Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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            <s xml:space="preserve">
              <pb file="0100" n="100" rhead="ARCHIMEDIS"/>
            quædam recta linea g i, ſectionibus a g q l, a x d interiecta,
              <lb/>
            & </s>
            <s xml:space="preserve">ipſi b d æquidiſtans; </s>
            <s xml:space="preserve">quæ mediam coni ſectionem in pun
              <lb/>
            cto h, & </s>
            <s xml:space="preserve">rectam
              <lb/>
              <anchor type="figure" xlink:label="fig-0100-01a" xlink:href="fig-0100-01"/>
            lineam r y in y
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            ſecet. </s>
            <s xml:space="preserve">demonſtra
              <lb/>
            bitur g h dupla
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            h i, quemadmo-
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            dum demonſtra
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            ta eſt o g ipſius
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            g x dupla. </s>
            <s xml:space="preserve">duca-
              <lb/>
            tur poſtea g ω cõ
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            tingens a g q l ſe
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            ctioneming: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            g c ad b d perpé
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            dicularis: </s>
            <s xml:space="preserve">iun-
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            ctaq; </s>
            <s xml:space="preserve">ai produ-
              <lb/>
            catur ad q. </s>
            <s xml:space="preserve">erit
              <lb/>
            ergo a i æqualis
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            i q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q ipſi g ω
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            æquidiſtans. </s>
            <s xml:space="preserve">Demonſtrandũ eſt portionẽ in humidũ demiſ
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            fam, inclinatamq; </s>
            <s xml:space="preserve">adeo, ut baſis ipſius non cõtingat humi-
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            dũ, conſiſtere inclinatã ita, ut axis cum ſuperficie humidi
              <lb/>
            angulum faciat minorem angulo φ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">baſis humidi ſuper-
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            ficiem nullo modo contingat. </s>
            <s xml:space="preserve">Demittatur enim in humi-
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            dum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">conſiſtat ita, ut baſis ipſius in uno puncto contin-
              <lb/>
            gat ſuperficiem humidi. </s>
            <s xml:space="preserve">ſecta autem portione per axem,
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            plano ad humidi ſuperficiem recto, ſit portionis ſectio a n
              <lb/>
            z l rectanguli coni ſectio: </s>
            <s xml:space="preserve">ſuperficiei humidi a z: </s>
            <s xml:space="preserve">axis autẽ
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            portionis, & </s>
            <s xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">b d in pun-
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            ctis _K_ r, ut ſuperius dictum eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducatur n f quidem ipſi
              <lb/>
            a z æquidiſtans, & </s>
            <s xml:space="preserve">contingens coni ſectionem in pũcto n;
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            </s>
            <s xml:space="preserve">n t uero æquidiſtans ipſi b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">n s ad eandem perpendi-
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            cularis. </s>
            <s xml:space="preserve">Quoniam igitur portio ad humidum in grauitate,
              <lb/>
            cam habet proportionem, quam quadratum, quod fit à χ</s>
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