Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s2674" xml:space="preserve">
              <pb o="43" file="0101" n="101" rhead="DEIIS QVAE VEH. IN AQVA."/>
            ad quadratum bd: </s>
            <s xml:id="echoid-s2675" xml:space="preserve">& </s>
            <s xml:id="echoid-s2676" xml:space="preserve">quam habet portio ad humidum in
              <lb/>
            grauitate, eandem quadratum nt habet ad bd quadratũ,
              <lb/>
            ex iis, quæ dicta ſunt: </s>
            <s xml:id="echoid-s2677" xml:space="preserve">conſtat n t lineæ ψ æqualem eſſe,
              <lb/>
            quare & </s>
            <s xml:id="echoid-s2678" xml:space="preserve">portio-
              <lb/>
              <figure xlink:label="fig-0101-01" xlink:href="fig-0101-01a" number="67">
                <image file="0101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0101-01"/>
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            nes a n z, a g q
              <lb/>
            ſunt æquales. </s>
            <s xml:id="echoid-s2679" xml:space="preserve">Et
              <lb/>
            quoniam in por
              <lb/>
            tionibus æquali
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s2680" xml:space="preserve">ſimilibus
              <lb/>
            a g q l, a n z l, ab
              <lb/>
            extremitatibus
              <lb/>
            baſiũ ductæ ſunt
              <lb/>
            a q, a z, quæ æ-
              <lb/>
            quales portiões
              <lb/>
            abſcindunt: </s>
            <s xml:id="echoid-s2681" xml:space="preserve">per
              <lb/>
            ſpicuum eſt an-
              <lb/>
            gulos facere æ-
              <lb/>
            quales cum por
              <lb/>
            tionum diame-
              <lb/>
            tris: </s>
            <s xml:id="echoid-s2682" xml:space="preserve">& </s>
            <s xml:id="echoid-s2683" xml:space="preserve">triangu-
              <lb/>
            lorum n fs, g ω c, angulos, qui ad f ω æquales eſſe: </s>
            <s xml:id="echoid-s2684" xml:space="preserve">itemque
              <lb/>
            æquales inter ſe, s b, c b; </s>
            <s xml:id="echoid-s2685" xml:space="preserve">& </s>
            <s xml:id="echoid-s2686" xml:space="preserve">s r, c r, quare & </s>
            <s xml:id="echoid-s2687" xml:space="preserve">n χ, g y æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s2688" xml:space="preserve">& </s>
            <s xml:id="echoid-s2689" xml:space="preserve">χ t y i. </s>
            <s xml:id="echoid-s2690" xml:space="preserve">cũq; </s>
            <s xml:id="echoid-s2691" xml:space="preserve">g h dupla ſit ipſius h i, erit n χ minor, quàm
              <lb/>
            duplaipſius χ t. </s>
            <s xml:id="echoid-s2692" xml:space="preserve">Sit igitur n m ipſius m t dupla: </s>
            <s xml:id="echoid-s2693" xml:space="preserve">& </s>
            <s xml:id="echoid-s2694" xml:space="preserve">iuncta
              <lb/>
            m K protrahatur ad e. </s>
            <s xml:id="echoid-s2695" xml:space="preserve">Itaque centrum grauitatis totius
              <lb/>
            erit punctum K: </s>
            <s xml:id="echoid-s2696" xml:space="preserve">partis eius, quæ eſt in humido, punctũ m: </s>
            <s xml:id="echoid-s2697" xml:space="preserve">
              <lb/>
            eius autem, quæ extra humidum in linea protracta, quod
              <lb/>
            ſit e. </s>
            <s xml:id="echoid-s2698" xml:space="preserve">ergo ex proxime demonſtratis patet, nõ manere por
              <lb/>
            tionem, ſed inclinari adeo, ut baſis nullo modo ſuperficiẽ
              <lb/>
            humidi contingat. </s>
            <s xml:id="echoid-s2699" xml:space="preserve">At uero portionem conſiſtere ita, uta-
              <lb/>
            xis cum ſuperficie humidi faciat angulum angulo φ mino-
              <lb/>
            rem, ſic demonſtrabitur. </s>
            <s xml:id="echoid-s2700" xml:space="preserve">conſiſtat enim, ſi fieri poteſt, ut
              <lb/>
            non faciat angulum minorem angulo φ: </s>
            <s xml:id="echoid-s2701" xml:space="preserve">& </s>
            <s xml:id="echoid-s2702" xml:space="preserve">alia eadem diſ-
              <lb/>
            ponantur; </s>
            <s xml:id="echoid-s2703" xml:space="preserve">ut in ſubiecta figura. </s>
            <s xml:id="echoid-s2704" xml:space="preserve">eodem modo </s>
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