Archimedes, Archimedis De insidentibvs aqvae

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              <pb o="10" file="0035" n="35" rhead="LIBER II."/>
              <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a" number="28">
                <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0035-01"/>
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            Ergo & </s>
            <s xml:id="echoid-s563" xml:space="preserve">quæ K, r, ad s, y, habet proportionem maiorem, quàm medietas
              <lb/>
            ipſius K, r, ad x, b, minor ergo, quæ s, y, quàm dupla ipſius x, b, & </s>
            <s xml:id="echoid-s564" xml:space="preserve">quæ s,
              <lb/>
            o, quàm x, b, minor quæ s, ***, ergo maior, quàm r, x, & </s>
            <s xml:id="echoid-s565" xml:space="preserve">quæ p, b, quam f,
              <lb/>
            & </s>
            <s xml:id="echoid-s566" xml:space="preserve">ſi portio in grauitate ad humidum habet proportionem, quam exceſ
              <lb/>
            ſus, quo tetragonum, quod a, b, d, eſt maius tetragono, quod a, b, f, q, ad te
              <lb/>
            tragonum, quod a, b, d. </s>
            <s xml:id="echoid-s567" xml:space="preserve">Quam autem proportionem habet proportio in
              <lb/>
            grauitate ad humidum, hanc proportionem habet demerſa ipſius portio
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            ad totam palam, eandem habebit proportionem demerſa ipſius portio ad
              <lb/>
            totam portionem, quam exceſſus, quo tetragonum, quod a, b, d, excedit
              <lb/>
            tetragonum, quod a, b, f, q, ad tetragonum, quod a, b, d, habebit igitur, & </s>
            <s xml:id="echoid-s568" xml:space="preserve">
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            tota portio a d, eam quæ extra humidum proportionem, quam tetrago-
              <lb/>
            num, quod a, b, d, ad id, quod a, b, f, q. </s>
            <s xml:id="echoid-s569" xml:space="preserve">Quam autem proportionem habet
              <lb/>
            tota proportio ad eam, quàm extra bumidum hanc habet, quod ab n, o,
              <lb/>
            ad id, quod a, p, m, æqualis ergo quæ m, p, ipſi f, q. </s>
            <s xml:id="echoid-s570" xml:space="preserve">Quæ autem p, b, demõ
              <lb/>
            ſtrata eſt maior, quàm quæ ergom, b, eſt minor, quàm q, ergo quæ o, m,
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            eſt maior, quàm dupla ipſius b, m. </s>
            <s xml:id="echoid-s571" xml:space="preserve">Sit igitur quæ p, z, dupla ipſius z, m,
              <lb/>
            & </s>
            <s xml:id="echoid-s572" xml:space="preserve">copulata, quę 2, t, educatur ad g, erit ergo totius quidem portionis cé
              <lb/>
            trum grauitatis t, eius autem quæ extra humidum z, eius uero quæ in-
              <lb/>
            tra in linea t, g. </s>
            <s xml:id="echoid-s573" xml:space="preserve">Sit autem g, demonſtrabitur autem ſimiliter prioribus,
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            quæ t, h, perpendicularis ad ſuperficiem humidi, & </s>
            <s xml:id="echoid-s574" xml:space="preserve">quæ per z, g, æquedi-
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            ſtanter ipſit, n, productæ perpendiculares, & </s>
            <s xml:id="echoid-s575" xml:space="preserve">ipſæ ſuper ſuperficiem bu-
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            midi ferretur, ergo quæ quidem extra humidum portio deor ſum ſecundũ
              <lb/>
            eam quæ per z. </s>
            <s xml:id="echoid-s576" xml:space="preserve">Quæ autem intra ſecundum eam, quæ per g, eleuabitur
              <lb/>
            non manet ergo tota portio ſine inclinatione, nec etiam conuertetur ita
              <lb/>
            ut axis ſit perpendicularis ſuperficiem humidi, quoniam quæ ex parte
              <lb/>
            l, ad ſuperiora ferrentur, propter proportionalia dictis in præcedenti, </s>
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Impressum