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

Table of handwritten notes

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              <pb o="51" file="0063" n="63" rhead="ARCHIMEDES."/>
            quadruplum erit cubus centapli diametri ſphæræ ctanneæ, grauita-
              <lb/>
            tem babentis quadruplam primæ, & </s>
            <s xml:id="echoid-s963" xml:space="preserve">ſic deinceps. </s>
            <s xml:id="echoid-s964" xml:space="preserve">itaque ſi ex eius
              <lb/>
            multiplicibus, neglectis fractis, eruãtur radices, tanquam ex accura-
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            tis numeris cubis, ipſæ indicabunt diametrorum magnitudines in
              <lb/>
            ratione centupla. </s>
            <s xml:id="echoid-s965" xml:space="preserve">Sed vt etiam euitetur labor multiplicandi prædi-
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            ctum numerum 5684210 {10/19}, bac ratione inuenientur eius multi-
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            plicia.</s>
            <s xml:id="echoid-s966" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s967" xml:space="preserve">Prædicto numero 5684210 {10/19}, addatur eius duplum, idect,
              <lb/>
            11368421 {1/19}, ſumma 17052631 {11/19}, dabit eius triplum, ſi vero ei
              <lb/>
            addatur eius triplum, id eſt, 17052631 {11/19}, ſumma 22736842 {2/19},
              <lb/>
            dabit eius quadruplum, & </s>
            <s xml:id="echoid-s968" xml:space="preserve">ſieius quadruplum ei addatur, ſumma
              <lb/>
            dabit eius quintuplum, & </s>
            <s xml:id="echoid-s969" xml:space="preserve">ſic ſola additione inuenientur eius quot-
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            cunque multiplicia.</s>
            <s xml:id="echoid-s970" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s971" xml:space="preserve">Eadem ratione inuenientur diametri ſpbærarum ex quacunque
              <unsure/>
              <lb/>
            alia materia, ſi enim quæratur de magnitudine diametri verbi gra-
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            tia ſpbæræ ferreæ, grauitatem babentis 1, lib. </s>
            <s xml:id="echoid-s972" xml:space="preserve">fiat vt grana 1314 {22/37},
              <lb/>
            id ect vt grauitas ſpbæræ ferreæ, cuius diameter eſt vnius vnciæ, ad
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            grauitatem vnius libræ, id ect ad grana 6912, ita cubus diametri
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            vnius vnciæ, boc eſt ita 1, ad alium numerum qui ſit 5 {49/190}, is igi-
              <lb/>
            tur numerus
              <emph style="sub">*</emph>
            erit cubus diametri ſpbæræ ferreæ, grauitatem baben-
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              <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">17.
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              buius.</note>
            tis 1, lib, quare radix cubica numeri 5 {49/190}, dabit quæſitam dia-
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            metrum, & </s>
            <s xml:id="echoid-s973" xml:space="preserve">quoniam numerus 5 {49/190}, non eſt præciſe cubus, & </s>
            <s xml:id="echoid-s974" xml:space="preserve">ideo
              <lb/>
            non explicabitur eius radix accurate, multiplicetur per 1000000, & </s>
            <s xml:id="echoid-s975" xml:space="preserve">
              <lb/>
            ex producto 5257894 {14/19}, neglecto fracto {14/19}, eruatur radix, tan-
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            quam ex accurato numero cubo, ea erit 174: </s>
            <s xml:id="echoid-s976" xml:space="preserve">ferè, & </s>
            <s xml:id="echoid-s977" xml:space="preserve">erit centupla ra-
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            dicis numeri 5 {49/190}, quia numerus 5 {49/190}, multiplicatus fuit per
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            cubum ex 100; </s>
            <s xml:id="echoid-s978" xml:space="preserve">diameter igitur ſpbæræ ferreæ, grauitatem babentis
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            1, lib. </s>
            <s xml:id="echoid-s979" xml:space="preserve">erit 1 {74/100}: </s>
            <s xml:id="echoid-s980" xml:space="preserve">deinde ſi duplicetur 5257894 {14/19}, & </s>
            <s xml:id="echoid-s981" xml:space="preserve">ex ita du-
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            plicato eruatur radix cubica 219, ea dabit centuplum diametri ſpbæ-
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            ræ ferreæ, grauitatem babentis 2, lib. </s>
            <s xml:id="echoid-s982" xml:space="preserve">& </s>
            <s xml:id="echoid-s983" xml:space="preserve">ſi triplicetur, triplicati radix
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            cubica 250 dabit centuplum diametri ſpbæræ ferreæ, cuius grauitas
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            erit 3, lib. </s>
            <s xml:id="echoid-s984" xml:space="preserve">& </s>
            <s xml:id="echoid-s985" xml:space="preserve">ſic reliquarum ſpbærarum in infinitum inuenientur
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            diametri. </s>
            <s xml:id="echoid-s986" xml:space="preserve">multiplicia autem numeri 5257894 {14/19}, ſola additione in-
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            uenientur, vt dictum ect ſupra de inuentione multiplicium numeri
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            5684210 {10/19}. </s>
            <s xml:id="echoid-s987" xml:space="preserve">Atque bac ratione prædictam tabulam compoſuimus.</s>
            <s xml:id="echoid-s988" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s989" xml:space="preserve">QVomodo Archimedes argenti mixtionem depre-
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            hendit in auro.</s>
            <s xml:id="echoid-s990" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s991" xml:space="preserve">Hiero (referente V itruuio lib. </s>
            <s xml:id="echoid-s992" xml:space="preserve">9. </s>
            <s xml:id="echoid-s993" xml:space="preserve">Cap. </s>
            <s xml:id="echoid-s994" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s995" xml:space="preserve">Siracuſis auctus </s>
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