoid-s526" xml:space="preserve"/>
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            <s xml:id="echoid-s527" xml:space="preserve">Accepto corpore ſolido D, & </s>
            <s xml:id="echoid-s528" xml:space="preserve">inuenta ſolidi corporis E, grauita-
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            te, vt ſupra dictum eſt, fiat vt grauitas H, ad grauitatem G, ita cu-
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            bus ex C, ad alium cubum, cuius latus ſit F. </s>
            <s xml:id="echoid-s529" xml:space="preserve">Quoniam igitur eadem
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            ratione, qua ſupra, demonſtrabitur, vt grauitas H, ad grauitatem G,
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            ita eſſe magnitudinem ſphæræ A, ad ſphæræ B, magnitudinem, ſed
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              <note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">18. 12.
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              Elem.</note>
            magnitudo ſphæræ A, ad ſphæræ B, magnitudinem triplicatam ra- tionem habet eius, quam C, diameter ſphæræ A, ad diametrum ſphæ-
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              <note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">33. 11.
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              Elem.</note>
            ræ B. </s>
            <s xml:id="echoid-s530" xml:space="preserve">Similiter & </s>
            <s xml:id="echoid-s531" xml:space="preserve">cubus ex C, ad cubum, ex diametro ſphæræ B, tri- plicatam rationem habet eius, quam C, ad ſphæræ B, diametrum; </s>
            <s xml:id="echoid-s532" xml:space="preserve">er-
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            go vt grauitas H, ad grauitatem G, ita erit cubus ex C, ad cubum ex
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            diametro ſphæræ B, ſed vt grauitas H, ad grauitatem G, ita eſt cubus
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            ex C, ad cubum ex F; </s>
            <s xml:id="echoid-s533" xml:space="preserve">ergo cubus ex F, æqualis erit cubo diametri
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            ſphæræ B; </s>
            <s xml:id="echoid-s534" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s535" xml:space="preserve">latus F, æquabitur ſphæræ B, diametro. </s>
            <s xml:id="echoid-s536" xml:space="preserve">inuenta
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            igitur eſt quantitas diametri ſphæræ B, quod facere oportebat.</s>
            <s xml:id="echoid-s537" xml:space="preserve"/>
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            <s xml:id="echoid-s538" xml:space="preserve">Neque hoc Problema inutile erit tormenti bellici magiſtro,
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            is enim cognita diametro alicuius globi, exempli gratia, ex
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            plumbo, ſtatim alterius globi eandem habentis grauitatem,
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            diametrum inueniet, ſit globus ille, vel ex lapide, vel ex fer-
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            ro, vel ex quocunque alio ſolidorum genere.</s>
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