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

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            <s xml:id="echoid-s1219" xml:space="preserve">
              <pb o="59" file="0071" n="71" rhead="ARCHIMEDES."/>
            tatum H, G, ad grauitatem EK, ita differentia grauitatum H, FV,
              <lb/>
            ad grauitatem E. </s>
            <s xml:id="echoid-s1220" xml:space="preserve">quod ſecundo loco fuit demonſtrandum.</s>
            <s xml:id="echoid-s1221" xml:space="preserve"/>
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        <div xml:id="echoid-div77" type="section" level="1" n="43">
          <head xml:id="echoid-head46" xml:space="preserve">Alia breuior Theorematis demonſtratio.</head>
          <p>
            <s xml:id="echoid-s1222" xml:space="preserve">RESVMATVR eadem figura vt ſupra. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Quoniam igitur
              <lb/>
            corpus D, æquale eſt corpori Q, magnitudine, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">portio C, æqualis
              <lb/>
            portioni L, erit vt D, ad Q, ita C, ad L, & </s>
            <s xml:id="echoid-s1225" xml:space="preserve">permutando vt D, ad C, ita
              <lb/>
            Q, ad L, & </s>
            <s xml:id="echoid-s1226" xml:space="preserve">quoniam eiuſdem ſunt generis D, C, ſimiliter & </s>
            <s xml:id="echoid-s1227" xml:space="preserve">Q, L, * erit
              <lb/>
              <note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">4. huius</note>
            vt grauitas corporis D, hoc eſt vt EK, ad K, ita H, ad V.</s>
            <s xml:id="echoid-s1228" xml:space="preserve"/>
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            <s xml:id="echoid-s1229" xml:space="preserve">Similiter quoniam ponuntur æqualia magnitudine corpora A, P,
              <lb/>
            & </s>
            <s xml:id="echoid-s1230" xml:space="preserve">æquales quoque portiones B, O, erit vt A, ad P, ita B, ad O, & </s>
            <s xml:id="echoid-s1231" xml:space="preserve">per-
              <lb/>
            mutando vt A, ad B, ita P, ad O, ſed eiuſdem ſunt generis A, B, ſimili-
              <lb/>
            ter & </s>
            <s xml:id="echoid-s1232" xml:space="preserve">P, O, * vt igitur grauitas corporis A, id eſt vt EK, ad E, ita erit
              <lb/>
              <note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">4. huius</note>
            G, ad F, & </s>
            <s xml:id="echoid-s1233" xml:space="preserve">per conuerſionem rationis erit vt EK, ad K, ita G, ad G,
              <lb/>
            minus F, ſed demonſtratum eſt, vt EK, ad K, ita eſſe H, ad V, ergo vt
              <lb/>
            H, ad V, ita erit G, ad G, minus F, & </s>
            <s xml:id="echoid-s1234" xml:space="preserve">permutando vt H, ad G, ita V,
              <lb/>
            ad G, minus F, & </s>
            <s xml:id="echoid-s1235" xml:space="preserve">diuidendo vt H, minus G, ad G, ita erit FV, minus
              <lb/>
            G, ad G, minus F, rurſus permutando erit vt H, minus G, ad FV, mi-
              <lb/>
            nus G, ita G, ad G, minus F, ſed vt EK, ad K, ita eſt G, ad G, minus F,
              <lb/>
            vt eſt demonſtratum, ergo vt H, minus G, ad FV, minus G, ita erit
              <lb/>
            EK, ad K, quare permutando vt H, minus G, ad EK, ita erit FV, mi-
              <lb/>
            nus G, ad K, quod eſtò primum.</s>
            <s xml:id="echoid-s1236" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1237" xml:space="preserve">Dico quoque vt H, minus G, ad EK, ita eſſe H, minus FV, ad E.
              <lb/>
            </s>
            <s xml:id="echoid-s1238" xml:space="preserve">Quoniam enim oſtenſum eſt vt EK, ad K, ita eſſe H, ad V, erit per
              <lb/>
            conuerſionem rationis vt EK, ad E, ita H, ad H, minus V, ſed demon-
              <lb/>
            ſtratum eſt vt EK, ad E, ita eſſe G, ad F, ergo vt H, ad H, minus V, ita
              <lb/>
            erit G, ad F, & </s>
            <s xml:id="echoid-s1239" xml:space="preserve">permutando vt H, ad G, ita H, minus V, ad F, & </s>
            <s xml:id="echoid-s1240" xml:space="preserve">diui-
              <lb/>
            dendo vt H, minus G, ad G, ita erit H, minus FV, ad F, & </s>
            <s xml:id="echoid-s1241" xml:space="preserve">permutan-
              <lb/>
            do vt H, minus G, ad H, minus FV, ita G, ad F, ſed vt EK, ad E, ita eſt
              <lb/>
            G, ad F, vt eſt demonſtratum, ergo vt H, minus G, ad H, minus FV,
              <lb/>
            ita erit EK, ad E, quare permutando, erit vt H, minus G, ad EK, ita
              <lb/>
            H, minus FV, ad E, quod erat ſecundo loco demonſtrandum.</s>
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          </p>
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            <s xml:id="echoid-s1243" xml:space="preserve">SVpereſt igitur vt dicamus, qua ratione ex grauitate auri
              <lb/>
            cognoſci poſſit eius qualitas; </s>
            <s xml:id="echoid-s1244" xml:space="preserve">id quod ex ijs, quæ dicta
              <lb/>
            ſunt facile colligitur; </s>
            <s xml:id="echoid-s1245" xml:space="preserve">ſi videlicet nota fiat cuiuſuis maſſæ auri
              <lb/>
            grauitas, quam habet tum in aere, tum in aqua. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">Sed ante
              <lb/>
            omnia, duo nobis ſunt præmittenda, & </s>
            <s xml:id="echoid-s1247" xml:space="preserve">explicanda. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">nimirum
              <lb/>
            quid ſit aurum 24. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">partium, ſeu (vt vulgo dicitur) di 24. </s>
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