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

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[31.] THEOREMA IX. PROPOS. XVII.
Page: 43 (31)
[32.] Ad comparandum inter ſe duodecim corporum genera grauitate, & magnitudine tabella.
Page: 44 (32)
[33.] Altera, ad comparandum inter ſe duodecim corporum genera, grauitate, & magnitudine, tabella.
Page: 45 (33)
[34.] Hic ſequitur tabula, ad inueniendas ſphærarum grauita-tes, ex data diametrorum magnitudine, cuius hæc eſt explicatio.
Page: 46 (34)
[35.] Qua ratione hanc Tabulam compoſuimus.
Page: 47 (35)
[36.] Ad inueniendas ſphæra-diametrorum TAB
Page: 48 (36)
[37.] Sequitur, ad inueniendas diametrorum magnitudines ex data ſphæ-rarum grauitate, tabula.
Page: 53 (41)
[38.] Hactenus Vitruuius.
Page: 64 (52)
[39.] PROBLEMA IX. PROPOS. XVIII.
Page: 66 (54)
[40.] Exemplum. I.
Page: 67 (55)
[41.] Exemplum. II.
Page: 67 (55)
[42.] THEOREMA X. PROPOS. XIX.
Page: 68 (56)
[43.] Alia breuior Theorematis demonſtratio.
Page: 71 (59)
[44.] Item.
Page: 74 (62)
[45.] Velin eadem denominatione.
Page: 75 (63)
[46.] Compoſitio eiuſdem tabulæ.
Page: 82 (70)
[47.] FINIS. ERRATA SIC CORRIGE.
Page: 84 (72)
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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-
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            tatem D, ita eſt magnitudo G, ad F, magnitudinem; </s>
            <s xml:id="echoid-s669" xml:space="preserve">ergo magnitudo
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            F, æqualis erit magnitudini liquidi B. </s>
            <s xml:id="echoid-s670" xml:space="preserve">inuenta igitur eſt corporis li-
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            quidi B, magnitudo F, quod facere oportebat.</s>
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          <p>
            <s xml:id="echoid-s672" xml:space="preserve">Quod ſi propoſita duo corpora æque grauia fuerint
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            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
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            ſphæræ B, ita faciendum erit.</s>
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          <p>
            <s xml:id="echoid-s675" xml:space="preserve">ACCEPTO aliquo cor
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                <image file="0038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0038-01"/>
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            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
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            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.
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            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-
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              <note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve">33. 11.
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            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
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            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>
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          <head xml:id="echoid-head31" xml:space="preserve">Exemplum.</head>
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            magnitudinis, & </s>
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            gnitudo liquidi alterius generis, </s>
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