Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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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:id="echoid-s3913" xml:space="preserve">Si uero axis k l non ſit perpendicularis
              <lb/>
            ad planum baſis; </s>
            <s xml:id="echoid-s3914" 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:id="echoid-s3915" xml:space="preserve">ſimiliter de-
              <lb/>
            mõſtrabimus ſolidum g m ad ſoli
              <gap/>
            m c ita eſſe, ut axis k q
              <lb/>
            ad axem q l. </s>
            <s xml:id="echoid-s3916" xml:space="preserve">Sed ut K q ad q l, ita k s altitudo ad altitudi-
              <lb/>
            nem s r, nam lineæ K l, K r à planis æquidiſtantibus in eaſ-
              <lb/>
              <note position="right" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">17. unde-
                <lb/>
              cimi</note>
            dem proportiones ſecantur. </s>
            <s xml:id="echoid-s3917" xml:space="preserve">ergo ſolidum g m ad ſolidum
              <lb/>
            m c eandẽ proportionem habet, quam altitudo ad altitu
              <lb/>
            dinẽ, uel quam axis ad axem. </s>
            <s xml:id="echoid-s3918" xml:space="preserve">quod demõſtrare oportebat.</s>
            <s xml:id="echoid-s3919" xml:space="preserve"/>
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        <div xml:id="echoid-div242" type="section" level="1" n="84">
          <head xml:id="echoid-head91" xml:space="preserve">THEOREMA XV. PROPOSITIO XIX.</head>
          <p>
            <s xml:id="echoid-s3920" xml:space="preserve">Solida parallelepipedain eadem baſi, uel in
              <lb/>
            æqualibus baſibus conſtituta eam inter ſe propor
              <lb/>
            tionem habent, quam altitudines: </s>
            <s xml:id="echoid-s3921" xml:space="preserve">& </s>
            <s xml:id="echoid-s3922" xml:space="preserve">ſi axes ipſo-
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            rum cum baſibus æquales angulos contineant,
              <lb/>
            eam quoque, quam axes proportionem habebũt.</s>
            <s xml:id="echoid-s3923" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3924" xml:space="preserve">Sint ſolida parallelepipeda in eadẽ baſi cõſtituta a b c d,
              <lb/>
            a b e f: </s>
            <s xml:id="echoid-s3925" xml:space="preserve">& </s>
            <s xml:id="echoid-s3926" xml:space="preserve">ſit ſolidi a b c d altitudo minor: </s>
            <s xml:id="echoid-s3927" xml:space="preserve">producatur au-
              <lb/>
            tem planum c d adeo, utſolidum a b e f ſecet; </s>
            <s xml:id="echoid-s3928" xml:space="preserve">cuius ſectio
              <lb/>
            ſit g h. </s>
            <s xml:id="echoid-s3929" xml:space="preserve">erũſoli
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              <figure xlink:label="fig-0157-01" xlink:href="fig-0157-01a" number="111">
                <image file="0157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0157-01"/>
              </figure>
              <note position="right" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">29. unde-
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              cimi</note>
            da a b c d, a b g h
              <lb/>
            in eadem baſi,
              <lb/>
            & </s>
            <s xml:id="echoid-s3930" xml:space="preserve">æquali altitu
              <lb/>
            dine inter ſe æ-
              <lb/>
            qualia. </s>
            <s xml:id="echoid-s3931" xml:space="preserve">Quoniã
              <lb/>
            igitur ſolidum
              <lb/>
            a b e f ſecatur
              <lb/>
            plano baſibus
              <lb/>
            æquidiſtãte, erit
              <lb/>
            ſolidum g h e f
              <lb/>
              <note position="right" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">18. huius</note>
            adipſum a b g </s>
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