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

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          <pb o="1" file="0013" n="13" rhead="MARINI GHETALDI PROMOTVS ARCHIMEDES"/>
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        <div xml:id="echoid-div6" type="section" level="1" n="6">
          <head xml:id="echoid-head8" xml:space="preserve">Seu,
            <lb/>
          DE VARIIS CORPORVM GENERIBVS
            <lb/>
          Grauitate, & magnitudine comparatis.</head>
          <head xml:id="echoid-head9" xml:space="preserve">THEOREMA I. PROPOS. I.</head>
          <p>
            <s xml:id="echoid-s123" xml:space="preserve">SI duorum Grauium Corporum eiuſdem ge-
              <lb/>
            neris alterum alterius fuerit multiplex, quo-
              <lb/>
            tuplex maius fuerit minoris, totuplex erit
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            maioris grauitas, grauitatis minoris.</s>
            <s xml:id="echoid-s124" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s125" xml:space="preserve">SINT duo corpora eiuſdem generis ABC, D, quorum grauita-
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            tes, EFG, ipſius ABC, & </s>
            <s xml:id="echoid-s126" xml:space="preserve">H, ip-
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              <figure xlink:label="fig-0013-01" xlink:href="fig-0013-01a" number="2">
                <image file="0013-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0013-01"/>
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            ſius D, ſit autem corpus ABC,
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            multiplex corporis D. </s>
            <s xml:id="echoid-s127" xml:space="preserve">Dico quo
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            tuplex eſt corpus ABC, corporis
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            D, totuplicem eſſe grauitatem
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            EFG, grauitatis H, diuidatur
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            enim corpus ABC, in partes ip-
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            ſi D, æquales, quæ ſint A, B, C,
              <lb/>
            quoniam igitur corpus A, æqua
              <lb/>
            le eſt corpori D, magnitudine,
              <lb/>
            & </s>
            <s xml:id="echoid-s128" xml:space="preserve">ſunt eiuſdem generis, erit grauitas vnius æqualis grauitati alterius.
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            </s>
            <s xml:id="echoid-s129" xml:space="preserve">Sumatur grauitas E, æqualis grauitati H, erit igitur corporis A, gra-
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            uitas E, & </s>
            <s xml:id="echoid-s130" xml:space="preserve">reliqui corporis BC, grauitas FG. </s>
            <s xml:id="echoid-s131" xml:space="preserve">Rurſus quoniam cor-
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            pora B, D, ſunt magnitudine æqualia, erunt æquè grauia, ſumatur
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            grauitati H, æqualis grauitas F, erit igitur corporis B, grauitas F, & </s>
            <s xml:id="echoid-s132" xml:space="preserve">
              <lb/>
            reliqui corporis C, grauitas G, & </s>
            <s xml:id="echoid-s133" xml:space="preserve">ſic fiat, donec perueniatur ad vlti-
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            mam partem corporis ABC, æqualem ipſi D, ſit ea vltima pars C, quo
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            niam igitur corpus C, æquatur magnitudine ipſi D, æquabitur, & </s>
            <s xml:id="echoid-s134" xml:space="preserve">gra-
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            uitate, quare grauitas G, æqualis erit grauitati H, ſequitur igitur
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            quot partes ſunt in corpore ABC, æquales ipſi D, tot eſſe partes in. </s>
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            grauitate EFG, æquales ipſi H, quoties enim ſumpſimus in corpore. </s>
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            ABC, corpus ipſi D æquale, toties & </s>
            <s xml:id="echoid-s137" xml:space="preserve">in grauitate EFG, </s>
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