Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s5336" xml:space="preserve">Præterea, ijſdem poſitis in eadem figura. </s>
            <s xml:id="echoid-s5337" xml:space="preserve">Dico rectangulum
              <lb/>
              <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">2.</note>
            B E F ſuperare rectangulum B G H maiori exceſſu quàm ſit qua-
              <lb/>
            dratum G E.</s>
            <s xml:id="echoid-s5338" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5339" xml:space="preserve">COmpletis enim rectangulis B E F I, B G H L, productiſque E F, L H
              <lb/>
            vſque ad occurſum in O; </s>
            <s xml:id="echoid-s5340" xml:space="preserve">cum ſit A E pluſquàm dimidium ipſius
              <lb/>
            A B, vt ſupra oſtendimus, erit A E maior E B; </s>
            <s xml:id="echoid-s5341" xml:space="preserve">cumque ſit B A ad A E,
              <lb/>
            ita B C ad E F, vel ad B I, erit diuidendo B E ad E A, vt C I ad I B,
              <lb/>
            ſed eſt B E minor ipſa E A, ergo, & </s>
            <s xml:id="echoid-s5342" xml:space="preserve">C I minor erit ipſa I B, quare ſum-
              <lb/>
            pta L M æquali ipſi C I punctum M non pertinget ad B.</s>
            <s xml:id="echoid-s5343" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5344" xml:space="preserve">Iam cum M L, I C ſint ęquales, erit
              <lb/>
              <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a" number="150">
                <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0190-01"/>
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            M L ad N H, vt I C ad N H, vel vt I F
              <lb/>
            ad F N, vel vt L O ad O H, quare pun-
              <lb/>
            cta M, N, O erunt in vna, eademque
              <lb/>
            recta M N O. </s>
            <s xml:id="echoid-s5345" xml:space="preserve">Poſtremò ducatur recta
              <lb/>
            M P Q parallela ad B E. </s>
            <s xml:id="echoid-s5346" xml:space="preserve">Erunt in re-
              <lb/>
            ctangulo Q L ſupplementa Q N, L N
              <lb/>
            inter ſe æqualia, quibus addito com-
              <lb/>
            muni rectangulo B N, fiet gnomon G I
              <lb/>
            Q æqualis rectangulo B H, ſed exceſ-
              <lb/>
            ſus rectanguli B F ſupra gnomonem G I
              <lb/>
            Q, eſt rectangulum G Q, quare exceſ-
              <lb/>
            ſus quoque rectanguli B F, ſupra B H,
              <lb/>
            erit idem rectangulum G Q. </s>
            <s xml:id="echoid-s5347" xml:space="preserve">Cumque
              <lb/>
            ſit C B minor B A, & </s>
            <s xml:id="echoid-s5348" xml:space="preserve">vt C B ad B A,
              <lb/>
            ita C L ad L H, erit quoque C L, vel M I, vel Q F minor L H, vel BG;
              <lb/>
            </s>
            <s xml:id="echoid-s5349" xml:space="preserve">eſtque tota E F, maior tota E B, vt ſuperiùs oſtendimus, ergo reliqua
              <lb/>
            Q E maior erit reliqua E G, vnde rectangulum G E Q, quod eſt exceſ-
              <lb/>
            ſus rectanguli B E F ſupra B G H maius erit quadrato G E. </s>
            <s xml:id="echoid-s5350" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s5351" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5352" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5353" xml:space="preserve">Poſtremò ijſdem poſitis, & </s>
            <s xml:id="echoid-s5354" xml:space="preserve">conſtructis, concipiatur quoque
              <lb/>
              <note position="left" xlink:label="note-0190-02" xlink:href="note-0190-02a" xml:space="preserve">3.</note>
            alia B R maior quidem B E, ſed minor adhuc dimidio ipſius B
              <lb/>
            A, & </s>
            <s xml:id="echoid-s5355" xml:space="preserve">non maior dimidio ipſius B C. </s>
            <s xml:id="echoid-s5356" xml:space="preserve">Dico tandem exceſſum
              <lb/>
            rectanguli B E F ſupra rectangulum B G H, quod eſt G E Q,
              <lb/>
            maius eſſe exceſſu quadrati G R ſupra R E.</s>
            <s xml:id="echoid-s5357" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5358" xml:space="preserve">NAm, vt primo loco ſuperiùs demonſtrauimus, erit tota linea E F
              <lb/>
            maior aggregato B R, cum R E, ſed pars Q F minor eſt parte BG
              <lb/>
            prædicti aggregati (nam eſt Q F æqualis M I, ſiue L C, & </s>
            <s xml:id="echoid-s5359" xml:space="preserve">B G æqualis
              <lb/>
            eſt L H, eſtque C L minor L H, cum ſit data C B minor quoque B A) er-
              <lb/>
            go reliqua E Q maior erit reliquo eiuſdem aggregati, quod eſt G R cum
              <lb/>
            R E; </s>
            <s xml:id="echoid-s5360" xml:space="preserve">vnde rectangulum ſub Q E, & </s>
            <s xml:id="echoid-s5361" xml:space="preserve">E G, quod eſt exceſſus rectanguli B
              <lb/>
            E F ſupra B G H, maius erit rectangulo ſub G E cum R E, in eadem G E:
              <lb/>
            </s>
            <s xml:id="echoid-s5362" xml:space="preserve">ſed rectangulum ſub G R cum R E, in G E, eſt exceſſus quadrati G
              <note symbol="a" position="left" xlink:label="note-0190-03" xlink:href="note-0190-03a" xml:space="preserve">1. huius.</note>
            ſupra R E, ideoque rectangulum B E F ſuperat rectangulum B G H maio-
              <lb/>
            ri exceſſu, quo quadratum G R ſuperat quadratum RE. </s>
            <s xml:id="echoid-s5363" xml:space="preserve">Quod tandem, &</s>
            <s xml:id="echoid-s5364" xml:space="preserve">c.</s>
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