Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <p>
            <s xml:id="echoid-s2617" xml:space="preserve">
              <pb o="44" file="0099" n="99" rhead="DE IIS QVAE VEH. IN AQVA."/>
            gura: </s>
            <s xml:id="echoid-s2618" xml:space="preserve">& </s>
            <s xml:id="echoid-s2619" xml:space="preserve">alia eadem diſponantur demonſtrabimus rurſum
              <lb/>
            n t æqualem eſſe ipſi u i: </s>
            <s xml:id="echoid-s2620" xml:space="preserve">& </s>
            <s xml:id="echoid-s2621" xml:space="preserve">portiones a u q, a n z inter
              <lb/>
            ſe ſe æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s2622" xml:space="preserve">
              <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a" number="65">
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            Itaque quoniã
              <lb/>
            ĩ portionibus
              <lb/>
            æqualibus, & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">ſi
              <lb/>
            milibus a u q l,
              <lb/>
            a n z g ductæ
              <lb/>
            sũt a q, a z, por
              <lb/>
            tiones æqua-
              <lb/>
            les auferentes;
              <lb/>
            </s>
            <s xml:id="echoid-s2624" xml:space="preserve">cum diametris
              <lb/>
            portionum æ-
              <lb/>
            quales angu-
              <lb/>
            los cõtinebũt. </s>
            <s xml:id="echoid-s2625" xml:space="preserve">
              <lb/>
            ergo triangulo
              <lb/>
            rum n l s, u ω c
              <lb/>
            anguli, qui cõ-
              <lb/>
            ſiſtũt ad l ω pũ-
              <lb/>
            cta, æquales ſunt: </s>
            <s xml:id="echoid-s2626" xml:space="preserve">& </s>
            <s xml:id="echoid-s2627" xml:space="preserve">b s recta linea æqualis ipſi b c: </s>
            <s xml:id="echoid-s2628" xml:space="preserve">ſ r ipſi cr,
              <lb/>
            n χ ipſi u h: </s>
            <s xml:id="echoid-s2629" xml:space="preserve">& </s>
            <s xml:id="echoid-s2630" xml:space="preserve">χ tipſi h i. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">quòd cum u y dupla ſit ipſius y i,
              <lb/>
            erit n χ maior, quàm dupla χ t. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">Sit igitur n m ipſius m t du
              <lb/>
            pla. </s>
            <s xml:id="echoid-s2633" xml:space="preserve">Rurſus ex his manifeſtum eſt, non manere ipſam por-
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            tionem; </s>
            <s xml:id="echoid-s2634" xml:space="preserve">ſed inclinari ex parte a: </s>
            <s xml:id="echoid-s2635" xml:space="preserve">ponebatur autem portio
              <lb/>
            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">ergo ne-
              <lb/>
            ceſſe eſt, ut eius baſis in humidum magis demergatur.</s>
            <s xml:id="echoid-s2637" xml:space="preserve"/>
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        <div xml:id="echoid-div184" type="section" level="1" n="57">
          <head xml:id="echoid-head62" xml:space="preserve">DEMONSTRATIO QVINT AE PARTIS.</head>
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            <s xml:id="echoid-s2638" xml:space="preserve">HABEAT denique portio ad humidum in grauitate
              <lb/>
            minorem proportionem, quàm quadratum f p ad quadra-
              <lb/>
            tum b d: </s>
            <s xml:id="echoid-s2639" xml:space="preserve">& </s>
            <s xml:id="echoid-s2640" xml:space="preserve">quam proportionem habet portio ad humidũ
              <lb/>
            in grauitate, eandem quadratum, quod fit à linea ψ habeat
              <lb/>
            ad quadratum b d. </s>
            <s xml:id="echoid-s2641" xml:space="preserve">erit χ minor ipſa p f. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Rurſus </s>
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