Archimedes, Archimedis De insidentibvs aqvae

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          <pb o="3" file="0009" n="9" rhead="LIBER I."/>
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        <div xml:id="echoid-div8" type="section" level="1" n="8">
          <head xml:id="echoid-head14" xml:space="preserve">Theorema ij. Propoſitio ij.</head>
          <p>
            <s xml:id="echoid-s41" xml:space="preserve">Omnis humidi conſiſtentis ita ut maneat in motum ſuperfi
              <lb/>
            cies habebit figuram ſphęrę habentis cẽtruni idem cum terra.</s>
            <s xml:id="echoid-s42" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s43" xml:space="preserve">INtelligatur enim bumidum conſiſtensita, ut maneat non motum, & </s>
            <s xml:id="echoid-s44" xml:space="preserve">
              <lb/>
            ſecetur ipſius. </s>
            <s xml:id="echoid-s45" xml:space="preserve">Superſicies plano per centrum terræ. </s>
            <s xml:id="echoid-s46" xml:space="preserve">Sit autemterra
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            centrum K, ſuperficiei autem ſecta linea a, b, g, d. </s>
            <s xml:id="echoid-s47" xml:space="preserve">Dico itaque line a a, b,
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            g, d, circuli eſſe periferiam centrum autem ipſius K. </s>
            <s xml:id="echoid-s48" xml:space="preserve">Sienim non est recte
              <lb/>
            a, K, ad lineam a, b, g, d, occurrentes non erunt æquales. </s>
            <s xml:id="echoid-s49" xml:space="preserve">Sumatur itaque
              <lb/>
            aliqua recta quę eſt quarundam quidem a, k, occurrentium ad lineam a, b,
              <lb/>
            g, d, maior quarundam autem minor, & </s>
            <s xml:id="echoid-s50" xml:space="preserve">centro quidem K, distantia autem
              <lb/>
            ſumptæ lineæ circulus deſcribatur. </s>
            <s xml:id="echoid-s51" xml:space="preserve">Cadetigitur periferia circuli habẽs hoc
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            quidem extra lineam a, b, g, d, hoc autem intra, quoniam quæ ex centro
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            quorundam qu dem a, K, occurrentium ad lineam a b, g, d, eſt maior quo-
              <lb/>
            rundam autem minor. </s>
            <s xml:id="echoid-s52" xml:space="preserve">Sint igitur deſcripti circuli periferia quæ r, b, b, & </s>
            <s xml:id="echoid-s53" xml:space="preserve">
              <lb/>
            a, b, ad K, recta ducantur, & </s>
            <s xml:id="echoid-s54" xml:space="preserve">copulentur quæ b, K, b, e, l, æquales facientes
              <lb/>
            angulos. </s>
            <s xml:id="echoid-s55" xml:space="preserve">Deſcribatur autem, & </s>
            <s xml:id="echoid-s56" xml:space="preserve">centro K, periferia quidem quæ x, o, p, in
              <lb/>
            plano & </s>
            <s xml:id="echoid-s57" xml:space="preserve">in bumido partes itaque bumidi, quæ ſecundum x, o, p, periferiã
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            ex æquo ſunt poſitæ cõtinue inuicem premuntur quæ quidem ſecundũ x, o,
              <lb/>
              <figure xlink:label="fig-0009-01" xlink:href="fig-0009-01a" number="5">
                <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0009-01"/>
              </figure>
            periferia p, o, b, e, humido quæ ſecundum 2, b, locum quæ autemſecundum
              <lb/>
            periferiam o, p, humido quod ſecundum b, e, locum æqualiter igitur premũ
              <lb/>
            tur partes bumidi, quod ſecundum periferiam x, o, ei quæſecundum o, p.
              <lb/>
            </s>
            <s xml:id="echoid-s58" xml:space="preserve">Quare non expelletur minus preſſa a magis preſſis. </s>
            <s xml:id="echoid-s59" xml:space="preserve">Non ettam ergo con-
              <lb/>
            ſtare fecimus aliquod humidum. </s>
            <s xml:id="echoid-s60" xml:space="preserve">Supponebatur autem constans ita ut ma-
              <lb/>
            neret non motum neceſſarium, ergo linea a, b, g, d, eſt circuli periferiam, et
              <lb/>
            centrum ipſius K. </s>
            <s xml:id="echoid-s61" xml:space="preserve">Similiter autem demonſtrabitur, & </s>
            <s xml:id="echoid-s62" xml:space="preserve">ſuperficies humidi
              <lb/>
            plano ſecta fuerit per centrum terræ, quòd ſectio erit circuliperiferia, &</s>
            <s xml:id="echoid-s63" xml:space="preserve"/>
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