Archimedes, Archimedis De insidentibvs aqvae

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          <pb file="0024" n="24" rhead="DE INSIDENTIBVS AQV AE"/>
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        <div xml:id="echoid-div29" type="section" level="1" n="22">
          <head xml:id="echoid-head32" xml:space="preserve">QVARTVS.</head>
          <p>
            <s xml:id="echoid-s290" xml:space="preserve">Recta portio rectanguli conoydalis quando fuerit leuior
              <lb/>
            humido, & </s>
            <s xml:id="echoid-s291" xml:space="preserve">axẽ habuerit maiorem, quàm emiolium eius, quę
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            uſque ad axem: </s>
            <s xml:id="echoid-s292" xml:space="preserve">ſi in grauitate ad humidum æque molis non
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            minorem proportionem habeat illa. </s>
            <s xml:id="echoid-s293" xml:space="preserve">quàm habet tetragonũ
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            quod ab exceſſu, quo maior eſt axis, quàm emiolius eius, quę
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            uſque ad axem dimiſſa in humido ita ut baſis ipſius non tan-
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            gat humidum poſita, inclinata, non manet inclinata, ſed re-
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            ſtituetur in rectum.</s>
            <s xml:id="echoid-s294" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s295" xml:space="preserve">_E_Sto portio rectangula conoydalis, qualis dicta est: </s>
            <s xml:id="echoid-s296" xml:space="preserve">& </s>
            <s xml:id="echoid-s297" xml:space="preserve">dimiſſa in
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            bumidum, ſi eſt poſſibile, ſit nõ recta, ſed ſit inclinata. </s>
            <s xml:id="echoid-s298" xml:space="preserve">Secta autem
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            ipſa per axem plano recto ad ſnperficiem humidi, portionis quidẽ
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            ſe
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            ctio ſit rectanguli coni: </s>
            <s xml:id="echoid-s299" xml:space="preserve">ſectio quæ apol. </s>
            <s xml:id="echoid-s300" xml:space="preserve">axis autem portionis, & </s>
            <s xml:id="echoid-s301" xml:space="preserve">dyæ
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            meter, quæn, o, ſuperficiei autem humidi ſectio ſit i, s. </s>
            <s xml:id="echoid-s302" xml:space="preserve">Siigitur portio non
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            eſt recta, non faciet quæ n, o, ad is angulos æquales: </s>
            <s xml:id="echoid-s303" xml:space="preserve">ducatur autẽ quæ
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            K, ***, contingens ſectionem rectanguli coni penes, p, æquidiſtans autem
              <lb/>
            ipſi i s. </s>
            <s xml:id="echoid-s304" xml:space="preserve">A, p, autem æquedistanter ipſi o, n, ducaturq́ue p, f, & </s>
            <s xml:id="echoid-s305" xml:space="preserve">accipian
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            tur contra grauitum, & </s>
            <s xml:id="echoid-s306" xml:space="preserve">erit ſolidi quidem apol. </s>
            <s xml:id="echoid-s307" xml:space="preserve">centrumr, eius autem
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            quod inter humidum centrum b, & </s>
            <s xml:id="echoid-s308" xml:space="preserve">copuletur g, t, r, & </s>
            <s xml:id="echoid-s309" xml:space="preserve">educatur ad g,
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            & </s>
            <s xml:id="echoid-s310" xml:space="preserve">ſit ſolidi, quod ſupra humidi centrum grauitatis g, & </s>
            <s xml:id="echoid-s311" xml:space="preserve">quoniam quæ
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            n, o, ipſius quidem r, o, eſt emiolia eius autem, quæ uſque ad axem eſt ma
              <lb/>
            ior, quàm emiolia, palam quòd quær, o, eſt maior, quàm quæ uſque ad a-
              <lb/>
            xem. </s>
            <s xml:id="echoid-s312" xml:space="preserve">Sit igitur quæ r, m, æqualis ei, quæ uſque ad axem, quæ autem o,
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            n, dupla ipſius r, m. </s>
            <s xml:id="echoid-s313" xml:space="preserve">Quoniam igitur ſit quæ quidem n, o, ipſius r, o, emio-
              <lb/>
            lia, quæ autem m, o, ipſius o, b, & </s>
            <s xml:id="echoid-s314" xml:space="preserve">reliqua, quæm, n, reliqua ſcilicet r, b,
              <lb/>
            æmiolia eſt ipſi m, o, eſt maior, quàm emiolius eſt axis eius, quæ uſque ad
              <lb/>
            axem, ſcilicet r, m, & </s>
            <s xml:id="echoid-s315" xml:space="preserve">quoniam ſupponebatur portio ad humidum in gra
              <lb/>
            uitate non minuerem proportionem habens illa, quam habet tetragonũ
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            quod ab exceſſu, quo. </s>
            <s xml:id="echoid-s316" xml:space="preserve">axis eſt maior, quàm æmiolius eius, quæ uſq; </s>
            <s xml:id="echoid-s317" xml:space="preserve">ad a-
              <lb/>
            xem ad tetragonum quod ab axe. </s>
            <s xml:id="echoid-s318" xml:space="preserve">palam quòd non minorem proportio
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            nem babet portio ad humidum in grauitate illa proportionem quam ha
              <lb/>
            bet tetragonum, quod ab m, o, ad id, quod ab n, o. </s>
            <s xml:id="echoid-s319" xml:space="preserve">Q uam autem propor-
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            tìonem habet portio ad humidum in grauitate, hanc habet demerſa ip-
              <lb/>
            ſius portio adtotam ſolidam portionem, demonſtratum eſt enim hoc, ſed
              <lb/>
            quam habet proportionem demerſa, proportio adtotam hanc habet te-
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            iragonum quod _Demonstratum_ eſt enim in ijs
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            quæ de conoydalibus quòd ſi a rectangulo conoydaliduæ portiones </s>
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