Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s1694" xml:space="preserve">
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            dem circa e z diametrum; </s>
            <s xml:id="echoid-s1695" xml:space="preserve">a t d uero circa diametrum t h;
              <lb/>
            </s>
            <s xml:id="echoid-s1696" xml:space="preserve">
              <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">K</note>
            quæ ſimiles ſint portioni a b l. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">tranſibit igitur a e i coni
              <lb/>
              <note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">L</note>
            ſectio per _K_: </s>
            <s xml:id="echoid-s1698" xml:space="preserve">& </s>
            <s xml:id="echoid-s1699" xml:space="preserve">quæ ab r ducta eſt perpendicularis ad b d,
              <lb/>
            ipſam a e i ſecabit. </s>
            <s xml:id="echoid-s1700" xml:space="preserve">ſecet in punctis y g: </s>
            <s xml:id="echoid-s1701" xml:space="preserve">& </s>
            <s xml:id="echoid-s1702" 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:id="echoid-s1703" xml:space="preserve">ducantur poſtremo, & </s>
            <s xml:id="echoid-s1704" xml:space="preserve">p χ, o φ contingentes ſectionẽ
              <lb/>
            a p o l in punctis p o. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">cũ
              <unsure/>
            ergo tres portiones ſint a p o l,
              <lb/>
              <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">M</note>
            a e i, a t d, contentæ rectis lineis, & </s>
            <s xml:id="echoid-s1706" xml:space="preserve">rectangulorum cono-
              <lb/>
            rum ſectionibus; </s>
            <s xml:id="echoid-s1707" xml:space="preserve">rectæq, ſimiles, & </s>
            <s xml:id="echoid-s1708" xml:space="preserve">inæquales, quæ contin
              <lb/>
            gunt ſe ſe ſuper unamquanque baſim: </s>
            <s xml:id="echoid-s1709" xml:space="preserve">à puncto autem n
              <lb/>
            ſurſum ducta ſit n x g o; </s>
            <s xml:id="echoid-s1710" xml:space="preserve">& </s>
            <s xml:id="echoid-s1711" xml:space="preserve">à q ipſa q fy p: </s>
            <s xml:id="echoid-s1712" 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:id="echoid-s1713" xml:space="preserve">& </s>
            <s xml:id="echoid-s1714" xml:space="preserve">ex proportione, quam a d habet ad d i.
              <lb/>
            </s>
            <s xml:id="echoid-s1715" xml:space="preserve">Sed i l ad l a
              <lb/>
              <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a" number="44">
                <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0070-01"/>
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            habet eandem,
              <lb/>
            quam duo ad
              <lb/>
            quinque. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">ete-
              <lb/>
            nim c b ad b d
              <lb/>
              <note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">N</note>
            eſt, ut ſex ad
              <lb/>
            quĩdecim; </s>
            <s xml:id="echoid-s1717" xml:space="preserve">hoc
              <lb/>
            eſt ut duo ad
              <lb/>
            quinque: </s>
            <s xml:id="echoid-s1718" xml:space="preserve">& </s>
            <s xml:id="echoid-s1719" xml:space="preserve">ut
              <lb/>
              <note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve">O</note>
            c b ad b d, ita
              <lb/>
            e b ad b a: </s>
            <s xml:id="echoid-s1720" xml:space="preserve">& </s>
            <s xml:id="echoid-s1721" xml:space="preserve">
              <lb/>
            d z ad d a. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">ha-
              <lb/>
            rum autẽ d z,
              <lb/>
              <note position="left" xlink:label="note-0070-06" xlink:href="note-0070-06a" xml:space="preserve">P</note>
            d a duplæ ſunt
              <lb/>
            ipſæ l i, l a: </s>
            <s xml:id="echoid-s1723" xml:space="preserve">& </s>
            <s xml:id="echoid-s1724" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0070-07" xlink:href="note-0070-07a" xml:space="preserve">Q</note>
            a d ad d i eã pro
              <lb/>
            portionem habet, quam quinque ad unum. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">ſed proportio
              <lb/>
            compoſita ex proportione, quam habet duo ad quinque;
              <lb/>
            </s>
            <s xml:id="echoid-s1726" xml:space="preserve">& </s>
            <s xml:id="echoid-s1727" xml:space="preserve">ex proportione, quam quinque ad unum; </s>
            <s xml:id="echoid-s1728" xml:space="preserve">eſt eadem,
              <lb/>
            quam habent duo ad unum: </s>
            <s xml:id="echoid-s1729" xml:space="preserve">duo autem ad unum duplam
              <lb/>
            proportionem habent. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">dupla eſt igitur g b ipſius g x: </s>
            <s xml:id="echoid-s1731" xml:space="preserve">&</s>
            <s xml:id="echoid-s1732" xml:space="preserve"/>
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