Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s8176" xml:space="preserve">
              <pb o="189" file="219" n="219" rhead="LIBER QVARTVS."/>
            9082689 {1/16}. </s>
            <s xml:id="echoid-s8177" xml:space="preserve">maius ſit, quam 9082321. </s>
            <s xml:id="echoid-s8178" xml:space="preserve">Igitur AB, ad BH, minorem proportio-
              <lb/>
            nem habebit, quam 3013 {3/4}. </s>
            <s xml:id="echoid-s8179" xml:space="preserve">ad 780. </s>
            <s xml:id="echoid-s8180" xml:space="preserve">ac proinde ſi BH, ponatur 780. </s>
            <s xml:id="echoid-s8181" xml:space="preserve"> erit AB,
              <note symbol="a" position="right" xlink:label="note-219-01" xlink:href="note-219-01a" xml:space="preserve">10. quinti.</note>
            nor quam 3013 {3/4}.</s>
            <s xml:id="echoid-s8182" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8183" xml:space="preserve">
              <emph style="sc">Secto</emph>
            rurſus angulo HAB, bifariam per rectam AI, ſecantem HB, in N;
              <lb/>
            </s>
            <s xml:id="echoid-s8184" xml:space="preserve">erunt vt prius, triangula BIN, AIB, æquiangula. </s>
            <s xml:id="echoid-s8185" xml:space="preserve">Ergo, vt ſupra, demonſtrabi-
              <lb/>
            mus, vtramque BA, AH, ſimul ad HB, habere eandem proportionem quam AI,
              <lb/>
            ad IB. </s>
            <s xml:id="echoid-s8186" xml:space="preserve">Eſt autem BA, oſtenſa minor, quam 3013 {3/4}. </s>
            <s xml:id="echoid-s8187" xml:space="preserve">& </s>
            <s xml:id="echoid-s8188" xml:space="preserve">AH, minor, quam 2911. </s>
            <s xml:id="echoid-s8189" xml:space="preserve">& </s>
            <s xml:id="echoid-s8190" xml:space="preserve">
              <lb/>
            ob id earum ſumma minor, quam 5924 {3/4}. </s>
            <s xml:id="echoid-s8191" xml:space="preserve">ipſa autem HB, poſita eſt 780. </s>
            <s xml:id="echoid-s8192" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-219-02" xlink:href="note-219-02a" xml:space="preserve">8. quinti.</note>
            tur vtraque BA, AH, ſimul ad HB, hoc eſt, AI, ad IB, minorem habebit propor-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-219-03" xlink:href="note-219-03a" xml:space="preserve">10. quinti.</note>
            tionem, quam 5924 {3/4}. </s>
            <s xml:id="echoid-s8193" xml:space="preserve">ad 780. </s>
            <s xml:id="echoid-s8194" xml:space="preserve">Siergo IB, ponatur 780. </s>
            <s xml:id="echoid-s8195" xml:space="preserve"> erit AI, minor, quam 5924 {3/4}. </s>
            <s xml:id="echoid-s8196" xml:space="preserve">Et quoniam eſt, vt 5924 {3/4}. </s>
            <s xml:id="echoid-s8197" xml:space="preserve">ad 780. </s>
            <s xml:id="echoid-s8198" xml:space="preserve">ita 1823. </s>
            <s xml:id="echoid-s8199" xml:space="preserve">ad 240, quod idem nu-
              <lb/>
            merus fiat ex primo in quartum, qui ex ſecundo in tertium, quæ quidem pro-
              <lb/>
            portio denominatur à 7 {143/240}. </s>
            <s xml:id="echoid-s8200" xml:space="preserve">habebit quoque AI, ad IB, minorem proportio-
              <lb/>
            nem, quam 1823. </s>
            <s xml:id="echoid-s8201" xml:space="preserve">ad 240. </s>
            <s xml:id="echoid-s8202" xml:space="preserve">ideoque poſita I B, 240. </s>
            <s xml:id="echoid-s8203" xml:space="preserve"> erit A I,
              <note symbol="d" position="right" xlink:label="note-219-04" xlink:href="note-219-04a" xml:space="preserve">10. quinti.</note>
            quam 1823. </s>
            <s xml:id="echoid-s8204" xml:space="preserve">atque ob id quadratum ipſius A I, minus, quam 3323329. </s>
            <s xml:id="echoid-s8205" xml:space="preserve">cui
              <lb/>
            ſi addatur quadratum 57600. </s>
            <s xml:id="echoid-s8206" xml:space="preserve">ipſius IB, fiet quadratum ipſius AB, (quod
              <note symbol="e" position="right" xlink:label="note-219-05" xlink:href="note-219-05a" xml:space="preserve">47. primi.</note>
            dratis rectarum A I, IB, æquale eſt) minus quam 3380929. </s>
            <s xml:id="echoid-s8207" xml:space="preserve">eiuſque radix pro-
              <lb/>
            pterea, vel recta AB, minor quam 1838. </s>
            <s xml:id="echoid-s8208" xml:space="preserve">{9/11}. </s>
            <s xml:id="echoid-s8209" xml:space="preserve">cum huius quadratum 3381252 {37/121}.
              <lb/>
            </s>
            <s xml:id="echoid-s8210" xml:space="preserve">maius ſit, quam 3380929. </s>
            <s xml:id="echoid-s8211" xml:space="preserve"> Igitur AB, ad BI, minorem proportionem
              <note symbol="f" position="right" xlink:label="note-219-06" xlink:href="note-219-06a" xml:space="preserve">8. quinti.</note>
            quam 1838 {9/11}. </s>
            <s xml:id="echoid-s8212" xml:space="preserve">ad 240. </s>
            <s xml:id="echoid-s8213" xml:space="preserve">ac proinde poſita BI, 240. </s>
            <s xml:id="echoid-s8214" xml:space="preserve"> erit A B, minor,
              <note symbol="g" position="right" xlink:label="note-219-07" xlink:href="note-219-07a" xml:space="preserve">10. quinti.</note>
            1838 {9/11}.</s>
            <s xml:id="echoid-s8215" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8216" xml:space="preserve">
              <emph style="sc">Secto</emph>
            item angulo IAB, bifariam per rectam AK, oſtendemus eodem mo-
              <lb/>
            do, vtramque BA, AI, ſimul ad IB, habere eandem pro portionem, quam AK, ad
              <lb/>
            KB. </s>
            <s xml:id="echoid-s8217" xml:space="preserve">Sunt autem BA, AI, ambæ ſimul minores, quam 3661 {9/11}. </s>
            <s xml:id="echoid-s8218" xml:space="preserve">(quod B A, oſ-
              <lb/>
              <figure xlink:label="fig-219-01" xlink:href="fig-219-01a" number="139">
                <image file="219-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/219-01"/>
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            tenſa ſit minor, quam 1838 {9/11}. </s>
            <s xml:id="echoid-s8219" xml:space="preserve">& </s>
            <s xml:id="echoid-s8220" xml:space="preserve">AI, minor, quam 1823.) </s>
            <s xml:id="echoid-s8221" xml:space="preserve">& </s>
            <s xml:id="echoid-s8222" xml:space="preserve">IB, poſita eſt 240.
              <lb/>
            </s>
            <s xml:id="echoid-s8223" xml:space="preserve"> Vtraq; </s>
            <s xml:id="echoid-s8224" xml:space="preserve">ergo BA, AI, ſimulad IB, hoc eſt, AK, ad KB, minorem habebit
              <note symbol="h" position="right" xlink:label="note-219-08" xlink:href="note-219-08a" xml:space="preserve">8. quinti.</note>
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