Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div491" type="section" level="1" n="179">
          <p>
            <s xml:id="echoid-s8010" xml:space="preserve">
              <pb o="187" file="217" n="217" rhead="LIBER QVARTVS."/>
            cta Eb, paulo maior quam 1172 {1/8}. </s>
            <s xml:id="echoid-s8011" xml:space="preserve">quip pè cum huius radicis quadratum ſit tan-
              <lb/>
            tum 1373877 {1/64}. </s>
            <s xml:id="echoid-s8012" xml:space="preserve"> Habebit ergo E b, ad b c, maiorem proportionem, quam
              <note symbol="a" position="right" xlink:label="note-217-01" xlink:href="note-217-01a" xml:space="preserve">8. quinti.</note>
            {1/8}. </s>
            <s xml:id="echoid-s8013" xml:space="preserve">ad 153.</s>
            <s xml:id="echoid-s8014" xml:space="preserve"/>
          </p>
          <figure number="138">
            <image file="217-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/217-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s8015" xml:space="preserve">
              <emph style="sc">Secto</emph>
            item angulo b E c, bifariam per rectam E a; </s>
            <s xml:id="echoid-s8016" xml:space="preserve"> erunt b E, E c, ſimul
              <note symbol="b" position="right" xlink:label="note-217-02" xlink:href="note-217-02a" xml:space="preserve">3. ſexti. &
                <lb/>
              componendo,
                <lb/>
              permutando-
                <lb/>
              que.</note>
            b c, vt E c, ad c a. </s>
            <s xml:id="echoid-s8017" xml:space="preserve">Quia verò b E, maior eſt, quam 1172 {1/8}. </s>
            <s xml:id="echoid-s8018" xml:space="preserve">& </s>
            <s xml:id="echoid-s8019" xml:space="preserve">E c, maior, quã
              <lb/>
            1162 {1/8}. </s>
            <s xml:id="echoid-s8020" xml:space="preserve">erunt b E, E c, ſimul maiores, quam 2334 {2/8}. </s>
            <s xml:id="echoid-s8021" xml:space="preserve">vel 2334 {1/4}. </s>
            <s xml:id="echoid-s8022" xml:space="preserve">Cum ergo
              <lb/>
            c b, poſita ſit 153. </s>
            <s xml:id="echoid-s8023" xml:space="preserve">habebunt b E, E c, ſimul ad c b, maiorem proportionem, quam 2334 {1/4}. </s>
            <s xml:id="echoid-s8024" xml:space="preserve">ad 153. </s>
            <s xml:id="echoid-s8025" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s8026" xml:space="preserve">E c, ad c a, proportionem habebit maiorem,
              <lb/>
              <note symbol="c" position="right" xlink:label="note-217-03" xlink:href="note-217-03a" xml:space="preserve">8. quinti.</note>
            quam 2334 {1/4}. </s>
            <s xml:id="echoid-s8027" xml:space="preserve">ad 153. </s>
            <s xml:id="echoid-s8028" xml:space="preserve">ac proinde, ſi c a, ponatur 153. </s>
            <s xml:id="echoid-s8029" xml:space="preserve"> erit E c, maior,
              <note symbol="d" position="right" xlink:label="note-217-04" xlink:href="note-217-04a" xml:space="preserve">10. quinti.</note>
            2334 {1/4}. </s>
            <s xml:id="echoid-s8030" xml:space="preserve">Igitur quadratum ipſius E c, maius erit, quam 5448723 {1/16}. </s>
            <s xml:id="echoid-s8031" xml:space="preserve">cui ſi ad
              <lb/>
              <note symbol="e" position="right" xlink:label="note-217-05" xlink:href="note-217-05a" xml:space="preserve">47. primi.</note>
            datur quadratum 23409. </s>
            <s xml:id="echoid-s8032" xml:space="preserve">ipſius c a, erit quadratum ipſius E a, quod quadra- tis rectarum E c, ca, æquale eſt, maius quam 5472132 {1/16}. </s>
            <s xml:id="echoid-s8033" xml:space="preserve">eiuſqueradix maior,
              <lb/>
              <note symbol="f" position="right" xlink:label="note-217-06" xlink:href="note-217-06a" xml:space="preserve">8. quinti.</note>
            quam 2339 {1/4}. </s>
            <s xml:id="echoid-s8034" xml:space="preserve">cum huius radicis quadratum ſit tantum 5472090 {9/16}. </s>
            <s xml:id="echoid-s8035" xml:space="preserve"> Ergo E a, ad a c, maiorem proportionem habebit, quam 2339 {1/4}. </s>
            <s xml:id="echoid-s8036" xml:space="preserve">ad 153.
