Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1003" type="section" level="1" n="358">
          <pb o="350" file="378" n="378" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s16332" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datus exceſſus FE, diametri ſupra latus minus, & </s>
            <s xml:id="echoid-s16333" xml:space="preserve">C E, ſupra maius, ita
              <lb/>
            vt differentia exceſſuum ſit F C. </s>
            <s xml:id="echoid-s16334" xml:space="preserve">Ex C, educatur ad FE, perpendicularis CL, ca-
              <lb/>
            piantur que CH, HI, EK, minori exceſſui CE, æquales, ita vt totæ CI, CK, æqua-
              <lb/>
            les ſint, vt pote ipſius CE, duplæ, perficiaturque parallelogrammum FI. </s>
            <s xml:id="echoid-s16335" xml:space="preserve">Diuiſa
              <lb/>
            deinde FK, bifariam in N, deſcribatur ex N, per F, & </s>
            <s xml:id="echoid-s16336" xml:space="preserve">K, ſemicirculus FLK, ſecans
              <lb/>
            CL; </s>
            <s xml:id="echoid-s16337" xml:space="preserve">in L. </s>
            <s xml:id="echoid-s16338" xml:space="preserve">Ducta denique HE, ſumatur illi æqualis CM, iungaturque recta LM.
              <lb/>
            </s>
            <s xml:id="echoid-s16339" xml:space="preserve">Dico L M, differentiam eſſe inter minus latus quæſitum, & </s>
            <s xml:id="echoid-s16340" xml:space="preserve">minorem exceſſum
              <lb/>
            datum CE, ita vt CE, addita ad LM, efficiat minus latus; </s>
            <s xml:id="echoid-s16341" xml:space="preserve">cui ſi addatur F C, dif-
              <lb/>
            ferentia datorum exceſſum, fiat maius la-
              <lb/>
              <figure xlink:label="fig-378-01" xlink:href="fig-378-01a" number="267">
                <image file="378-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/378-01"/>
              </figure>
            tus. </s>
            <s xml:id="echoid-s16342" xml:space="preserve">(Eſt enim differentia exceſſuum dia-
              <lb/>
            metri ſupra vtrumque latus rectanguli æ-
              <lb/>
            qualis exceſſui maioris lateris ſupra mi-
              <lb/>
            nus: </s>
            <s xml:id="echoid-s16343" xml:space="preserve">vt in figura præcedentis propoſ. </s>
            <s xml:id="echoid-s16344" xml:space="preserve">pa-
              <lb/>
            tet; </s>
            <s xml:id="echoid-s16345" xml:space="preserve">vbidiameter eſt BD, vel BE; </s>
            <s xml:id="echoid-s16346" xml:space="preserve">exceſſus
              <lb/>
            maior F E, quo diameter minus latus B F,
              <lb/>
            ſuperat; </s>
            <s xml:id="echoid-s16347" xml:space="preserve">exceſſus minor CE, quo eadem
              <lb/>
            diameter maius latus B C, ſuperat: </s>
            <s xml:id="echoid-s16348" xml:space="preserve">eſt que
              <lb/>
            FC, differentia exceſſuum, exceſſus, quo
              <lb/>
            maius latus B C, ſuperat minus B F,) Ac
              <lb/>
            tandem maiori lateriinuẽto adijciatur minor exceſſus CE, vt diameter habeatur.
