Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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              <pb o="40" file="0091" n="91" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ipſi i m æquidiſtãs, & </s>
            <s xml:space="preserve">contingens ſectionem in p; </s>
            <s xml:space="preserve">pt uero
              <lb/>
            æquidiſtans b d, & </s>
            <s xml:space="preserve">p s ad ipſam b d perpendicularis. </s>
            <s xml:space="preserve">Demõ
              <lb/>
            ſtrandũ eſt, portionẽ non cõſiſtereita, ſed inclinari, donec
              <lb/>
            baſis in uno puncto ſuperficiem humidi cõtingat. </s>
            <s xml:space="preserve">Maneãt
              <lb/>
            enim eadem, quæ in ſuperiori figura: </s>
            <s xml:space="preserve">ducaturq; </s>
            <s xml:space="preserve">o c ad b d
              <lb/>
            perpendicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a x ad q producatur. </s>
            <s xml:space="preserve">erit a x
              <lb/>
            æqualis ipſi x q. </s>
            <s xml:space="preserve">deĩde ducatur o χ ipſi a q æquidiſtãs. </s>
            <s xml:space="preserve">Quo
              <lb/>
            niã igitur portio ad humidũ eã in grauitate proportione
              <lb/>
            habere ponitur, quam quadratum x o ad quadratum b d:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eandem proportionem habet pars ipſius demerſa ad to
              <lb/>
            tam; </s>
            <s xml:space="preserve">hoc eſt quadratum t p ad quadratum b d: </s>
            <s xml:space="preserve">æqualis uti
              <lb/>
            que erit t p ipſi x o: </s>
            <s xml:space="preserve">cumq; </s>
            <s xml:space="preserve">portionum i p m, a o q diame-
              <lb/>
            tri ſint æquales, & </s>
            <s xml:space="preserve">portiones ipſæ æquales erunt. </s>
            <s xml:space="preserve">Rurſus
              <lb/>
              <anchor type="note" xlink:label="note-0091-01a" xlink:href="note-0091-01"/>
            quoniam in por
              <lb/>
              <anchor type="note" xlink:label="note-0091-02a" xlink:href="note-0091-02"/>
              <anchor type="figure" xlink:label="fig-0091-01a" xlink:href="fig-0091-01"/>
            tionibus æquali
              <lb/>
            bus, & </s>
            <s xml:space="preserve">ſimilibus
              <lb/>
            a o q l, a p m l,
              <lb/>
            ductæ ſunt lineæ
              <lb/>
            a q, i m, quæ æ-
              <lb/>
            quales portio-
              <lb/>
            nes auferunt; </s>
            <s xml:space="preserve">il-
              <lb/>
            la quidem ab ex
              <lb/>
            tremitate baſis,
              <lb/>
            hæc autem non
              <lb/>
            ab extremitate:
              <lb/>
            </s>
            <s xml:space="preserve">cõſtat eam, quæ
              <lb/>
            ab extremitate
              <lb/>
            baſis ducta eſt,
              <lb/>
            minorem facere
              <lb/>
            angulum acutũ
              <lb/>
            cum diametro totius portionis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam angulus, qui
              <lb/>
              <anchor type="note" xlink:label="note-0091-03a" xlink:href="note-0091-03"/>
            ad χ minor eſt angulo, qui ad n; </s>
            <s xml:space="preserve">maior erit b c, quàm b s:
              <lb/>
            </s>
            <s xml:space="preserve">cr autem, quàm ſr minor. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">o g minor, quàm p z: </s>
            <s xml:space="preserve">
              <lb/>
            & </s>
            <s xml:space="preserve">g x maior, quàm z t. </s>
            <s xml:space="preserve">ergo p z maior eſt, quàm dupla z t;</s>
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