              <lb/>
            </s>
            <s xml:id="echoid-s8037" xml:space="preserve">
              <note symbol="g" position="right" xlink:label="note-217-07" xlink:href="note-217-07a" xml:space="preserve">3. ſexti. &
                <lb/>
              componendo,
                <lb/>
              permutando-
                <lb/>
              que.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s8038" xml:space="preserve">
              <emph style="sc">Secto</emph>
            denique angulo quoque a E c, bifariam per rectam E o, erunt a E, E c, ſimul ad a c, vt E c, ad c o. </s>
            <s xml:id="echoid-s8039" xml:space="preserve">Quia verò a E, maior eſt, quam 2339 {1/4}. </s>
            <s xml:id="echoid-s8040" xml:space="preserve">a & </s>
            <s xml:id="echoid-s8041" xml:space="preserve">
              <lb/>
            E c, maior quam 2334 {1/4}. </s>
            <s xml:id="echoid-s8042" xml:space="preserve">erunta E, E c, ſimul maiores, quam 4673 {1/2}. </s>
            <s xml:id="echoid-s8043" xml:space="preserve">Cum er-
              <lb/>
            go c a, poſita ſit 153. </s>
            <s xml:id="echoid-s8044" xml:space="preserve"> habebunt a E, E c, ſimul ad c a, hoc eſt, E c, ad c o,
              <note symbol="h" position="right" xlink:label="note-217-08" xlink:href="note-217-08a" xml:space="preserve">8. quinti.</note>
            iorem proportionem, quam 4673 {1/2}. </s>
            <s xml:id="echoid-s8045" xml:space="preserve">ad 153. </s>
            <s xml:id="echoid-s8046" xml:space="preserve">ac propterea ſi ponatur c o, 153.
              <lb/>
            </s>
            <s xml:id="echoid-s8047" xml:space="preserve">
              <note symbol="i" position="right" xlink:label="note-217-09" xlink:href="note-217-09a" xml:space="preserve">10. quinti.</note>
            erit E c, maior quam 4673 {1/2}.</s>
            <s xml:id="echoid-s8048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8049" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            igitur angulus e E c, tertia pars eſt recti, erit eius ſemiſsis d E c, ſexta
              <lb/>
            pars recti, & </s>
            <s xml:id="echoid-s8050" xml:space="preserve">huius ſemiſsis b E c, {1/@}. </s>
            <s xml:id="echoid-s8051" xml:space="preserve">recti, & </s>
            <s xml:id="echoid-s8052" xml:space="preserve">huius ſemiſsis a E c, {1/24}. </s>
            <s xml:id="echoid-s8053" xml:space="preserve">recti, & </s>
            <s xml:id="echoid-s8054" xml:space="preserve">deni-
              <lb/>
              <note symbol="k" position="right" xlink:label="note-217-10" xlink:href="note-217-10a" xml:space="preserve">33 ſexti.</note>
            que huius ſemiſsis o E c, {1/48}. </s>
            <s xml:id="echoid-s8055" xml:space="preserve">recti. </s>
            <s xml:id="echoid-s8056" xml:space="preserve"> Qualium ergo partium 48. </s>
            <s xml:id="echoid-s8057" xml:space="preserve">eſt quadrans A c, talium 1. </s>
            <s xml:id="echoid-s8058" xml:space="preserve">erit arcus c o: </s>
            <s xml:id="echoid-s8059" xml:space="preserve">& </s>
            <s xml:id="echoid-s8060" xml:space="preserve">id circo erit c o, {1/192}. </s>
            <s xml:id="echoid-s8061" xml:space="preserve">to tius circumferentiæ. </s>
            <s xml:id="echoid-s8062" xml:space="preserve">Fiat angulus
              <lb/>
              <note symbol="l" position="right" xlink:label="note-217-11" xlink:href="note-217-11a" xml:space="preserve">33. ſexti.</note>
            cEi, angulo cEo, æqualis; </s>
            <s xml:id="echoid-s8063" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s8064" xml:space="preserve">totus angulus oEi, {1/96}. </s>
            <s xml:id="echoid-s8065" xml:space="preserve">quatuor rectorũ: </s>
            <s xml:id="echoid-s8066" xml:space="preserve"> ideoq;</s>
            <s xml:id="echoid-s8067" xml:space="preserve">arc
              <emph style="sub">9</emph>
            o i, {1/98}. </s>
            <s xml:id="echoid-s8068" xml:space="preserve">totius circũferentiæ. </s>
            <s xml:id="echoid-s8069" xml:space="preserve">Per do ctrinã ergo ꝓpoſ. </s>
            <s xml:id="echoid-s8070" xml:space="preserve">12. </s>
            <s xml:id="echoid-s8071" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8072" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8073" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s8074" xml:space="preserve">recta o </s>
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