Archimedes, Archimedis De insidentibvs aqvae

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            <s xml:id="echoid-s682" xml:space="preserve">
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            ipſius s, a, u, palã ꝙ quæ p, Z, ipſius Z, t, est minor, ꝗ̃ dupla. </s>
            <s xml:id="echoid-s683" xml:space="preserve">Sit igitur
              <lb/>
            quæ p, ***, ipſius, ***, t, dupla, & </s>
            <s xml:id="echoid-s684" xml:space="preserve">copulata quæK, ***, educa
              <lb/>
            tur ad e, totius quidem igitur cetrum grauitatis erit K, eius autẽ por
              <lb/>
            tionis, quæ inter humidũ centrũ, ***, eius autẽ quæ extrain linea K, e,
              <lb/>
            & </s>
            <s xml:id="echoid-s685" xml:space="preserve">ſite. </s>
            <s xml:id="echoid-s686" xml:space="preserve">Quæ auté K, Z, perpẽdicularis erit ſuꝑ ſuꝑſiciẽ humidi, quare
              <lb/>
            & </s>
            <s xml:id="echoid-s687" xml:space="preserve">quæ ꝑ ſigna, e, ***, æquediſtãter ipſi K, Z, non ergo manet portio ſed
              <lb/>
            inreclinabitur ut baſis ipſius, nec ſecundum unum tangat ſuperſiciem
              <lb/>
            humidi, quoniam nunc ſecundum unum tacta ipſa reclinatur. </s>
            <s xml:id="echoid-s688" xml:space="preserve">Mani-
              <lb/>
            feſtum ergo quòd portio conſiſtet, ita ut axis ad ſuperficiem humidi fa
              <lb/>
            ciat angulum maiorem anguloy.</s>
            <s xml:id="echoid-s689" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s690" xml:space="preserve">HAbeat autem portio ad humidum in grauitate hanc proportio-
              <lb/>
            nem, quam habet tetragonum, quod a, b, x, o, ad id, quod a, b, d, & </s>
            <s xml:id="echoid-s691" xml:space="preserve">
              <lb/>
            dimittatur in humidum ita inclinata. </s>
            <s xml:id="echoid-s692" xml:space="preserve">Secta autem ipſa per axcm
              <lb/>
            plano recto ad ſuperficiem humidi ſolidi quidem, ſectio ſit quæ apol re
              <lb/>
            ctanguli coni ſectio. </s>
            <s xml:id="echoid-s693" xml:space="preserve">ſuperficiei autem humidi, quæ o, i, axis autem por
              <lb/>
            tionis & </s>
            <s xml:id="echoid-s694" xml:space="preserve">dyametris ſectionis quæ b, d, & </s>
            <s xml:id="echoid-s695" xml:space="preserve">ſecetur quæ b, d, ut prius & </s>
            <s xml:id="echoid-s696" xml:space="preserve">
              <lb/>
            ducatur. </s>
            <s xml:id="echoid-s697" xml:space="preserve">quæ quidem p, n, æquediſtanter ipſi i, o, cõtingens ſectionẽ ſe-
              <lb/>
            cundum p. </s>
            <s xml:id="echoid-s698" xml:space="preserve">Quæ autem p, t, æquediſtanter ipſi b, d, quæ autem p, s, per
              <lb/>
            pendicularis ſuper b, d. </s>
            <s xml:id="echoid-s699" xml:space="preserve">Demonstrãdum quòd portio non manet incli
              <lb/>
            nata ſic, ſed inclinatur donec utique baſis ſecundum unum ſignum tã
              <lb/>
            gat ſuperficiem humidi præiaceant auté & </s>
            <s xml:id="echoid-s700" xml:space="preserve">quæ in ſuperiori figura
              <lb/>
            prius diſpoſita ſunt, & </s>
            <s xml:id="echoid-s701" xml:space="preserve">quæ c, o, perpendicularis ducatur ſuper b, d,
              <lb/>
            & </s>
            <s xml:id="echoid-s702" xml:space="preserve">quæ a, x, copulata educatur ad q, erit autem quæ a, x, ipſi x, q,
              <lb/>
            æqualis, & </s>
            <s xml:id="echoid-s703" xml:space="preserve">ducatur ipſi a, q, quæ o, y, æquediſtans, & </s>
            <s xml:id="echoid-s704" xml:space="preserve">quoniam ſuppo
              <lb/>
            nitur portio ad humidum in grauitate hanc habere proportioné, quã
              <lb/>
            habet tetragonum quod ab x, a, ad id, quod a, b, d, habet autem hanc
              <lb/>
            proportionem & </s>
            <s xml:id="echoid-s705" xml:space="preserve">demerſa portio ad totam hoc eſt quòd a, t, p, ad id.
              <lb/>
            </s>
            <s xml:id="echoid-s706" xml:space="preserve">quod a, b, d, æqualis utique erit, quæ p, t, ipſi x, o, et quoniam portionũ
              <lb/>
            i, b, o, a, b, q, dyametri ſunt æquales, & </s>
            <s xml:id="echoid-s707" xml:space="preserve">portiones rurſum quoniam in
              <lb/>
            portionibus æqualibus & </s>
            <s xml:id="echoid-s708" xml:space="preserve">ſimilib. </s>
            <s xml:id="echoid-s709" xml:space="preserve">apol a, o, q, l, productæ ſunt a, q, i, o,
              <lb/>
            æquales portiones auferentes, hoc quidem ab extremitate baſis hoc
              <lb/>
            autem non ab extremitate, palàm quòd minorem facit acutum
              <lb/>
            angulum ad dyametrum totius portionis, quæ ab extremitate baſis
              <lb/>
            producta eſt. </s>
            <s xml:id="echoid-s710" xml:space="preserve">Et quoniam angulus, qui apud y, eſt minor, qui apud h,
              <lb/>
            maior eſt, quæ b, c, quàm b, s. </s>
            <s xml:id="echoid-s711" xml:space="preserve">Quæ autem e, r, minor, quàm r, s, quare
              <lb/>
            & </s>
            <s xml:id="echoid-s712" xml:space="preserve">quæ o, y, minor quàm p, n, maior eſt quam du-
              <lb/>
            pla, & </s>
            <s xml:id="echoid-s713" xml:space="preserve">quoniam quàm o, y, dupla, est ipſius s, 3, palàm quod quæ p, a,
              <lb/>
            maior eſt, quàm dupla ipſis a, t. </s>
            <s xml:id="echoid-s714" xml:space="preserve">Sit igitur quæ p, h, dupla ipſius h, t,
              <lb/>
            & </s>
            <s xml:id="echoid-s715" xml:space="preserve">copuletur quæ h, K, & </s>
            <s xml:id="echoid-s716" xml:space="preserve">educatur ad, ***, erit autem totius </s>
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