Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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        <div type="section" level="1" n="29">
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              <pb file="0046" n="46" rhead="ARCHIMEDIS"/>
            pla eſt, aut minor, quàm dupla. </s>
            <s xml:space="preserve">Sit autem p t dupla t i. </s>
            <s xml:space="preserve">erit
              <lb/>
            centrum grauitatis eius, quod eſt in humido, punctum t.
              <lb/>
            </s>
            <s xml:space="preserve">Itaque iuncta t f producatur; </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">eius, quod extra humi
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            dum grauitatis centrum g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto b ad rectos angu-
              <lb/>
            los ipſi n o ducatur b r. </s>
            <s xml:space="preserve">Quòd cum p i quidem ſit æqui-
              <lb/>
            diſtans diametro n o: </s>
            <s xml:space="preserve">br autem ad diametrum perpendi
              <lb/>
            cularis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">f b æqualis ei, quæ uſque ad axem: </s>
            <s xml:space="preserve">perſpicuum
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            eſt f r productam æquales facere angulos cum ea, quæ ſe-
              <lb/>
            ctionem a p o l in puncto p contingit. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">cum a s: </s>
            <s xml:space="preserve">
              <lb/>
            & </s>
            <s xml:space="preserve">cum ſuperficie humidi. </s>
            <s xml:space="preserve">lineæ autem ductæ per tg æqui-
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            diſtantes ipſi f r, erunt & </s>
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              <lb/>
              <anchor type="figure" xlink:label="fig-0046-01a" xlink:href="fig-0046-01"/>
            ad humidi ſuperficiẽ per-
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            pendiculares: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidi
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            a p o l magnitudo, quæ ẽ
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            intra humidum ſurſum fe
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            retur ſecundum perpen-
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            dicularem per t ductam;
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            </s>
            <s xml:space="preserve">quæ uero extra humidum
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            ſecundum eam, quæ per g
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            deorſum feretur. </s>
            <s xml:space="preserve">reuolue
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              <anchor type="note" xlink:label="note-0046-01a" xlink:href="note-0046-01"/>
            tur ergo ſolidum a p o l:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">baſis ipſius nullo modo
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            humidi ſuperficiem con-
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            tinget. </s>
            <s xml:space="preserve">At ſi pi lineam k ω
              <lb/>
            non ſecet, ut in ſecunda
              <lb/>
            figura; </s>
            <s xml:space="preserve">manifeſtum eſt punctum t, quod eſt centrum gra-
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            uitatis demerſæ portionis, cadere inter p & </s>
            <s xml:space="preserve">i: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliqua
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            ſimiliter demonſtrabuntur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">A</note>
            <figure xlink:label="fig-0045-01" xlink:href="fig-0045-01a">
              <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0045-01"/>
            </figure>
            <note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">D</note>
            <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a">
              <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0046-01"/>
            </figure>
            <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">E</note>
          </div>
        </div>
        <div type="section" level="1" n="30">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:space="preserve">Demonſtrandum eſt non manere ipſam portionem, ſed
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              <anchor type="note" xlink:label="note-0046-02a" xlink:href="note-0046-02"/>
            reuolui ita, ut baſis nullo modo ſuperficiem humidi con-
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            tingat.</s>
            <s xml:space="preserve">] _Hæcnos addidimus tanquam ab interprete omiſſa_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">A</note>
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