Archimedes, Archimedis De insidentibvs aqvae

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            <s xml:id="echoid-s716" xml:space="preserve">
              <pb file="0042" n="42" rhead="DE INSIDENTIBVS AQVAE"/>
            portionis centrum grauitatis K. </s>
            <s xml:id="echoid-s717" xml:space="preserve">Eius autem, quæ intra humidum h,
              <lb/>
            eius autem, quæ extra in linea K. </s>
            <s xml:id="echoid-s718" xml:space="preserve">***, & </s>
            <s xml:id="echoid-s719" xml:space="preserve">ſit***, demonſtrabitur autẽ
              <lb/>
            ſimiliter quæ K. </s>
            <s xml:id="echoid-s720" xml:space="preserve">2. </s>
            <s xml:id="echoid-s721" xml:space="preserve">ꝑpendicularis ſuper ſuperſiciem humidi, & </s>
            <s xml:id="echoid-s722" xml:space="preserve">quæ
              <lb/>
            per ſigna, h, ***, æqued ſtãter. </s>
            <s xml:id="echoid-s723" xml:space="preserve">ipſi K. </s>
            <s xml:id="echoid-s724" xml:space="preserve">Z, manifeſtũ igitur. </s>
            <s xml:id="echoid-s725" xml:space="preserve">quòd non ma
              <lb/>
            nebit portio, ſed inclinabiturd, onec utique baſis ipſius ſecundum unũ
              <lb/>
            ſignum tangat ſuperſiciem humidi, ſicut demonſtrabitur in tertia fi-
              <lb/>
            gura, quomodo ſe habet in tertio theoremate, & </s>
            <s xml:id="echoid-s726" xml:space="preserve">manebit portio ita cõ
              <lb/>
            ſiſtens. </s>
            <s xml:id="echoid-s727" xml:space="preserve">In portionibus h, æqualibus apol a, o, q, l, productæ erit ab ex-
              <lb/>
            tremitatibus baſium, quæ a, q, a, o, æquales auferentes demonſtrabitur
              <lb/>
            h, a, p, q, æqualis ipſi a, p, o, ſimiliter prioribus, æquales igitur facient
              <lb/>
            acutos angulos, quæ a, o, a, q, ad dyametros portionum. </s>
            <s xml:id="echoid-s728" xml:space="preserve">quoniam æqua
              <lb/>
            les ſunt qui apud n, y, anguli & </s>
            <s xml:id="echoid-s729" xml:space="preserve">Z, t, copulata autem ipſi Z, K, & </s>
            <s xml:id="echoid-s730" xml:space="preserve">edu
              <lb/>
            cta ad, ***, erit totius quidem portionis centrum grauitatis K, eius
              <lb/>
            autem quidem intra humidum, h, eius autem quæ extra in line a K,
              <lb/>
            ***, & </s>
            <s xml:id="echoid-s731" xml:space="preserve">ſit, ***, & </s>
            <s xml:id="echoid-s732" xml:space="preserve">quæ K, h, perpendicularis eſt ſuper ſuper ficiem hu-
              <lb/>
            midi, ſecundum eaſdem igitur rectas quod quidem in humido ſurſum
              <lb/>
            feretur, & </s>
            <s xml:id="echoid-s733" xml:space="preserve">quod extra humidum deorſum feretur. </s>
            <s xml:id="echoid-s734" xml:space="preserve">Manebit autem
              <lb/>
            portio, & </s>
            <s xml:id="echoid-s735" xml:space="preserve">baſis, & </s>
            <s xml:id="echoid-s736" xml:space="preserve">magnitudo, & </s>
            <s xml:id="echoid-s737" xml:space="preserve">ſecũdum unum ſignum tanget ſu-
              <lb/>
            perficiem humidi & </s>
            <s xml:id="echoid-s738" xml:space="preserve">axis portionis ad ſuperficiem humidi faciet an-
              <lb/>
            gulum æqualẽ præſcripto. </s>
            <s xml:id="echoid-s739" xml:space="preserve">Similiter autem demonstrabitur, & </s>
            <s xml:id="echoid-s740" xml:space="preserve">ſi por-
              <lb/>
            tio ad humidum in grauitate habeat proportionem eandem, quã te-
              <lb/>
            tragonum quod h, p. </s>
            <s xml:id="echoid-s741" xml:space="preserve">ad id. </s>
            <s xml:id="echoid-s742" xml:space="preserve">quod a, b, d, dimiſſa in humidum ita, ut ba-
              <lb/>
            ſis ipſius non tangat ſuperficiem humidi. </s>
            <s xml:id="echoid-s743" xml:space="preserve">conſiſtet inclinata ita, ut ba-
              <lb/>
            ſis ipſius ſecumdum unum ſignũ tangat ſuperficiem humidi, & </s>
            <s xml:id="echoid-s744" xml:space="preserve">axis
              <lb/>
            ipſius ad ſuperficiem humidi faciat angulum æqualem angulo, quæ
              <lb/>
            apudf.</s>
            <s xml:id="echoid-s745" xml:space="preserve"/>
          </p>
          <figure number="33">
            <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0042-01"/>
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