Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb file="0014" n="14" rhead="ARCHIMEDIS"/>
          <p>
            <s xml:id="echoid-s105" xml:space="preserve">SECETVR ſuperficies aliqua plano per k punctum
              <lb/>
            ducto: </s>
            <s xml:id="echoid-s106" xml:space="preserve">& </s>
            <s xml:id="echoid-s107" xml:space="preserve">ſicſectio ſemper circuli circunferentia, centrum
              <lb/>
            habens punctum k. </s>
            <s xml:id="echoid-s108" xml:space="preserve">Dico eam ſphæræ ſuperficiem eſſe. </s>
            <s xml:id="echoid-s109" xml:space="preserve">Si
              <lb/>
            enim non eſt ſphæræ ſuperfi-
              <lb/>
              <figure xlink:label="fig-0014-01" xlink:href="fig-0014-01a" number="4">
                <image file="0014-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0014-01"/>
              </figure>
            cies; </s>
            <s xml:id="echoid-s110" xml:space="preserve">rectæ lineæ, quæ à pun-
              <lb/>
            cto k ad circunferentiam du-
              <lb/>
            cuntur non omnes æquales e-
              <lb/>
            runt. </s>
            <s xml:id="echoid-s111" xml:space="preserve">Itaque ſint a b puncta
              <lb/>
            in ſuperficie; </s>
            <s xml:id="echoid-s112" xml:space="preserve">& </s>
            <s xml:id="echoid-s113" xml:space="preserve">inæquales li-
              <lb/>
            neæ a k k b: </s>
            <s xml:id="echoid-s114" xml:space="preserve">per ipſas autem
              <lb/>
            a k k b planum ducatur, quod
              <lb/>
            ſectionem faciat in ſuperficie
              <lb/>
            lineam d a b c. </s>
            <s xml:id="echoid-s115" xml:space="preserve">ergo d a b c cir
              <lb/>
            culi circunferentia eſt, cuius
              <lb/>
            centrum k; </s>
            <s xml:id="echoid-s116" xml:space="preserve">quoniam ſuperficies eiuſmodi ponebatur: </s>
            <s xml:id="echoid-s117" xml:space="preserve">& </s>
            <s xml:id="echoid-s118" xml:space="preserve">
              <lb/>
            idcirco æquales inter ſe ſunt a k k b, ſed & </s>
            <s xml:id="echoid-s119" xml:space="preserve">inæquales; </s>
            <s xml:id="echoid-s120" xml:space="preserve">quod
              <lb/>
            fieri non poteſt. </s>
            <s xml:id="echoid-s121" xml:space="preserve">conſtat igitur ſuperficiem eam eſſe ſphæ-
              <lb/>
            ræ ſuperficiem.</s>
            <s xml:id="echoid-s122" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div10" type="section" level="1" n="9">
          <head xml:id="echoid-head12" xml:space="preserve">PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s123" xml:space="preserve">
              <emph style="sc">Omnis</emph>
            humidi conſiſtentis, atque manen-
              <lb/>
            tis ſuperficies ſphærica eſt; </s>
            <s xml:id="echoid-s124" xml:space="preserve">cuius ſphæræ centrũ
              <lb/>
            eſtidem, quod centrum terræ.</s>
            <s xml:id="echoid-s125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s126" xml:space="preserve">INTELLIGATVR humidũ conſiſtens, manẽsq;</s>
            <s xml:id="echoid-s127" xml:space="preserve">:
              <lb/>
            & </s>
            <s xml:id="echoid-s128" xml:space="preserve">ſecetur ipſius ſuperficies plano per centrum terræ du-
              <lb/>
            cto. </s>
            <s xml:id="echoid-s129" xml:space="preserve">ſit autem terræ centrum k: </s>
            <s xml:id="echoid-s130" xml:space="preserve">& </s>
            <s xml:id="echoid-s131" xml:space="preserve">ſuperficieiſectio, linea
              <lb/>
            a b c d. </s>
            <s xml:id="echoid-s132" xml:space="preserve">Dico lineam a b c d circuli circunferentiam eſſe, cu
              <lb/>
            ius centrum k. </s>
            <s xml:id="echoid-s133" xml:space="preserve">Si enim non eſt, rectæ lineæ à puncto k ad
              <lb/>
            lineam a b c d ductæ non erunt æquales. </s>
            <s xml:id="echoid-s134" xml:space="preserve">Sumatur recta li
              <lb/>
            nea quibuſdam quidem à puncto k ad ipſam a b c d ductis
              <lb/>
            maior; </s>
            <s xml:id="echoid-s135" xml:space="preserve">quibuſdam uero minor; </s>
            <s xml:id="echoid-s136" xml:space="preserve">& </s>
            <s xml:id="echoid-s137" xml:space="preserve">ex centro k, </s>
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