Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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          <p>
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              <pb o="23" file="0157" n="157" rhead="DE CENTRO GRAVIT. SOLID."/>
            eſtſolidi g m altitudo ad o e altitudinem ſolidi m c, uel quã
              <lb/>
            axis k q ad q l axem. </s>
            <s xml:space="preserve">Si uero axis k l non ſit perpendicularis
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            ad planum baſis; </s>
            <s xml:space="preserve">ducatur a puncto k ad idem planum per
              <lb/>
            pendicularis k r, occurrẽs plano m n o p in s. </s>
            <s xml:space="preserve">ſimiliter de-
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            mõſtrabimus ſolidum g m ad ſoli
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            m c ita eſſe, ut axis k q
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            ad axem q l. </s>
            <s xml:space="preserve">Sed ut K q ad q l, ita k s altitudo ad altitudi-
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            nem s r, nam lineæ K l, K r à planis æquidiſtantibus in eaſ-
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              <anchor type="note" xlink:label="note-0157-01a" xlink:href="note-0157-01"/>
            dem proportiones ſecantur. </s>
            <s xml:space="preserve">ergo ſolidum g m ad ſolidum
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            m c eandẽ proportionem habet, quam altitudo ad altitu
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            dinẽ, uel quam axis ad axem. </s>
            <s xml:space="preserve">quod demõſtrare oportebat.</s>
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          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a">
              <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0156-01"/>
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            <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">2. undeci
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            mi.</note>
            <note position="left" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">i. ſexti.</note>
            <note position="right" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">17. unde-
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            cimi</note>
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        </div>
        <div type="section" level="1" n="84">
          <head xml:space="preserve">THEOREMA XV. PROPOSITIO XIX.</head>
          <p>
            <s xml:space="preserve">Solida parallelepipedain eadem baſi, uel in
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            æqualibus baſibus conſtituta eam inter ſe propor
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            tionem habent, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi axes ipſo-
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            rum cum baſibus æquales angulos contineant,
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            eam quoque, quam axes proportionem habebũt.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Sint ſolida parallelepipeda in eadẽ baſi cõſtituta a b c d,
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            a b e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit ſolidi a b c d altitudo minor: </s>
            <s xml:space="preserve">producatur au-
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            tem planum c d adeo, utſolidum a b e f ſecet; </s>
            <s xml:space="preserve">cuius ſectio
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            ſit g h. </s>
            <s xml:space="preserve">erũſoli
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              <anchor type="figure" xlink:label="fig-0157-01a" xlink:href="fig-0157-01"/>
              <anchor type="note" xlink:label="note-0157-02a" xlink:href="note-0157-02"/>
            da a b c d, a b g h
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            in eadem baſi,
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            & </s>
            <s xml:space="preserve">æquali altitu
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            dine inter ſe æ-
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            qualia. </s>
            <s xml:space="preserve">Quoniã
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            igitur ſolidum
              <lb/>
            a b e f ſecatur
              <lb/>
            plano baſibus
              <lb/>
            æquidiſtãte, erit
              <lb/>
            ſolidum g h e f
              <lb/>
              <anchor type="note" xlink:label="note-0157-03a" xlink:href="note-0157-03"/>
            adipſum a b g h</s>
          </p>
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