Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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              <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
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            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
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            ſe ſe æquales.
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            <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
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            ĩ portionibus
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            æqualibus, & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">ſi
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            milibus a u q l,
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            a n z g ductæ
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            sũt a q, a z, por
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            tiones æqua-
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            les auferentes;
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            </s>
            <s xml:id="echoid-s2624" xml:space="preserve">cum diametris
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            portionum æ-
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            quales angu-
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            los cõtinebũt. </s>
            <s xml:id="echoid-s2625" xml:space="preserve">
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            ergo triangulo
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            rum n l s, u ω c
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            anguli, qui cõ-
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            ſiſtũt ad l ω pũ-
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            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,
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            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,
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            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
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            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
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            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">ergo ne-
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            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
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            minorem proportionem, quàm quadratum f p ad quadra-
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            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
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            in grauitate, eandem quadratum, quod fit à linea ψ habeat
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            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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