Archimedes, Archimedis De insidentibvs aqvae

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            <s xml:id="echoid-s335" xml:space="preserve">
              <pb file="0026" n="26" rhead="DE INSIDENTIBVS AQV AE"/>
            ut baſis ipſius tota ſit in humido poſita, inclinata, non manet
              <lb/>
            inclinata, ſed reſtituetur ita ut axis ipſius ſecundum perpen
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            dicularem ſit.</s>
            <s xml:id="echoid-s336" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s337" xml:space="preserve">_D_Emittatur enim in humidum aliqua portio qualis dicta eſt, & </s>
            <s xml:id="echoid-s338" xml:space="preserve">ſit
              <lb/>
            baſis ipſius tota in bumido. </s>
            <s xml:id="echoid-s339" xml:space="preserve">Secta autem ipſa plano per axem re-
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            cto ad ſuperficiem humidi erit ſectio rectanguli, coni ſectio, & </s>
            <s xml:id="echoid-s340" xml:space="preserve">ſit
              <lb/>
            quæ apol, axis autem, & </s>
            <s xml:id="echoid-s341" xml:space="preserve">dyameter ſectionis quàm n, o, ſuperficiei autem
              <lb/>
            bumidi ſectio, quæ i, s, & </s>
            <s xml:id="echoid-s342" xml:space="preserve">quoniam non eſt axis ſecundum perpendicula-
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            rem non faciet, quæ n, o, ad i, s, angulos æquales: </s>
            <s xml:id="echoid-s343" xml:space="preserve">ducatur autem quæ K,
              <lb/>
            ***, contingens ſectionem apol ſecundum p, æquidiſtans ipſi i, s, & </s>
            <s xml:id="echoid-s344" xml:space="preserve">per
              <lb/>
            p, ipſi n, o, æquediſtans quæ p, f, & </s>
            <s xml:id="echoid-s345" xml:space="preserve">accipiantur centra grauitatem: </s>
            <s xml:id="echoid-s346" xml:space="preserve">& </s>
            <s xml:id="echoid-s347" xml:space="preserve">
              <lb/>
            ſit ipſius quidem apol. </s>
            <s xml:id="echoid-s348" xml:space="preserve">centrum r. </s>
            <s xml:id="echoid-s349" xml:space="preserve">eius autem quod extra humidum b,
              <lb/>
            & </s>
            <s xml:id="echoid-s350" xml:space="preserve">copulata quæ b, r, educatur ad g, & </s>
            <s xml:id="echoid-s351" xml:space="preserve">ſit g, centrum grauitatis ſolidi
              <lb/>
            aſſumpti in humido : </s>
            <s xml:id="echoid-s352" xml:space="preserve">& </s>
            <s xml:id="echoid-s353" xml:space="preserve">accipiatur quæ r, m, æqualis ei quæ uſque ad
              <lb/>
            axe Quæ autem o, h, dupla ipſius h, m, & </s>
            <s xml:id="echoid-s354" xml:space="preserve">alia fiant conſimili-
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            ter ſuperiori. </s>
            <s xml:id="echoid-s355" xml:space="preserve">Quoniam igitur ſupponitur portio ad humidum in graui-
              <lb/>
            tate non maiorem proportionem habens proportione, quam habet exceſ
              <lb/>
            ſus, quo maius eſt tetragonũ, quod ab n, o, tetragono, quod ab m, o, tetra
              <lb/>
            gonum, quod ab n, o, ſed quam proportionem habet in grauitate porti***
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              <figure xlink:label="fig-0026-01" xlink:href="fig-0026-01a" number="22">
                <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/>
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            ad humidum æqualis molis, hanc proportionẽ habet demerſa ipſius por
              <lb/>
            tio ad totum ſolidum : </s>
            <s xml:id="echoid-s356" xml:space="preserve">demonstratum est enim hoc in primo theorema-
              <lb/>
            te. </s>
            <s xml:id="echoid-s357" xml:space="preserve">Non maiorem ergo proportionem habet demerſa magnitudo por-
              <lb/>
            tionis ad totam portionem, quàm ſit dicta portio. </s>
            <s xml:id="echoid-s358" xml:space="preserve">Quare non maiorem
              <lb/>
            proportionem habet tota portio ad eam, quæ e xtra humidum proportio
              <lb/>
            nem, quam habet tetragonũ, quod ab n, o, ad tetragonum, quod ab m, t,
              <lb/>
            habet autem tota portio ad portionem, quàm extra bumidum </s>
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