Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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        <div type="section" level="1" n="68">
          <p>
            <s xml:space="preserve">
              <pb o="7" file="0125" n="125" rhead="DE CENTRO GRAVIT. SOLID."/>
            metrum habens e d. </s>
            <s xml:space="preserve">Quoniam igitur circuli uel ellipſis
              <lb/>
            a e c b grauitatis centrum eſt in diametro b e, & </s>
            <s xml:space="preserve">portio-
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            nis a e c centrum in linea e d: </s>
            <s xml:space="preserve">reliquæ portionis, uidelicet
              <lb/>
            a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
              <lb/>
            octaua propoſitione eiuſdem.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
        <div type="section" level="1" n="69">
          <head xml:space="preserve">THEOREMA V. PROPOSITIO V.</head>
          <p>
            <s xml:space="preserve">SI priſma ſecetur plano oppoſitis planis æqui
              <lb/>
            diſtante, ſectio erit figura æqualis & </s>
            <s xml:space="preserve">ſimilis ei,
              <lb/>
            quæ eſt oppoſitorum planorum, centrum graui
              <lb/>
            tatis in axe habens.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Sit priſma, in quo plana oppoſita ſint triangula a b c,
              <lb/>
            d e f; </s>
            <s xml:space="preserve">axis g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano iam dictis planis æquidiſtã
              <lb/>
            te; </s>
            <s xml:space="preserve">quod faciat ſectionem
              <emph style="sc">K</emph>
            l m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axi in pũcto n occurrat.
              <lb/>
            </s>
            <s xml:space="preserve">Dico _k_ l m triangulum æquale eſſe, & </s>
            <s xml:space="preserve">ſimile triangulis a b c
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            d e f; </s>
            <s xml:space="preserve">atque eius grauitatis centrum eſſe punctum n. </s>
            <s xml:space="preserve">Quo-
              <lb/>
            niam enim plana a b c
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              <anchor type="figure" xlink:label="fig-0125-01a" xlink:href="fig-0125-01"/>
            K l m æquidiſtantia ſecã
              <lb/>
              <anchor type="note" xlink:label="note-0125-01a" xlink:href="note-0125-01"/>
            tur a plano a e; </s>
            <s xml:space="preserve">rectæ li-
              <lb/>
            neæ a b, K l, quæ ſunt ip
              <lb/>
            ſorum cõmunes ſectio-
              <lb/>
            nes inter ſe ſe æquidi-
              <lb/>
            ſtant. </s>
            <s xml:space="preserve">Sed æquidiſtant
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            a d, b e; </s>
            <s xml:space="preserve">cum a e ſit para
              <lb/>
            lelogrammum, ex priſ-
              <lb/>
            matis diffinitione. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">al parallelogrammũ
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            erit; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea linea
              <lb/>
              <anchor type="note" xlink:label="note-0125-02a" xlink:href="note-0125-02"/>
            _k_l, ipſi a b æqualis. </s>
            <s xml:space="preserve">Si-
              <lb/>
            militer demonſtrabitur
              <lb/>
            l m æquidiſtans, & </s>
            <s xml:space="preserve">æqua
              <lb/>
            lis b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">m
              <emph style="sc">K</emph>
            ipſi c a.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a">
              <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0125-01"/>
            </figure>
            <note position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">16. unde-
              <lb/>
            cimi.</note>
            <note position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">34. prim@</note>
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