              <lb/>
            </s>
            <s xml:id="echoid-s16349" xml:space="preserve">quæ omnia ita demonſtrabuntur. </s>
            <s xml:id="echoid-s16350" xml:space="preserve">Per præcedentem, rectangulum ſub FC, dif-
              <lb/>
            ferentia exceſſuum, & </s>
            <s xml:id="echoid-s16351" xml:space="preserve">CE, minori exceſſu bis ſumptum, hoc eſt, rectangulum
              <lb/>
            FI, vna cum quadrato rectæ CE, bis etiam ſumpto, hoc eſt, vna cum quadrato
              <lb/>
            rectæ HE, vel CM, æquale eſt quadrato rectæ, qua minus latus quæſitum, mi-
              <lb/>
            norem exceſſum CE, ſuperat. </s>
            <s xml:id="echoid-s16352" xml:space="preserve">Cum ergo quadratum rectæ CL, æquale ſit re-
              <lb/>
            ctangulo FI, vt ex demonſtratione vltimæ propoſ. </s>
            <s xml:id="echoid-s16353" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16354" xml:space="preserve">2. </s>
            <s xml:id="echoid-s16355" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16356" xml:space="preserve">conſtat; </s>
            <s xml:id="echoid-s16357" xml:space="preserve">erunt
              <lb/>
            quo que quadrata rectarum CL, CM, æqualia quadrato eiuſdem rectæ, qua mi-
              <lb/>
            nuslatus quæſitum ſuperat minorem exceſſum CE, Ac proinde cum
              <note symbol="a" position="left" xlink:label="note-378-01" xlink:href="note-378-01a" xml:space="preserve">47. primi.</note>
            tis rectarum CL, CM, ſit æquale quadratum rectæ LM: </s>
            <s xml:id="echoid-s16358" xml:space="preserve">erit quo que quadratum
              <lb/>
            rectæ LM, æquale quadrato rectæ, qua minus latus quæſitum minorem exceſ-
              <lb/>
            ſum CE, ſuperat. </s>
            <s xml:id="echoid-s16359" xml:space="preserve">Eſt ergo LM, exceſſus minoris lateris quæſiti ſupra minorem
              <lb/>
            exceſſum CE. </s>
            <s xml:id="echoid-s16360" xml:space="preserve">Ideo que recta ex LM, CE, conflata erit minus latus quæſitum:
              <lb/>
            </s>
            <s xml:id="echoid-s16361" xml:space="preserve">cui ſi addatur FC, differentia exceſſuum, fiet maius latus quæſitum: </s>
            <s xml:id="echoid-s16362" xml:space="preserve">cui ſi tan-
              <lb/>
            dem minor exceſſus C E, adijciatur, conflabitur diameter quæſita. </s>
            <s xml:id="echoid-s16363" xml:space="preserve">quæ omnia
              <lb/>
            demonſtranda erant.</s>
            <s xml:id="echoid-s16364" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1005" type="section" level="1" n="359">
          <head xml:id="echoid-head386" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s16365" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            recta LM, cuius quadratum æquale eſt rectangulo FI, ſub FC, dif-
              <lb/>
            ferentia exceſſuum, & </s>
            <s xml:id="echoid-s16366" xml:space="preserve">dupla minoris exceſſus CE, comprehenſo vna cum du-
              <lb/>
            plo quadrati exceſſus minoris CE, addita minori exceſſui CE, efficit minus latus
              <lb/>
            quæſitum, &</s>
            <s xml:id="echoid-s16367" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16368" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16369" xml:space="preserve">
              <emph style="sc">Immo</emph>
            quia quadratum rectæ, CL, rectangulo FI, ſub FC, differentia exceſ-
              <lb/>
            ſuum, & </s>
            <s xml:id="echoid-s16370" xml:space="preserve">C K, duplo minoris exceſſus C E, comprehenſo æquale eſt, vt in de-
              <lb/>
            monſtratione dictum eſt; </s>
            <s xml:id="echoid-s16371" xml:space="preserve">& </s>
            <s xml:id="echoid-s16372" xml:space="preserve">rectangulum CP, duplum eſt quadrati exceſſus mi-
              <lb/>
            noris CE, hoc eſt, quadrato rectæ CM, æquale: </s>
            <s xml:id="echoid-s16373" xml:space="preserve">erit quadratũ rectæ LM, toti re-
              <lb/>
            ctãgulo FP, ſub maiori exceſſu FE, & </s>
            <s xml:id="echoid-s16374" xml:space="preserve">EP, dupla minoris exceſſus CE, </s>
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