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

Table of Notes

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              <pb o="6" file="0018" n="18" rhead="PROMOTVS"/>
            neris liquidi corpora E, F, G, quorum E, ſit æquale corpori A, vel B,
              <lb/>
            magnitudine, ipſum vero F, æqua
              <lb/>
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            le corpori C, & </s>
            <s xml:id="echoid-s230" xml:space="preserve">ipſum G, æquale
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            corpori D. </s>
            <s xml:id="echoid-s231" xml:space="preserve">Quoniam igitur eſt vt
              <lb/>
            D, ad G, ita B, ad E, æquale vi-
              <lb/>
            delicet ad æquale, erit permutan-
              <lb/>
            do vt D, ad B, ita G, ad E, & </s>
            <s xml:id="echoid-s232" xml:space="preserve">quo-
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            niam ſunt eiuſdem generis corpo
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            ra D, B, ſimiliter & </s>
            <s xml:id="echoid-s233" xml:space="preserve">corpora G, E,
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            erit vt grauitas corporis D,
              <note position="left" xlink:label="note-0018-01" xlink:href="note-0018-01a" xml:space="preserve">2. & 3.
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              huins.</note>
            eſt ipſius C, ponuntur enim æque
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            grauia corpora C, D, ad grauita-
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            tem corporis B, ita liquidi G, gra-
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            uitas ad grauitatem liquidi E.
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            </s>
            <s xml:id="echoid-s234" xml:space="preserve">Similiter quoniam eſt vt A, ad E,
              <lb/>
            ita C, ad F, æquale videlicet ad
              <lb/>
            æquale, erit permutando vt A, ad
              <lb/>
            C, ita E, ad F, & </s>
            <s xml:id="echoid-s235" xml:space="preserve">quoniam ponun
              <emph style="sub">t</emph>
            ur eiuſdem generis corpora A, C,
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              <note position="left" xlink:label="note-0018-02" xlink:href="note-0018-02a" xml:space="preserve">2. & 3.
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              huius.</note>
            itidem E, F, erit vt grauitas corporis A, ad grauitatem ipſius C, ita liquidi E, grauitas ad grauitatem liquidi F, ſed vt grauitas corporis
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            C, ad grauitatem corporis B, ita eſt grauitas liquidi G, ad grauita-
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            tem liquidi E, vt eſt demonſtratum, ergo in perturbata
              <note position="left" xlink:label="note-0018-03" xlink:href="note-0018-03a" xml:space="preserve">23. 5.
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              Elem.</note>
            erit vt grauitas corporis A, ad ipſius corporis B, grauitatem, ita liqui
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            di G, grauitas, ad grauitatem liquidi F. </s>
            <s xml:id="echoid-s236" xml:space="preserve">ſi igitur quatuor grauium
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            corporum primum, & </s>
            <s xml:id="echoid-s237" xml:space="preserve">ſecundum, & </s>
            <s xml:id="echoid-s238" xml:space="preserve">c. </s>
            <s xml:id="echoid-s239" xml:space="preserve">quod erat demonſtrandum.</s>
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          <head xml:id="echoid-head15" xml:space="preserve">THEOREMA VII. PROPOS. VII.</head>
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            <s xml:id="echoid-s241" xml:space="preserve">SI quatuor grauium corporum primum, & </s>
            <s xml:id="echoid-s242" xml:space="preserve">ſecundũ,
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            fuerint magnitudine æqualia, tertium vero, & </s>
            <s xml:id="echoid-s243" xml:space="preserve">quar-
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            tum æque grauia, fuerint autem primum, & </s>
            <s xml:id="echoid-s244" xml:space="preserve">tertium
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            eiuſdem generis, itidem ſecundum, & </s>
            <s xml:id="echoid-s245" xml:space="preserve">quartum; </s>
            <s xml:id="echoid-s246" xml:space="preserve">primum
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            ad ſecundum eandem in grauitate rationem habebit,
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            quam habet in magnitudine quartum ad tertium.</s>
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          <p>
            <s xml:id="echoid-s248" xml:space="preserve">SINT quatuor grauia corpora A, B, C, D, quorum A, primum
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            & </s>
            <s xml:id="echoid-s249" xml:space="preserve">B, ſecundum ſint magnitudine æqualia, tertium vero C, & </s>
            <s xml:id="echoid-s250" xml:space="preserve">D, quar-
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            tum æque grauia, ſint autem A, & </s>
            <s xml:id="echoid-s251" xml:space="preserve">C, eiuſdem generis, itidem B, & </s>
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            D. </s>
            <s xml:id="echoid-s253" xml:space="preserve">Dico corpus A, eandem in grauitate rationem habere ad </s>
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