Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s8224" xml:space="preserve">
              <pb o="190" file="220" n="220" rhead="GEOMETR. PRACT."/>
            tionem, quam 3661 {9/11}. </s>
            <s xml:id="echoid-s8225" xml:space="preserve">ad 240. </s>
            <s xml:id="echoid-s8226" xml:space="preserve">Vt autem 3661 {9/11}. </s>
            <s xml:id="echoid-s8227" xml:space="preserve">ad 240. </s>
            <s xml:id="echoid-s8228" xml:space="preserve">ita eſt 1007. </s>
            <s xml:id="echoid-s8229" xml:space="preserve">ad
              <lb/>
            66. </s>
            <s xml:id="echoid-s8230" xml:space="preserve">quod idem gignatur numerus ex primo in quartum, qui ex ſecundo in ter-
              <lb/>
            tium, quę quidem proportio denominatur à 15 {17/66}. </s>
            <s xml:id="echoid-s8231" xml:space="preserve">Igitur AK, ad KB, minorem
              <lb/>
            quo queprop ortionem habebit, quam 1007. </s>
            <s xml:id="echoid-s8232" xml:space="preserve">ad 66. </s>
            <s xml:id="echoid-s8233" xml:space="preserve">ideoque poſita K B, 66.
              <lb/>
            </s>
            <s xml:id="echoid-s8234" xml:space="preserve"> erit A K, minor, quam 1007. </s>
            <s xml:id="echoid-s8235" xml:space="preserve">ac propterea eius quadratum minus,
              <note symbol="a" position="left" xlink:label="note-220-01" xlink:href="note-220-01a" xml:space="preserve">10. quinti.</note>
            1014049. </s>
            <s xml:id="echoid-s8236" xml:space="preserve">cuiſi ad datur quadratum 4356. </s>
            <s xml:id="echoid-s8237" xml:space="preserve">ipſius KB; </s>
            <s xml:id="echoid-s8238" xml:space="preserve">fiet qua dratum ipſius A B,
              <lb/>
            (quod illis duobus æquale eſt) minus quam 1018405. </s>
            <s xml:id="echoid-s8239" xml:space="preserve">eiuſque radix
              <note symbol="b" position="left" xlink:label="note-220-02" xlink:href="note-220-02a" xml:space="preserve">47. primi.</note>
            ea, id eſt, recta AB, minor, quam 1009 {1/4}. </s>
            <s xml:id="echoid-s8240" xml:space="preserve">cum huius quadratum 1018417 {13/36}. </s>
            <s xml:id="echoid-s8241" xml:space="preserve">ſit
              <lb/>
            maius, quam 1018405. </s>
            <s xml:id="echoid-s8242" xml:space="preserve"> Quocirca AB, ad BK, minorem proportionem
              <note symbol="c" position="left" xlink:label="note-220-03" xlink:href="note-220-03a" xml:space="preserve">8. quinti.</note>
            bit, quam 1009 {1/6}. </s>
            <s xml:id="echoid-s8243" xml:space="preserve">ad 66. </s>
            <s xml:id="echoid-s8244" xml:space="preserve">atqueidcirco poſita BK, 66. </s>
            <s xml:id="echoid-s8245" xml:space="preserve"> erit AB, minor,
              <note symbol="d" position="left" xlink:label="note-220-04" xlink:href="note-220-04a" xml:space="preserve">10. quinti.</note>
            1009 {1/6}.</s>
            <s xml:id="echoid-s8246" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8247" xml:space="preserve">
              <emph style="sc">Secto</emph>
            denique angulo KAB, bifariam, perrectam AL, demonſtrabimus
              <lb/>
            eadem ratione, vtramque BA, AK, ſimul ad CK, eſſe, vt AL, ad LB. </s>
            <s xml:id="echoid-s8248" xml:space="preserve">Sunt autem
              <lb/>
            ambę B A, A K, ſimul minores, quam 2016 {1/6}. </s>
            <s xml:id="echoid-s8249" xml:space="preserve">(quod BA, ſit oſtenſa minor,
              <lb/>
            quam 1009 {1/6}. </s>
            <s xml:id="echoid-s8250" xml:space="preserve">& </s>
            <s xml:id="echoid-s8251" xml:space="preserve">AK, minor, quam 1007.) </s>
            <s xml:id="echoid-s8252" xml:space="preserve">& </s>
