Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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            <s xml:space="preserve">
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            dem circa e z diametrum; </s>
            <s xml:space="preserve">a t d uero circa diametrum t h;
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0070-01a" xlink:href="note-0070-01"/>
            quæ ſimiles ſint portioni a b l. </s>
            <s xml:space="preserve">tranſibit igitur a e i coni
              <lb/>
              <anchor type="note" xlink:label="note-0070-02a" xlink:href="note-0070-02"/>
            ſectio per _K_: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ ab r ducta eſt perpendicularis ad b d,
              <lb/>
            ipſam a e i ſecabit. </s>
            <s xml:space="preserve">ſecet in punctis y g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per y g ducan
              <lb/>
            tur ipſi b d æquidiſtantes p y q, o g n, quæ ſecent a t d in
              <lb/>
            f x. </s>
            <s xml:space="preserve">ducantur poſtremo, & </s>
            <s xml:space="preserve">p χ, o φ contingentes ſectionẽ
              <lb/>
            a p o l in punctis p o. </s>
            <s xml:space="preserve">cũ
              <unsure/>
            ergo tres portiones ſint a p o l,
              <lb/>
              <anchor type="note" xlink:label="note-0070-03a" xlink:href="note-0070-03"/>
            a e i, a t d, contentæ rectis lineis, & </s>
            <s xml:space="preserve">rectangulorum cono-
              <lb/>
            rum ſectionibus; </s>
            <s xml:space="preserve">rectæq, ſimiles, & </s>
            <s xml:space="preserve">inæquales, quæ contin
              <lb/>
            gunt ſe ſe ſuper unamquanque baſim: </s>
            <s xml:space="preserve">à puncto autem n
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            ſurſum ducta ſit n x g o; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à q ipſa q fy p: </s>
            <s xml:space="preserve">habebit o g ad
              <lb/>
            g x proportionem compoſitam ex proportione, quam ha
              <lb/>
            bet i l ad l a; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex proportione, quam a d habet ad d i.
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            </s>
            <s xml:space="preserve">Sed i l ad l a
              <lb/>
              <anchor type="figure" xlink:label="fig-0070-01a" xlink:href="fig-0070-01"/>
            habet eandem,
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            quam duo ad
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            quinque. </s>
            <s xml:space="preserve">ete-
              <lb/>
            nim c b ad b d
              <lb/>
              <anchor type="note" xlink:label="note-0070-04a" xlink:href="note-0070-04"/>
            eſt, ut ſex ad
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            quĩdecim; </s>
            <s xml:space="preserve">hoc
              <lb/>
            eſt ut duo ad
              <lb/>
            quinque: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut
              <lb/>
              <anchor type="note" xlink:label="note-0070-05a" xlink:href="note-0070-05"/>
            c b ad b d, ita
              <lb/>
            e b ad b a: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            d z ad d a. </s>
            <s xml:space="preserve">ha-
              <lb/>
            rum autẽ d z,
              <lb/>
              <anchor type="note" xlink:label="note-0070-06a" xlink:href="note-0070-06"/>
            d a duplæ ſunt
              <lb/>
            ipſæ l i, l a: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0070-07a" xlink:href="note-0070-07"/>
            a d ad d i eã pro
              <lb/>
            portionem habet, quam quinque ad unum. </s>
            <s xml:space="preserve">ſed proportio
              <lb/>
            compoſita ex proportione, quam habet duo ad quinque;
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex proportione, quam quinque ad unum; </s>
            <s xml:space="preserve">eſt eadem,
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            quam habent duo ad unum: </s>
            <s xml:space="preserve">duo autem ad unum duplam
              <lb/>
            proportionem habent. </s>
            <s xml:space="preserve">dupla eſt igitur g b ipſius g x: </s>
            <s xml:space="preserve">&</s>
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