Archimedes, Archimedis De insidentibvs aqvae

Table of figures

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[Figure 11]
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[Figure 13]
[14] Explicit de Inſidentibus Aquæ Liber Primus.
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              <pb o="15" file="0045" n="45" rhead="LIBER II."/>
              <figure xlink:label="fig-0045-01" xlink:href="fig-0045-01a" number="35">
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            a, i, ipſi i, q, æqualis & </s>
            <s xml:id="echoid-s796" xml:space="preserve">quæ a, q, ipſi p, ***, æquediſtans. </s>
            <s xml:id="echoid-s797" xml:space="preserve">Demonſtran-
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            dum eſt autem quod portio demiſſa in humidum poſita inclinata ita,
              <lb/>
            ut baſis ipſis non tang at humidnm inclinata conſiſtet ita ut axis ip-
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            ſius ad ſuperficiem humidi faciat angulum minorem angulo f, baſis
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            autem ipſius nec ſecundum unum tangat ſuperficiem humidi. </s>
            <s xml:id="echoid-s798" xml:space="preserve">Demit
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            tatur h, in humidum, & </s>
            <s xml:id="echoid-s799" xml:space="preserve">conſiſtat ita, ut baſis ipſius ſecundum unum
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            ſignum tangat ſuperſiciem humidi. </s>
            <s xml:id="echoid-s800" xml:space="preserve">Secta autem portione per axem
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            plano recto ad ſuperficiem humidi, ſectio ſit ſuperficiei quidem por-
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            tionis, quæ a, h, b, l, rectanguli coni ſectio, ſuperficiei autem humidi,
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            quæ a, Z, axis autem portioni, & </s>
            <s xml:id="echoid-s801" xml:space="preserve">dyameter ſectionis, quæ b, d, & </s>
            <s xml:id="echoid-s802" xml:space="preserve">ſece-
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            tur quæ b, d, penes ſigna, K, r, conſimiliter ſuperioribus, ducatur au-
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            tem & </s>
            <s xml:id="echoid-s803" xml:space="preserve">quæ h, i, æquedistanter ipſi a, Z, contingens ſectionem conipe-
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            nes h. </s>
            <s xml:id="echoid-s804" xml:space="preserve">Quæ autem habet æquediſtanter ipſi b, d, quàm autem h, s,
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            perpendicularis ſuper b, d, quoniam igitur portio ad humidum in gra-
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            uitate hanc habet proportionem, quam tetragonum a, x, ad id quod
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            a, b, d. </s>
            <s xml:id="echoid-s805" xml:space="preserve">Quam autem proportionem habet proportio ad humidum in
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            grauitate, hanc habet tetragonum, quod ab h, t, ad id quod a, b, d, pro-
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            pter eandem prioribus. </s>
            <s xml:id="echoid-s806" xml:space="preserve">palam ꝙ quæ habet, eſt æqualis ipſi, x, qua-
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            re & </s>
            <s xml:id="echoid-s807" xml:space="preserve">portiones, a, m, Z, a, p, q, ſunt æquales. </s>
            <s xml:id="echoid-s808" xml:space="preserve">et quoniā in portioni-
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            bus æqualibus, & </s>
            <s xml:id="echoid-s809" xml:space="preserve">ſimilibus. </s>
            <s xml:id="echoid-s810" xml:space="preserve">apol a, K, h, l, K, ab extremitatib. </s>
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