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

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              <pb o="29" file="0041" n="41" rhead="AR CHIMEDES."/>
            & </s>
            <s xml:id="echoid-s738" xml:space="preserve">accipiatur aliquod corpus L, leuius quam aqua, ita vt cum ipſi
              <lb/>
            corpori I.</s>
            <s xml:id="echoid-s739" xml:space="preserve">, appendatur corpus B, & </s>
            <s xml:id="echoid-s740" xml:space="preserve">ambo ſimul demittantur in aquã,
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            ſint æque grauia atque aqua, neque ſurſum, neque deorſum feran-
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            tur, ſimiliter accipiatur alterum corpus M, eiuſdem generis cum
              <lb/>
            corpore L, ipſique ſimile, & </s>
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              <figure xlink:label="fig-0041-01" xlink:href="fig-0041-01a" number="18">
                <image file="0041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0041-01"/>
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            æquale, & </s>
            <s xml:id="echoid-s742" xml:space="preserve">corpori M, appen
              <lb/>
            datur corpus A. </s>
            <s xml:id="echoid-s743" xml:space="preserve">Deinde in-
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            teligatur aqua conſiſtens, & </s>
            <s xml:id="echoid-s744" xml:space="preserve">
              <lb/>
            manens, eiuſque ſuperfi-
              <lb/>
            cies ſphærica C D E, cuius
              <lb/>
            ſphæræ centrum K, aquæ
              <lb/>
            enim conſiſtentis, atque
              <unsure/>
              <lb/>
            manentis ſuperficies ſphæ-
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            rica eſt, cuius ſphæræ cen-
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            trum idem eſt, quod centrũ
              <lb/>
            terræ, hoc autem demonſtratum eſt ab Archimede Prop. </s>
            <s xml:id="echoid-s745" xml:space="preserve">2. </s>
            <s xml:id="echoid-s746" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s747" xml:space="preserve">1. </s>
            <s xml:id="echoid-s748" xml:space="preserve">de
              <lb/>
            ijs, quæ vehuntur in aqua. </s>
            <s xml:id="echoid-s749" xml:space="preserve">Inteligantur etiam duæ pyramides con-
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            iunctæ, & </s>
            <s xml:id="echoid-s750" xml:space="preserve">continuatæ, æquales, & </s>
            <s xml:id="echoid-s751" xml:space="preserve">ſimiles KCD, KDE, pro baſibus
              <lb/>
            habentes in ſuperficie aquæ parallelogramma, vertices autem pun-
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            ctum K, & </s>
            <s xml:id="echoid-s752" xml:space="preserve">corpora L, B, comprehendantur à pyramide KDE, corpo-
              <lb/>
            ra vero M, A, à pyramide KCD, & </s>
            <s xml:id="echoid-s753" xml:space="preserve">ſub corporibus L, B, deſcribatur
              <lb/>
            quædam alterius ſphæræ ſuperficies FGH, in a qua, circa centrum K,
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            poterit autem huiuſmodi ſuperficies ſub corporibus L, B, deſcribi,
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            quoniam & </s>
            <s xml:id="echoid-s754" xml:space="preserve">ſi ipſi corpora demerguntur tota, non ideo feruntur
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            deorſum, ponuntur enim æque grauia @atque aqua. </s>
            <s xml:id="echoid-s755" xml:space="preserve">Quoniam
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            igitur eiuſdem generis ponuntur corpora M, L, & </s>
            <s xml:id="echoid-s756" xml:space="preserve">æqualia, & </s>
            <s xml:id="echoid-s757" xml:space="preserve">ſimilia,
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            erunt æque grauia, tum in aqua, tum in aere, & </s>
            <s xml:id="echoid-s758" xml:space="preserve">quoniam corpus
              <lb/>
            A, leuius eſt in aqua, corpore B, erunt corpora M, A, ſimul, in aqua
              <lb/>
            leuiora corporibus L, B, ſed corpora L, B, ſimul, æque grauia ſunt at-
              <lb/>
            que aqua, ergo corpora M, A, ſimul, leuiora erunt quam aqua; </s>
            <s xml:id="echoid-s759" xml:space="preserve">quare
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            corpus M, non demergetur totum, ſed aliqua pars ipſius ex aquæ ſu-
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            perficie extabit.</s>
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            <s xml:id="echoid-s761" xml:space="preserve">Et quoniam eiuſdem generis, & </s>
            <s xml:id="echoid-s762" xml:space="preserve">grauitatis ponuntur corpora A, B,
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            erunt magnitudine æqualia, & </s>
            <s xml:id="echoid-s763" xml:space="preserve">per additionem æqualium æquali-
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            bus, corpora M, A, erunt æqualia corporibus L, B,</s>
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          <p>
            <s xml:id="echoid-s764" xml:space="preserve">Quoniam igitur corpora M, A, æqualia ſunt corporibus L, B, pars
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            autem corporis M, extat ex aquæ ſuperficie, & </s>
            <s xml:id="echoid-s765" xml:space="preserve">corpora L, B, tota de-
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            merguntur, minus loci ocupabunt in aqua corpora M, A, quam cor-
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            pora L, B, quare maior erit grauitas corporum M, A, & </s>
            <s xml:id="echoid-s766" xml:space="preserve">aquæ conti-
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            nentis ipſa corpora, quæ eſt in loco pyramidis CDGF, quam corpo-
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            rum L, B, & </s>
            <s xml:id="echoid-s767" xml:space="preserve">aquæ ipſa corpora continĕtis in loco pyramidis </s>
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