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

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          <head xml:id="echoid-head115" xml:space="preserve">LEMMA V. PROP. XXXXIII.</head>
          <p>
            <s xml:id="echoid-s2562" xml:space="preserve">Si duo triangula ABC, DEF, habuerint circa angulos B, E,
              <lb/>
            latera AB, BE, item@altera BC, EF inter ſe æqualia, & </s>
            <s xml:id="echoid-s2563" xml:space="preserve">in angulis
              <lb/>
            BAC, EDF applicatæ ſint GH, IL parallelæ ad BC, EF, ſitque
              <lb/>
            rectangulum BGH æquale rectangulo EIL. </s>
            <s xml:id="echoid-s2564" xml:space="preserve">Dico latera BG, EI
              <lb/>
            inter ſe æqualia eſſe.</s>
            <s xml:id="echoid-s2565" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2566" xml:space="preserve">SEd conſultò omiſſa, præter mei inſtituti morem, affirmatiua demonſtra-
              <lb/>
            tione, libet potiùs indirectam, ac breuiorem afferre, ſimulque egregiæ
              <lb/>
            indolis ſpecimen exhibere nobiliſsimi, ac ingenioſiſsimi Romani Adoleſcentis,
              <lb/>
            Bruti Annibali della Molara, ex ſelectiſsimis Ephebis SERENISSIMO
              <lb/>
            MAGNO DVCI miniſtrantibus, de quo non auſim aſſerere, quæ ſint ei
              <lb/>
            maioris oblectamenti, an equeſtrium exercitationum ornamenta, quibus
              <lb/>
            elegantiſsimè inſignitur, an mathematicæ contemplationes, dum, etiam
              <lb/>
            inter Aulæ ſtrepitus, pacatos ſubtilioris Geometriæ nouit inuenire receſſus,
              <lb/>
            prout varia teſtantur problemata, ac theoremata, à me identidem ei propoſi-
              <lb/>
            ta, & </s>
            <s xml:id="echoid-s2567" xml:space="preserve">ab ipſo quàm feliciter ſoluta, quorum, licet facillimum, poſteriori
              <lb/>
            tamen inſeruiens hic habes.</s>
            <s xml:id="echoid-s2568" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2569" xml:space="preserve">ESto, ſi fieri poteſt, alterum ipſorum laterum, quale eſt BG, maius alte-
              <lb/>
            ro EI: </s>
            <s xml:id="echoid-s2570" xml:space="preserve">habebit ergo GB ad BA, maiorem rationem quam IE ad ED ipſi
              <lb/>
            BA æqualem, & </s>
            <s xml:id="echoid-s2571" xml:space="preserve">componendo GA
              <lb/>
              <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a" number="68">
                <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0099-01"/>
              </figure>
            ad AB maiorem rationem quàm ID
              <lb/>
            ad DE, ſed GA ad AB, eſt vt GH ad
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s2572" xml:space="preserve">ID ad DE, vt IL ad EF; </s>
            <s xml:id="echoid-s2573" xml:space="preserve">ergo
              <lb/>
            GH ad BC habet maiorem rationem
              <lb/>
            quàm IL ad EF, hoc eſt ad ſibi æqua-
              <lb/>
            lem BC, quare GH erit maior IL, & </s>
            <s xml:id="echoid-s2574" xml:space="preserve">
              <lb/>
            ponitur BG maior EI, vnde rectan-
              <lb/>
            gulum BGH maius eſt rectangulo
              <lb/>
            EIL: </s>
            <s xml:id="echoid-s2575" xml:space="preserve">quod eſt contra hypoteſim.
              <lb/>
            </s>
            <s xml:id="echoid-s2576" xml:space="preserve">Sunt ergo BG, EI interſe æquales. </s>
            <s xml:id="echoid-s2577" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s2578" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2579" xml:space="preserve"/>
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