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="14" file="0026" n="26" rhead="PROMOTVS"/>
              <note position="left" xlink:label="note-0026-01" xlink:href="note-0026-01a" xml:space="preserve">13. 12.
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            triplicatam rationem habet eius, quam C, ad diametrum ſphæræ B, ergo vt grauitas H, ad grauitatem G, ita erit cubus ex C, ad cubum
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            ex diametro ſphæræ B, ſed vt grauitas H, ad grauitatem G, ita eſt cu
              <lb/>
            bus ex C, ad cubum ex F, ergo cubus ex F, æqualis erit cubo diame-
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            tri ſphæræ B; </s>
            <s xml:id="echoid-s401" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s402" xml:space="preserve">latus F, æquabitur ſphæræ B, diametro. </s>
            <s xml:id="echoid-s403" xml:space="preserve">inuen-
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            ta igitur eſt quantitas diametri liquidæ ſphæræ B, quod facere opor-
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            tebat.</s>
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          <head xml:id="echoid-head21" xml:space="preserve">Exemplum.</head>
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            <s xml:id="echoid-s405" xml:space="preserve">Q Vidam proponit aliquod corpus ſolidum notæ
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            magnitudinis, & </s>
            <s xml:id="echoid-s406" xml:space="preserve">vult ſcire quanta erit magnitudo
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            alicuius liquidi, grauitatem habentis propoſito corpori
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            ſolido æqualem.</s>
            <s xml:id="echoid-s407" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s408" xml:space="preserve">Sit propoſitum aliquod corpus plumbeum A, cuius magnitudo ſit
              <lb/>
            10, & </s>
            <s xml:id="echoid-s409" xml:space="preserve">oporteat ſcire quanta erit magnitudo aquæ grauitatem haben-
              <lb/>
            tis æqualem propoſito plumbo A, accipiatur aliquod corpus plumbeũ
              <lb/>
            D, cuius grauitas 23, deinde aquæ magnitudinem habentis æqualem
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            plumbo D, inueniatur grauitas, vt in exemplo propoſ. </s>
            <s xml:id="echoid-s410" xml:space="preserve">8. </s>
            <s xml:id="echoid-s411" xml:space="preserve">dictum eſt,
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            quæ ſit 2, & </s>
            <s xml:id="echoid-s412" xml:space="preserve">fiat vt 2, ad 23, ita 10, ad alium numerum qui ſit 115, is
              <lb/>
            igitur indicabit quanta erit magnitudo aquæ grauitatem habentis
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            æqualem propoſito plumbo A.</s>
            <s xml:id="echoid-s413" xml:space="preserve"/>
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            <s xml:id="echoid-s414" xml:space="preserve">Quod ſi propoſitũ corpus plumbeum A ſit regulare vt po-
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            te ſphæricum, cuius ſphæræ diameter ſit 10, & </s>
            <s xml:id="echoid-s415" xml:space="preserve">oporteat inue-
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            nire quanta erit diameter ſphæræ ex aqua, grauitatem haben-
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            tis æqualem propoſitæ ſphæræ A, ita faciendum erit.</s>
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            <s xml:id="echoid-s417" xml:space="preserve">Accipiatur, vt diximus, aliquod corpus plumbeum D, cuius gra-
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            uitas 23, deinde aquæ habentis magnitudinem æqualem plumbo D,
              <lb/>
            inueniatur grauitas quæ ſit 2, & </s>
            <s xml:id="echoid-s418" xml:space="preserve">fiat vt 2, ad 23, ita cubus ex 10, qui
              <lb/>
            eſt 1000, ad alium numerum qui ſit 11500, is igitur numerus erit
              <lb/>
            cubus diametri ſpbæræ ex aqua grauitatem habentis æqualem propo-
              <lb/>
            ſitæ ſpbæræ A, quare eius latus cubicum, quod est 22 {57/100}, proximũ
              <lb/>
            vero indicabit ipſam diametrum.</s>
            <s xml:id="echoid-s419" xml:space="preserve"/>
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            <s xml:id="echoid-s420" xml:space="preserve">Similiter ſi propoſitum corpus plumbeum A, fuerit cubicum, vel
              <lb/>
            alicuius alterius formæ regularis, eadem ratione inueniemus latus cu
              <lb/>
            bi ex aqua grauitatem habentis æqualem propoſito cubo A, nam ſi cu-
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            bi A, datum ſit latus 10, erit numerus 11500, cubus ex aqua æqualis
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            grauitate propoſito cubo A, quare latus cubicum numeri 11500, </s>
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