Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s16291" xml:space="preserve">
              <pb o="349" file="377" n="377" rhead="LIBER OCTAVVS."/>
            re exceſſu bis ſumptum, vna cum quadrato minoris exceſſus bis ſum-
              <lb/>
            pto, æquale eſt quadrato rectæ, qua minus latus minorem exceſſum
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            ſuperat.</s>
            <s xml:id="echoid-s16292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16293" xml:space="preserve">
              <emph style="sc">Sit</emph>
            rectangulum A C, cuius diametro B D, æqualis ſit recta B E, vt exceſſus
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            minor, quo diameter maius latus BC, ſuperat, ſit CE; </s>
            <s xml:id="echoid-s16294" xml:space="preserve">Sumpta autem BF, æqua-
              <lb/>
            liminorilateri CD, vt EF, exceſſus ſit, quo diameter BD, velilli æqualis BE, mi-
              <lb/>
            nus latus CD, velilli æqualem BF, ſuperat: </s>
            <s xml:id="echoid-s16295" xml:space="preserve">ac proinde CF, ſit differentia exceſ-
              <lb/>
            ſuum EC, EF. </s>
            <s xml:id="echoid-s16296" xml:space="preserve"> Et quia latera BC, CD, maiora ſunt latere BD hoc eſt, recta
              <note symbol="a" position="right" xlink:label="note-377-01" xlink:href="note-377-01a" xml:space="preserve">20. primi.</note>
            dempta communi B C, erit reliqua C D, maior, quam reli-
              <lb/>
              <figure xlink:label="fig-377-01" xlink:href="fig-377-01a" number="266">
                <image file="377-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/377-01"/>
              </figure>
            qua CE; </s>
            <s xml:id="echoid-s16297" xml:space="preserve">ideo que & </s>
            <s xml:id="echoid-s16298" xml:space="preserve">BF, æqualis ip ſi CD, maior erit, quam
              <lb/>
            C E. </s>
            <s xml:id="echoid-s16299" xml:space="preserve">Abſc@ſſa ergo F G, ipſi C E, æquali, erit B G, exceſſus
              <lb/>
            quo minus latus BF, minorem exceſſum FG, ſuperat. </s>
            <s xml:id="echoid-s16300" xml:space="preserve">Di-
              <lb/>
            corectangulum bis ſumptum ſub F C, differentia exceſſu-
              <lb/>
            um, vna cum quadrato minoris exceſſus CE, bis ſumpto,
              <lb/>
            æquale eſſe quadrato rectæ BG, quaminus latus BF, mino-
              <lb/>
            rem exceſſum F G, ſuperat. </s>
            <s xml:id="echoid-s16301" xml:space="preserve"> Quoniam enim
              <note symbol="b" position="right" xlink:label="note-377-02" xlink:href="note-377-02a" xml:space="preserve">4. ſecundi.</note>
            rectæ B E, æquale eſt quadratis rectarum B C, C E, vna cumrectangulo bis ſub
              <lb/>
            BC, CE, hoc eſt, rectangulo ſemel ſumpto ſub B C, & </s>
            <s xml:id="echoid-s16302" xml:space="preserve">recta ipſius C E, dupla: </s>
            <s xml:id="echoid-s16303" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-377-03" xlink:href="note-377-03a" xml:space="preserve">1. ſecundi.</note>
            Eſt autem rectangulum ſub B C, & </s>
            <s xml:id="echoid-s16304" xml:space="preserve">dupla ipſius C E, æquale rectangulis ſub
              <lb/>
            B F, & </s>
            <s xml:id="echoid-s16305" xml:space="preserve">dupla ipſius C E, æquale rectangulis ſub B F, & </s>
            <s xml:id="echoid-s16306" xml:space="preserve">duplaipſius C E, & </s>
            <s xml:id="echoid-s16307" xml:space="preserve">ſub
              <lb/>
            FC, & </s>
            <s xml:id="echoid-s16308" xml:space="preserve">dupla ipſius CE; </s>
            <s xml:id="echoid-s16309" xml:space="preserve">hoc eſt, rectangulo ſub BF, & </s>
            <s xml:id="echoid-s16310" xml:space="preserve">CE, bis vna cum rectan-
