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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              <pb o="41" file="0093" n="93" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ſtrabitur portionem, quæ ad humidum in grauitate eandẽ
              <lb/>
            proportionem habeat, quàm quadratum p f ad quadratũ
              <lb/>
            b d in humidum demiſſam, ita ut baſis ipſius nõ cõtingat
              <lb/>
            humidum, inclinatam conſiſtere adeo, ut baſis in uno pun
              <lb/>
            cto humidi ſuperficiem contingat. </s>
            <s xml:id="echoid-s2438" xml:space="preserve">& </s>
            <s xml:id="echoid-s2439" xml:space="preserve">axis cum ipſa faciat
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            angulum angulo φ æqualem.</s>
            <s xml:id="echoid-s2440" xml:space="preserve"/>
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        <div xml:id="echoid-div175" type="section" level="1" n="55">
          <head xml:id="echoid-head60" xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:id="echoid-s2441" xml:space="preserve">_Hoc eſt quadratum t p ad quadratum b d.</s>
            <s xml:id="echoid-s2442" xml:space="preserve">]_ Ex uigeſima
              <lb/>
              <note position="right" xlink:label="note-0093-01" xlink:href="note-0093-01a" xml:space="preserve">A</note>
            ſexta libri Archimedis de conoidibus, & </s>
            <s xml:id="echoid-s2443" xml:space="preserve">ſphæroidibus. </s>
            <s xml:id="echoid-s2444" xml:space="preserve">ergo ex no
              <lb/>
            na quinti erit quadratum t p æquale quadrato x o: </s>
            <s xml:id="echoid-s2445" xml:space="preserve">& </s>
            <s xml:id="echoid-s2446" xml:space="preserve">propterea li
              <lb/>
            nea t p lineæ x o æqualis.</s>
            <s xml:id="echoid-s2447" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s2448" xml:space="preserve">_Et portiones ipſæ æquales erunt.</s>
            <s xml:id="echoid-s2449" xml:space="preserve">]_ Ex uigeſimaquinta eiuſ-
              <lb/>
              <note position="right" xlink:label="note-0093-02" xlink:href="note-0093-02a" xml:space="preserve">B</note>
            dem libri.</s>
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          </p>
          <p>
            <s xml:id="echoid-s2451" xml:space="preserve">Rurſus
              <lb/>
              <note position="right" xlink:label="note-0093-03" xlink:href="note-0093-03a" xml:space="preserve">C</note>
              <figure xlink:label="fig-0093-01" xlink:href="fig-0093-01a" number="59">
                <image file="0093-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0093-01"/>
              </figure>
            quoniam
              <lb/>
            in portio
              <lb/>
            nibus æ-
              <lb/>
            qualibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s2452" xml:space="preserve">ſimili-
              <lb/>
            bus a o q
              <lb/>
            l, a p m l.</s>
            <s xml:id="echoid-s2453" xml:space="preserve">]
              <lb/>
            _In portio-_
              <lb/>
            _ne enim a p_
              <lb/>
            _m l deſcri-_
              <lb/>
            _batur por-_
              <lb/>
            _tio a o q æ-_
              <lb/>
            _qualis por_
              <lb/>
            _tioni i p m_,
              <lb/>
            _cadet pun-_
              <lb/>
            _ctum q in-_
              <lb/>
            _fram, alio-_
              <lb/>
            _qui totum parti eſſet æquale. </s>
            <s xml:id="echoid-s2454" xml:space="preserve">Ducatur deinde i u æquidiſtans a </s>
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