Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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            cuius grauitas ſitipſi b æqualis: </s>
            <s xml:id="echoid-s328" xml:space="preserve">humidi ucro molem ha-
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            bentis æqualem magnitudini d, ſit grauitas æqualis b c.
              <lb/>
            </s>
            <s xml:id="echoid-s329" xml:space="preserve">Itaque compoſitis magnitudinibus a d, magnitudo ex
              <lb/>
            utriſque conſtans æque grauis erit, atque ipſum humidũ: </s>
            <s xml:id="echoid-s330" xml:space="preserve">
              <lb/>
            grauitas enim utrarũque magnitudinum eſt æqualis utriſ-
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            que grauitatibus, uidelicet b c, & </s>
            <s xml:id="echoid-s331" xml:space="preserve">b: </s>
            <s xml:id="echoid-s332" xml:space="preserve">grauitas autem humi
              <lb/>
            di habentis molem æqualem utriſque magnitudinibus, eſt
              <lb/>
            eiſdem grauitatibus æqualis. </s>
            <s xml:id="echoid-s333" xml:space="preserve">Demisſis igitur magnitudini
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s334" xml:space="preserve">in humidum proiectis æque graues erunt, atque hu
              <lb/>
            midum: </s>
            <s xml:id="echoid-s335" xml:space="preserve">neque ſurſum, neque deorſum ferentur: </s>
            <s xml:id="echoid-s336" xml:space="preserve">quoniam
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            magnitudo quidem a
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              <figure xlink:label="fig-0022-01" xlink:href="fig-0022-01a" number="11">
                <image file="0022-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0022-01"/>
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            grauior humido feretur
              <lb/>
            deorſum; </s>
            <s xml:id="echoid-s337" xml:space="preserve">& </s>
            <s xml:id="echoid-s338" xml:space="preserve">eadem ui à
              <lb/>
            magnitudine d ſurſum
              <lb/>
            retrahetur: </s>
            <s xml:id="echoid-s339" xml:space="preserve">magnitudo
              <lb/>
            autem d humido leuior
              <lb/>
            feretur ſurſum tanta ui,
              <lb/>
            quanta eſt grauitas c:
              <lb/>
            </s>
            <s xml:id="echoid-s340" xml:space="preserve">demõſtratũ enim eſt ma
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              <note position="left" xlink:label="note-0022-01" xlink:href="note-0022-01a" xml:space="preserve">6. huius.</note>
            gnitudines ſolidas hu-
              <lb/>
            mido leuiores, impulſas
              <lb/>
            in humidum tanta uiretrahi ſurſum, quanto humidum ha
              <lb/>
            bens molem magnitudini æqualem grauius eſt ipſa magni
              <lb/>
            tudine. </s>
            <s xml:id="echoid-s341" xml:space="preserve">Athumidum molem habens æqualem d, grauius
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            eſt, quam d, ipſa c grauitate. </s>
            <s xml:id="echoid-s342" xml:space="preserve">Conſtatigitur magnitudinem
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            a deorſum ferri tanta grauitate, quanta eſt c. </s>
            <s xml:id="echoid-s343" xml:space="preserve">quod de-
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            monſtrare oportebat.</s>
            <s xml:id="echoid-s344" xml:space="preserve"/>
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          <head xml:id="echoid-head18" xml:space="preserve">POSITIO II.</head>
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              <emph style="sc">Ponatvr</emph>
            eorum, quæ in humido ſurſum
              <lb/>
            feruntur, vnumquodque ſurſum ferri ſecundum
              <lb/>
            perpendicularem, quæ per centrum grauitatis ip
              <lb/>
            ſorum ducitur.</s>
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