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

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            dæ ſphæræ B, data diameter F, & </s>
            <s xml:id="echoid-s440" xml:space="preserve">oporteat inuenire quan
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            ta erit diameter ſolidæ ſphæræ A, ita faciendum erit.</s>
            <s xml:id="echoid-s441" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s442" xml:space="preserve">Accepto vt ſupra corpore ſolido D, & </s>
            <s xml:id="echoid-s443" xml:space="preserve">liquidi E, inuenta grauitate,
              <lb/>
            vt dictum eſt, fiat vt grauitas G, ad prauitatem H, ita cubus ex F, ad
              <lb/>
            alium cubum, cuius latus ſit C, Quoniam igitur eadem ratione qua
              <lb/>
            ſupra oſtendetur, vt grauitas G, ad grauitatem H, ita eſſe magnitudi-
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            nem ſphæræ B, ad ſphæræ A, magnitudinem, ſed magnitudo ſphæræ B,
              <lb/>
            ad magnitudinem ſphæræ A, triplicatam rationem habet eius,
              <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">18. 12.
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            F, diameter ſphæræ B, ad diametrum ſphæræ A, ſimiliter, & </s>
            <s xml:id="echoid-s444" xml:space="preserve">cubus ex
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            F, ad cubum ex diametro
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            ſphæræ A, triplicatã rationem habet
              <note position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve">33. 11.
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            quam F, ad diametrum ſphæræ A, ergo, vt grauitas G, ad grauitatĕ
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            H, ita erit cubus ex F, ad cubum ex diametro ſphæræ A, ſed vt graui-
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            tas G, ad grauitatem H, ita eſt cubus ex F, ad cubum ex C, ergo cubus
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            ex C, æqualis erit cubo diametri ſphæræ A, quare, & </s>
            <s xml:id="echoid-s445" xml:space="preserve">latus C, æquabi-
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            tur ipſius ſphæræ A, diametro, inuenta igitur eſt quantitas diametri
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            ſolidæ ſphæræ A, quod facere oportebat.</s>
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          <head xml:id="echoid-head23" xml:space="preserve">Exemplum.</head>
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            <s xml:id="echoid-s447" xml:space="preserve">Q Vidam proponit aliquod corpus liquidum notæ
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            magnitudinis, & </s>
            <s xml:id="echoid-s448" xml:space="preserve">vult inuenire quanta erit magni-
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            tudo alicuius ſolidi grauitatem habentis propoſi-
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            to corpori liquido æqualem.</s>
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            <s xml:id="echoid-s450" xml:space="preserve">Sit propoſitum aliquod corpus aqueum B, cuius magnitudo ſit 115,
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            & </s>
            <s xml:id="echoid-s451" xml:space="preserve">oporteat inuenire quanta erit magnitudo plumbi grauitatem ha-
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            bentis æqualem propo ſitæ aquæ B, accipiatur aliquod corpus plumbeũ
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            D, cuius grauitas ſit verbi gratia 23, deinde aquæ magnitudinem ha-
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            bentis æqualem plumbo D, inueniatur grauitas quæ ſit 2. </s>
            <s xml:id="echoid-s452" xml:space="preserve">id autem do-
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            cuit propoſitionis octauæ exemplum, & </s>
            <s xml:id="echoid-s453" xml:space="preserve">fiat vi 23, ad 2, ita 115, ad
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            alium numerum qui ſit 10, is igitur numerus indicabit quanta erit
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            magnitudo plumbi grauitatem habentis æqualem propoſitæ aquæ B.</s>
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            <s xml:id="echoid-s455" xml:space="preserve">Quod ſi propoſitum corpus aqueum B, ſit ſphæricum, cuius
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            ſphæræ diameter ſit 10, & </s>
            <s xml:id="echoid-s456" xml:space="preserve">oporteat inuenire quanta erit dia-
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            meter ſphæræ ex plumbo, grauitatem habentis æqualem pro-
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            poſitæ ſphæræ B, ita faciendum erit.</s>
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            <s xml:id="echoid-s458" xml:space="preserve">Accepto, vt diximus aliquo corpore plumbeo D, cuius grauitas 23,
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            & </s>
            <s xml:id="echoid-s459" xml:space="preserve">aquæ magnitudinem habentis æqualem plumbo D, inuenta </s>
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