Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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              <pb o="11" file="0033" n="33" rhead="DE IIS QVAE VEH. IN AQVA."/>
            cundum eam, quæ per g, deorſum ferctur; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">non ita mane
              <lb/>
            bit ſolidum a p o l: </s>
            <s xml:space="preserve">nam quod eſt ad a feretur ſurſum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            quod ad b deorſum, donec n o ſecundum perpendicu-
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            larem conſtituatur.</s>
            <s xml:space="preserve">]</s>
          </p>
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            <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">Suppleta
              <lb/>
            a. Federi-
              <lb/>
            co Cõm.</note>
            <note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">B</note>
            <note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">C</note>
            <note position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve">D</note>
            <note position="left" xlink:label="note-0032-05" xlink:href="note-0032-05a" xml:space="preserve">E</note>
            <note position="left" xlink:label="note-0032-06" xlink:href="note-0032-06a" xml:space="preserve">F</note>
            <figure xlink:label="fig-0032-01" xlink:href="fig-0032-01a">
              <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0032-01"/>
            </figure>
            <note position="left" xlink:label="note-0032-07" xlink:href="note-0032-07a" xml:space="preserve">G</note>
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        </div>
        <div type="section" level="1" n="23">
          <head xml:space="preserve">COMMENTARIVS.</head>
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              <emph style="sc">D_esideratvr_</emph>
            propoſitionis huius demonstratio, quam nos
              <lb/>
            etiam ad Archimedis figuram appoſite restituimus, commentarijs-
              <lb/>
            que illustrauimus.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">_Recta portio conoidis rectanguli, quando axem habue_
              <lb/>
              <anchor type="note" xlink:label="note-0033-01a" xlink:href="note-0033-01"/>
            _rit minorem, quàm ſeſquialterum eius, quæ uſque ad axẽ]_
              <lb/>
            In tranſlatione mendoſe legebatur. </s>
            <s xml:space="preserve">maiorem quàm ſeſquialterum:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita legebatur in ſequenti propoſitione. </s>
            <s xml:space="preserve">est autem recta portio co
              <lb/>
            noidis, quæ plano ad axem recto abſcinditur: </s>
            <s xml:space="preserve">eâmque rectam tunc
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            conſiſtere dicimus, quando planum abſcindens, uidelicet baſis pla-
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            num, ſuperficiei humidi æquidiſtans fuerit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0033-01" xlink:href="note-0033-01a" xml:space="preserve">A</note>
          </div>
          <p>
            <s xml:space="preserve">Quæ erit ſectionis i p o s diameter, & </s>
            <s xml:space="preserve">axis portionis in
              <lb/>
              <anchor type="note" xlink:label="note-0033-02a" xlink:href="note-0033-02"/>
            humido demerſæ] _ex_ 46 _primi conicorum Apollonij: </s>
            <s xml:space="preserve">uel ex co-_
              <lb/>
            _rollario_ 51 _eiuſdem_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0033-02" xlink:href="note-0033-02a" xml:space="preserve">B</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Sitque ſolidæ magnitudinis a p o l grauitatis centrum r,_
              <lb/>
              <anchor type="note" xlink:label="note-0033-03a" xlink:href="note-0033-03"/>
            _ipſius uero i p o s centrum ſit b.</s>
            <s xml:space="preserve">]_ Portionis enim conoidis
              <lb/>
            rectanguli centrum grauitatis eſt in axe, quem ita diuidit, ut pars
              <lb/>
            eius, quæ ad uerticem terminatur, reliquæ partis, quæ ad baſim, ſit
              <lb/>
            dupla: </s>
            <s xml:space="preserve">quod nos in libro de centro grauitatis ſolidorum propoſitio-
              <lb/>
            ne 29 demonstrauimus. </s>
            <s xml:space="preserve">Cum igitur portionis a p o l centrum gra-
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            uitatis ſit r, erit o r dupla r n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea n o ipſius o r ſeſqui-
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            altera. </s>
            <s xml:space="preserve">Eadem ratione b centrum grauitatis portionis i p o s est in
              <lb/>
            axe p f, ita ut p b dupla ſit b f.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0033-03" xlink:href="note-0033-03a" xml:space="preserve">C</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Etiuncta b r producatur ad g, quod ſit centrum graui_
              <lb/>
              <anchor type="note" xlink:label="note-0033-04a" xlink:href="note-0033-04"/>
            _tatis reliquæ figuræ i s l a]_ Si enim linea b r in g producta, ha
              <lb/>
            beat g r ad r b proportionem eam, quam conoidis portio i p o s ad
              <lb/>
            reliquam figuram, quæ ex humidi ſuperficie extat: </s>
            <s xml:space="preserve">erit punctum g
              <lb/>
            ipſius grauitatis centrum, ex octaua Archimedis.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="right" xlink:label="note-0033-04" xlink:href="note-0033-04a" xml:space="preserve">D</note>
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