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

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[Item 1.]
[2.] MARINI GHETALDI PATRICII RAGVSINI PROMOTVS ARCHIMEDIS SEV De varijs corporum generibus grauitate & magnitudine comparatis.
[3.] ROM AE, Apud Aloyſium Zannettum. MDCIII. SVPERIORV M PERMISSV.
[4.] REVERENDISSIMO SERAPHINO OLIVARIO RAZZALIO. PATRIARCH AE ALEXANDRINO. Marinus Ghetaldus. S. P. D.
[5.] BENEVOLO LECTORI.
[6.] Seu, DE VARIIS CORPORVM GENERIBVS Grauitate, & magnitudine comparatis. THEOREMA I. PROPOS. I.
[7.] THEOREMA II. PROPOS. II.
[8.] THEOREMA III. PROPOS. III.
[9.] THEOREMA IV. PROPOS. IV.
[10.] THEOREMA V. PROPOS. V.
[11.] THEOREMA VI. PROPOS. VI.
[12.] THEOREMA VII. PROPOS. VII.
[13.] PROBLEMA I. PROPOS. VIII.
[14.] Exemplum.
[15.] PROBLEMA II. PROPOS. IX.
[16.] Exemplum.
[17.] PROBLEMA III. PROPOS. X.
[18.] Exemplum.
[19.] PROBLEMA IV. PROPOS. XI.
[20.] Exemplum.
[21.] PROBLEMAV. PROPOS. XII.
[22.] Exemplum.
[23.] PROBLEMA VI. PROPOS. XIII.
[24.] Exemplum.
[25.] PROBLEMA VII. PROPOS. XIV.
[26.] Exemplum.
[27.] PROBLEMA VIII. PROPOS. XV.
[28.] Exemplum.
[29.] THEOREMA VIII. PROPOS. XVI.
[30.] ALITER.
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            magis igitur aquæ pars premetur, quæ eſt ſub ſuperficie FG, quam
              <lb/>
            ea quæ eſt ſub ſuperficie GH; </s>
            <s xml:id="echoid-s768" xml:space="preserve">quare expellet partem minus preſſam,
              <lb/>
            (æqualiter enim & </s>
            <s xml:id="echoid-s769" xml:space="preserve">continuatæ iacent inter ſeſe) & </s>
            <s xml:id="echoid-s770" xml:space="preserve">nõ manebit aqua,
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            quod eſt abſurdum, ponebatur enim manens. </s>
            <s xml:id="echoid-s771" xml:space="preserve">non igitur corpus A,
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            leuius eſt in aqua corpore B. </s>
            <s xml:id="echoid-s772" xml:space="preserve">eadem ratione oſtendetur neque corpus
              <lb/>
            B, leuius eſſe in aqua corpore A, quare conſtat propoſitum.</s>
            <s xml:id="echoid-s773" xml:space="preserve"/>
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        <div xml:id="echoid-div53" type="section" level="1" n="30">
          <head xml:id="echoid-head33" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s774" xml:space="preserve">Sint duo eiuſdem generi@, & </s>
            <s xml:id="echoid-s775" xml:space="preserve">grauitatis corpora A, B, grauiora
              <lb/>
            quam aqua, & </s>
            <s xml:id="echoid-s776" xml:space="preserve">ſint diſſimilia. </s>
            <s xml:id="echoid-s777" xml:space="preserve">oſtendendum eſt ipſa corpora æqualem
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            in aqua grauitatem habere, ſit enim corporis A, vel ipſius B, graui-
              <lb/>
            tas CD, aquæ vero magni-
              <lb/>
              <figure xlink:label="fig-0042-01" xlink:href="fig-0042-01a" number="19">
                <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0042-01"/>
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            tudinem habentis æqua-
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            lem ipſi A, vel B, ſit graui-
              <lb/>
            tas C, & </s>
            <s xml:id="echoid-s778" xml:space="preserve">accipiatur ali-
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            quod corpus L, leuius quã
              <lb/>
            aqua, cuius grauitas ſit
              <lb/>
            ipſi C, æqualis, aquæ ve-
              <lb/>
            ro, magnitudinem haben-
              <lb/>
            tis æqualem corpori L, ſit
              <lb/>
            grauitas æqualis ipſi CD,
              <lb/>
            itaque appenſo corpore
              <lb/>
            B, corpori L, corpus ex
              <lb/>
            vtriſque conſtans æque graue erit atque aqua, grauitas enim vtro-
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            runque corporum B, L, eſt æqualis vtriſque grauitatibus CD, & </s>
            <s xml:id="echoid-s779" xml:space="preserve">C, & </s>
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            grauitas aquæ, magnitudinem habentis æqualem vtriſq; </s>
            <s xml:id="echoid-s781" xml:space="preserve">corporibus
              <lb/>
            L, B, æqualis eſt eiſdem grauitatibus CD, & </s>
            <s xml:id="echoid-s782" xml:space="preserve">C, corpora igitur B, L,
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            demiſſa in aquam, neque ſurſum, neque deorſum ſerentur, quia cor-
              <lb/>
            pus B, grauius quam aqua fertur deorſum tanta vi, quanta à corpo-
              <lb/>
            re L, ſurſum retrahitur.</s>
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          </p>
          <p>
            <s xml:id="echoid-s784" xml:space="preserve">Rurſus accipiatur alterum corpus ſolidum M, eiuſdem generis
              <lb/>
            cum corpore L, ipſique ſimile, & </s>
            <s xml:id="echoid-s785" xml:space="preserve">æquale, & </s>
            <s xml:id="echoid-s786" xml:space="preserve">corpore A, appenſo ipſi
              <lb/>
            M, & </s>
            <s xml:id="echoid-s787" xml:space="preserve">demiſſis ambobus in aquam, eadem ratione qua ſupra oſten-
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            detur, corpora A, M, ſimul, eſſe æque grauia atque aqua, & </s>
            <s xml:id="echoid-s788" xml:space="preserve">corpus
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            A, tanta vi deorſum ferri, quanta retrahitur ſurſum à corpore M,
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            ſed corpora M, L, æqualem vim habent retrahendi ſurſum, cum
              <lb/>
            ſint eiuſdem generis, & </s>
            <s xml:id="echoid-s789" xml:space="preserve">æqualia, & </s>
            <s xml:id="echoid-s790" xml:space="preserve">ſimilia, ergo æquali vi retra-
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            hentur corpora A, B, ne deſcendant; </s>
            <s xml:id="echoid-s791" xml:space="preserve">quare conſtat ipſa corpora A,
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            B, æqualem in aqua grauitatem habere quod erat oſtendendum.</s>
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