Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s2098" xml:space="preserve">_Etenim c b ad b d eſt ut ſex ad quindecim.</s>
            <s xml:id="echoid-s2099" xml:space="preserve">]_ Poſuimus
              <lb/>
              <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">N</note>
            enim b K duplam eſſe ipſius K d. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">quare componendo b d ad k d erit,
              <lb/>
            ut tria ad unum; </s>
            <s xml:id="echoid-s2101" xml:space="preserve">hoc eſt ut quindecim ad quinque. </s>
            <s xml:id="echoid-s2102" xml:space="preserve">ſed b d ad K c
              <lb/>
            erat ut quídecim
              <lb/>
              <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a" number="51">
                <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0082-01"/>
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            ad quatuor. </s>
            <s xml:id="echoid-s2103" xml:space="preserve">ergo
              <lb/>
            b d ad d c, ut quin
              <lb/>
            decim ad nouem:
              <lb/>
            </s>
            <s xml:id="echoid-s2104" xml:space="preserve">& </s>
            <s xml:id="echoid-s2105" xml:space="preserve">per conuerſio
              <lb/>
            nem rationis, con
              <lb/>
            uertendôq; </s>
            <s xml:id="echoid-s2106" xml:space="preserve">c b ad
              <lb/>
            b d, ut ſex ad quí
              <lb/>
            decim.</s>
            <s xml:id="echoid-s2107" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2108" xml:space="preserve">Etut c b ad
              <lb/>
              <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">O</note>
            b d, ita e b ad
              <lb/>
            b a, & </s>
            <s xml:id="echoid-s2109" xml:space="preserve">d z ad
              <lb/>
            d a.</s>
            <s xml:id="echoid-s2110" xml:space="preserve">] _Nam cum_
              <lb/>
            _triangula c b e,_
              <lb/>
            _d b a ſint ſimilia,_
              <lb/>
            _erit ut c b ad b e,_
              <lb/>
            _ita d b, ad b a & </s>
            <s xml:id="echoid-s2111" xml:space="preserve">permutando, ut c b ad b d; </s>
            <s xml:id="echoid-s2112" xml:space="preserve">ita e b ad b a. </s>
            <s xml:id="echoid-s2113" xml:space="preserve">Rurſus_
              <lb/>
            _ut b c ad c e, ita b d ad d a: </s>
            <s xml:id="echoid-s2114" xml:space="preserve">permutandôq; </s>
            <s xml:id="echoid-s2115" xml:space="preserve">ut c b ad b d, ita c e, hoc_
              <lb/>
            _eſt d z ei æqualis ad d a._</s>
            <s xml:id="echoid-s2116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2117" xml:space="preserve">Harum autem d z d a duplæ ſuntipſæ l i, la.</s>
            <s xml:id="echoid-s2118" xml:space="preserve">] _Lineam_
              <lb/>
              <note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">P</note>
            _quidem l a duplam eſſe ipſius d a, cum b d ſit portionis diameter,_
              <lb/>
            _manifeſte conſtat. </s>
            <s xml:id="echoid-s2119" xml:space="preserve">At uero l i ipſius d z dupla hoc pacto demon-_
              <lb/>
            _ſtrabitur. </s>
            <s xml:id="echoid-s2120" xml:space="preserve">Quoniam enim z d ad d a eſt, ut duo ad quinque; </s>
            <s xml:id="echoid-s2121" xml:space="preserve">erit có_
              <lb/>
            _uertendo, diuidendôq; </s>
            <s xml:id="echoid-s2122" xml:space="preserve">a z, hoc eſt i z ad z d, ut tria ad duo: </s>
            <s xml:id="echoid-s2123" xml:space="preserve">&_</s>
            <s xml:id="echoid-s2124" xml:space="preserve">
              <lb/>
            _rurſus diuidendo i d ad d z, ut
              <gap/>
            m ad duo. </s>
            <s xml:id="echoid-s2125" xml:space="preserve">erat autem z d ad_
              <lb/>
            _d a, hoc eſt ad d l, ut duo ad quinque. </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ergo ex æquali, conuertendóq;_
              <lb/>
            </s>
            <s xml:id="echoid-s2127" xml:space="preserve">_l d ad d i, ut quinque ad unum: </s>
            <s xml:id="echoid-s2128" xml:space="preserve">& </s>
            <s xml:id="echoid-s2129" xml:space="preserve">per conuerſionem rationis d l ad_
              <lb/>
            _li, ut quinque ad quatuor. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">ſed d z ad d l erat, ut duo ad quinque._ </s>
            <s xml:id="echoid-s2131" xml:space="preserve">
              <lb/>
            _ergo rurſus ex æquali d z ad l i, ut duo ad quatuor. </s>
            <s xml:id="echoid-s2132" xml:space="preserve">dupla eſt igitur_
              <lb/>
            _l i ipſius d z. </s>
            <s xml:id="echoid-s2133" xml:space="preserve">quod demonſtrandum fuerat._</s>
            <s xml:id="echoid-s2134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2135" xml:space="preserve">Et a d ad d i eam proportionem habet, quã quinque
              <lb/>
              <note position="left" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve">Q</note>
            </s>
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