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

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[Item 1.]
[2.] MARINI GHETALDI PATRICII RAGVSINI PROMOTVS ARCHIMEDIS SEV De varijs corporum generibus grauitate & magnitudine comparatis.
[3.] ROM AE, Apud Aloyſium Zannettum. MDCIII. SVPERIORV M PERMISSV.
[4.] REVERENDISSIMO SERAPHINO OLIVARIO RAZZALIO. PATRIARCH AE ALEXANDRINO. Marinus Ghetaldus. S. P. D.
[5.] BENEVOLO LECTORI.
[6.] Seu, DE VARIIS CORPORVM GENERIBVS Grauitate, & magnitudine comparatis. THEOREMA I. PROPOS. I.
[7.] THEOREMA II. PROPOS. II.
[8.] THEOREMA III. PROPOS. III.
[9.] THEOREMA IV. PROPOS. IV.
[10.] THEOREMA V. PROPOS. V.
[11.] THEOREMA VI. PROPOS. VI.
[12.] THEOREMA VII. PROPOS. VII.
[13.] PROBLEMA I. PROPOS. VIII.
[14.] Exemplum.
[15.] PROBLEMA II. PROPOS. IX.
[16.] Exemplum.
[17.] PROBLEMA III. PROPOS. X.
[18.] Exemplum.
[19.] PROBLEMA IV. PROPOS. XI.
[20.] Exemplum.
[21.] PROBLEMAV. PROPOS. XII.
[22.] Exemplum.
[23.] PROBLEMA VI. PROPOS. XIII.
[24.] Exemplum.
[25.] PROBLEMA VII. PROPOS. XIV.
[26.] Exemplum.
[27.] PROBLEMA VIII. PROPOS. XV.
[28.] Exemplum.
[29.] THEOREMA VIII. PROPOS. XVI.
[30.] ALITER.
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              <pb o="26" file="0038" n="38" rhead="PROMOTVS"/>
              <note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">7. buius</note>
            cundum & </s>
            <s xml:id="echoid-s668" xml:space="preserve">quartum, Erit vt grauitas E, ad grauitatem D, ita ma- gnitudo G, ad liquidi B, magnitudinem, ſed vt grauitas E, ad graui-
              <lb/>
            tatem D, ita eſt magnitudo G, ad F, magnitudinem; </s>
            <s xml:id="echoid-s669" xml:space="preserve">ergo magnitudo
              <lb/>
            F, æqualis erit magnitudini liquidi B. </s>
            <s xml:id="echoid-s670" xml:space="preserve">inuenta igitur eſt corporis li-
              <lb/>
            quidi B, magnitudo F, quod facere oportebat.</s>
            <s xml:id="echoid-s671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s672" xml:space="preserve">Quod ſi propoſita duo corpora æque grauia fuerint
              <lb/>
            regularia, vtpote ſphærica, fuerit autem ſphęræ A, data
              <lb/>
            diameter G, & </s>
            <s xml:id="echoid-s673" xml:space="preserve">oporteat inuenire, quanta erit diameter
              <lb/>
            ſphæræ B, ita faciendum erit.</s>
            <s xml:id="echoid-s674" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s675" xml:space="preserve">ACCEPTO aliquo cor
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              <figure xlink:label="fig-0038-01" xlink:href="fig-0038-01a" number="17">
                <image file="0038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0038-01"/>
              </figure>
            pore ſolido C, & </s>
            <s xml:id="echoid-s676" xml:space="preserve">inuentis
              <lb/>
            grauitatibus D, E, liquidorũ
              <lb/>
            H, I, vt ſupra, fiat vt grauitas
              <lb/>
            E, ad grauitatem D, ita cu-
              <lb/>
            bus ex G, ad alium cubum,
              <lb/>
            cuius latus ſit F. </s>
            <s xml:id="echoid-s677" xml:space="preserve">Quoniam
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            igitur eadem ratione, qua
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            ſupra oſtendetur, vt grauitas
              <lb/>
            E, ad grauitatem D, ita eſſe
              <lb/>
            magnitudinem ſphæræ A, ad
              <lb/>
            ſphæræ B, magnitudinem, ſed
              <lb/>
            magnitudo ſphæræ A, ad
              <lb/>
              <note position="left" xlink:label="note-0038-02" xlink:href="note-0038-02a" xml:space="preserve">18. 12.
                <lb/>
              Elem.</note>
            ſphæræ B, magnitudinem, triplicatã rationem habet eius, quam G, diameter ſphæræ A, ad dia-
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            metrum ſphæræ B, ſimiliter & </s>
            <s xml:id="echoid-s678" xml:space="preserve">cubus ex G, ad cubum diametri ſphæ-
              <lb/>
              <note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve">33. 11.
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              Elem.</note>
            ræ B, triplicatam rationem habet eius, quam G, ad ſphæræ B, dia- metrum; </s>
            <s xml:id="echoid-s679" xml:space="preserve">ergo vt grauitas E, ad grauitatem D, ita erit cubus ex G, ad
              <lb/>
            cubum diametri ſphæræ B, ſed vt grauitas D, ita grauitatem D, ita
              <lb/>
            eſt cubus ex G, ad cubum ex F; </s>
            <s xml:id="echoid-s680" xml:space="preserve">ergo cubus ex F, æqualis erit cubo
              <lb/>
            diametri ſphæræ B; </s>
            <s xml:id="echoid-s681" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s682" xml:space="preserve">latus F, æquabitur diametro ipſius ſphæ
              <lb/>
            ræ B. </s>
            <s xml:id="echoid-s683" xml:space="preserve">inuenta igitur eſt quantitas diametri ſphæræ B, quod facere
              <lb/>
            oportebat.</s>
            <s xml:id="echoid-s684" xml:space="preserve"/>
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          <head xml:id="echoid-head31" xml:space="preserve">Exemplum.</head>
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            <s xml:id="echoid-s685" xml:space="preserve">QVidam proponit aliquod corpus liquidum notæ
              <lb/>
            magnitudinis, & </s>
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            gnitudo liquidi alterius generis, </s>
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