            <s xml:id="echoid-s8253" xml:space="preserve">BK, poſita eſt 66. </s>
            <s xml:id="echoid-s8254" xml:space="preserve">Igitur
              <note symbol="e" position="left" xlink:label="note-220-05" xlink:href="note-220-05a" xml:space="preserve">8. quinti.</note>
            que BA, AK, ſimul ad CK, hoc eſt, AL, ad LB, habebit proportionem minorem,
              <lb/>
            quam 2016 {1/6}. </s>
            <s xml:id="echoid-s8255" xml:space="preserve">ad 66. </s>
            <s xml:id="echoid-s8256" xml:space="preserve">atque idcirco ſi LB, ponatur 66. </s>
            <s xml:id="echoid-s8257" xml:space="preserve"> erit AL, minor,
              <note symbol="f" position="left" xlink:label="note-220-06" xlink:href="note-220-06a" xml:space="preserve">10. quinti.</note>
            2016 {1/6}. </s>
            <s xml:id="echoid-s8258" xml:space="preserve">ideo que quadratum eius minus quam 4064928 {1/36}. </s>
            <s xml:id="echoid-s8259" xml:space="preserve">cui ſi ad datur qua-
              <lb/>
            dratum 4356. </s>
            <s xml:id="echoid-s8260" xml:space="preserve">ipſius LB; </s>
            <s xml:id="echoid-s8261" xml:space="preserve">fiet quadratum ipſius A B, quod duobus illis eſt
              <note symbol="g" position="left" xlink:label="note-220-07" xlink:href="note-220-07a" xml:space="preserve">47. primi.</note>
            quale) minus, quam numerus 4069284 {1/36}. </s>
            <s xml:id="echoid-s8262" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s8263" xml:space="preserve">eius radix, id eſt, recta AB,
              <lb/>
            minor, quam 2017 {1/4}. </s>
            <s xml:id="echoid-s8264" xml:space="preserve">cum huius quadratum 4069297 {9/36}. </s>
            <s xml:id="echoid-s8265" xml:space="preserve">ſuperet 4069284 {1/36}.
              <lb/>
            </s>
            <s xml:id="echoid-s8266" xml:space="preserve"> Quamobrem AB, ad BL, minorem proportionem habebit, quam 2017 {1/4}. </s>
            <s xml:id="echoid-s8267" xml:space="preserve">
              <note symbol="h" position="left" xlink:label="note-220-08" xlink:href="note-220-08a" xml:space="preserve">8. quinti.</note>
            66. </s>
            <s xml:id="echoid-s8268" xml:space="preserve">ideoque ſi BL, ponatur 66. </s>
            <s xml:id="echoid-s8269" xml:space="preserve"> erit AB, minor, quam 2017 {1/4}.</s>
            <s xml:id="echoid-s8270" xml:space="preserve"/>
          </p>
          <note symbol="i" position="left" xml:space="preserve">10. quinti.</note>
          <p>
            <s xml:id="echoid-s8271" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            igitur angulus G A H, angulo H A B, æqualis eſt; </s>
            <s xml:id="echoid-s8272" xml:space="preserve">erit
              <note symbol="k" position="left" xlink:label="note-220-10" xlink:href="note-220-10a" xml:space="preserve">26. tertij.</note>
              <figure xlink:label="fig-220-01" xlink:href="fig-220-01a" number="140">
                <image file="220-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/220-01"/>
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            GH, arcui HB, æqualis: </s>
            <s xml:id="echoid-s8273" xml:space="preserve">eademqueratione arcus HI, arcui IB, & </s>
            <s xml:id="echoid-s8274" xml:space="preserve">IK, ipſi KB, & </s>
            <s xml:id="echoid-s8275" xml:space="preserve">
              <lb/>
            KL, ipſi LB, æqualis erit. </s>
            <s xml:id="echoid-s8276" xml:space="preserve">Cum ergo GB, ſit {1/6}. </s>
            <s xml:id="echoid-s8277" xml:space="preserve">totius circumſerentiæ, erit HB.</s>
            <s xml:id="echoid-s8278" xml:space="preserve"/>
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