              <lb/>
            gulo ſub FC, & </s>
            <s xml:id="echoid-s16311" xml:space="preserve">CE, bis; </s>
            <s xml:id="echoid-s16312" xml:space="preserve">Erit quadratum rectæ BE, ſiue rectæ BD, æquale quo-
              <lb/>
            que quadratis rectarum BC, CE, vna cum rectangulis ſub BF, CE, bis, & </s>
            <s xml:id="echoid-s16313" xml:space="preserve">ſub FC,
              <lb/>
            CE, bis; </s>
            <s xml:id="echoid-s16314" xml:space="preserve">Ac proinde & </s>
            <s xml:id="echoid-s16315" xml:space="preserve">quadrata rectarum BC, CD, quæ quadrato rectæ
              <note symbol="d" position="right" xlink:label="note-377-04" xlink:href="note-377-04a" xml:space="preserve">47. primi.</note>
            æqualia ſunt, æqualia erunt quadratis rectarum B C, C E, vna cum rectangulis
              <lb/>
            ſub BF, CE, bis, & </s>
            <s xml:id="echoid-s16316" xml:space="preserve">ſub FC, CE, bis. </s>
            <s xml:id="echoid-s16317" xml:space="preserve">Ablato ergo communi quadrato rectæ BC,
              <lb/>
            erit reliquum quadratum rectæ CD, hoc eſt, rectæ BF, æqualereliquis rectangu-
              <lb/>
            lis ſub BF, CE, bis, & </s>
            <s xml:id="echoid-s16318" xml:space="preserve">ſub FC, CE, bis, vna cum quadrato rectæ C E. </s>
            <s xml:id="echoid-s16319" xml:space="preserve">Addito
              <lb/>
            igitur communi quadrato rectæ FG, erunt quadrata rectarum B F, F G, æqualia
              <lb/>
            rectangulis ſub BF, CE, bis, & </s>
            <s xml:id="echoid-s16320" xml:space="preserve">ſub FC, CE, bis, vna cum quadratis rectarum CE,
              <lb/>
              <note symbol="e" position="right" xlink:label="note-377-05" xlink:href="note-377-05a" xml:space="preserve">7 ſecundi.</note>
            FG. </s>
            <s xml:id="echoid-s16321" xml:space="preserve"> Sed quadratarectarum BF, FG, æqualia ſunt rectangulo ſub BF, FG, bis, vna cum quadrato rectæ BG. </s>
            <s xml:id="echoid-s16322" xml:space="preserve">Igitur rectangulum quoque ſub BF, FG, hoc eſt,
              <lb/>
            ſub BF, CE, bis, vna cum quadrato rectæ BG, æquale erit rectangulis ſub BF, CE,
              <lb/>
            bis, & </s>
            <s xml:id="echoid-s16323" xml:space="preserve">ſub FC, CE, bis, vna cum quadratis rectarũ CE, FG. </s>
            <s xml:id="echoid-s16324" xml:space="preserve">Ablato ergo cõmu-
              <lb/>
            ni rectangulo ſub BF, CE, bis ſumpto; </s>
            <s xml:id="echoid-s16325" xml:space="preserve">erit reliquum quadratum BG, æquale re-
              <lb/>
            liquo rectangulo ſub F C, C E, bis, vna cum quadratis rectarum C E, F G: </s>
            <s xml:id="echoid-s16326" xml:space="preserve">hoc
              <lb/>
            eſt, rectangulum ſub F C, diſferentia exceſſuum, & </s>
            <s xml:id="echoid-s16327" xml:space="preserve">CE, minore exceſſu bis ſum-
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            ptum, vna cum quadrato minoris exceſſus CE, bis ſumpto, æquale eſt qua dra-
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            to rectæ B G, qua minus latus B F, minorem exceſſum F G, ſuperat, quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s16328" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head385" xml:space="preserve">PROBL. 8. PROPOS. 16.</head>
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            <s xml:id="echoid-s16329" xml:space="preserve">DATIS duobus exceſſibus, quibus diameter rectanguli vtrumque la-
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            tus ſuperat, vtrumque latus, & </s>
            <s xml:id="echoid-s16330" xml:space="preserve">diametrum inuenire.</s>
            <s xml:id="echoid-s16331" xml:space="preserve"/>
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