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

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        <div xml:id="echoid-div525" type="section" level="1" n="219">
          <head xml:id="echoid-head224" xml:space="preserve">VINCENTII VIVIANI
            <lb/>
          DE MAXIMIS, ET MINIMIS</head>
          <head xml:id="echoid-head225" xml:space="preserve">Geometrica diuinatio in V. conic.
            <lb/>
          Apoll. Pergæi.</head>
          <head xml:id="echoid-head226" style="it" xml:space="preserve">LIBER SECVNDVS.</head>
          <head xml:id="echoid-head227" xml:space="preserve">LEMMA I. PROP. I.</head>
          <p>
            <s xml:id="echoid-s5153" xml:space="preserve">Si recta linea vtcunque ſecta fuerit: </s>
            <s xml:id="echoid-s5154" xml:space="preserve">quadratum totius æqua-
              <lb/>
            bitur quadrato vnius partis, vnà cum rectangulo ſub tota, & </s>
            <s xml:id="echoid-s5155" xml:space="preserve">di-
              <lb/>
            cta parte, tanquam ab vna linea, & </s>
            <s xml:id="echoid-s5156" xml:space="preserve">ſub altera parte contento.</s>
            <s xml:id="echoid-s5157" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5158" xml:space="preserve">ESTO data recta A B vtcunque ſecta in C. </s>
            <s xml:id="echoid-s5159" xml:space="preserve">Dico quadratum
              <lb/>
            A B æquale eſſe quadrato alterius partis, nempe A C, vna
              <lb/>
            cum rectangulo ſub B A cum A C, tanquam vna linea, & </s>
            <s xml:id="echoid-s5160" xml:space="preserve">
              <lb/>
            ſub reliqua parte B C comprehenſo. </s>
            <s xml:id="echoid-s5161" xml:space="preserve">Nam producta B A ſu-
              <lb/>
            matur A D æqualis ipſi BC. </s>
            <s xml:id="echoid-s5162" xml:space="preserve">Quoniam igitur D C eſt bifa-
              <lb/>
            riam ſecta in A, ipſique adiecta C B, erit
              <lb/>
            quadratum A B æquale rectangulo ſub
              <lb/>
            D B, B C, vnà cum quadrato C A; </s>
            <s xml:id="echoid-s5163" xml:space="preserve">ſed
              <lb/>
            DB linea conficitur ex D A cum A B, vel
              <lb/>
              <figure xlink:label="fig-0183-01" xlink:href="fig-0183-01a" number="143">
                <image file="0183-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0183-01"/>
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            ex A C cum A B; </s>
            <s xml:id="echoid-s5164" xml:space="preserve">ergo quadratum totius
              <lb/>
            A B æquatur quadrato partis C A, vna
              <lb/>
            cum rectangulo ſub B A cum A C, tan-
              <lb/>
            quam vna linea, & </s>
            <s xml:id="echoid-s5165" xml:space="preserve">ſub reliqua parte B C
              <lb/>
            comprehenſo. </s>
            <s xml:id="echoid-s5166" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s5167" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5168" xml:space="preserve"/>
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          <head xml:id="echoid-head228" xml:space="preserve">LEMMA II. PROP. II.</head>
          <p>
            <s xml:id="echoid-s5169" xml:space="preserve">Si quatuor quantitatum eiuſdem generis, prima ſuperet ſecun-
              <lb/>
            dam maiori exceſſu, quo tertia ſuperat quartam, aggregatum
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            extremarum maius erit aggregato mediarum.</s>
            <s xml:id="echoid-s5170" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5171" xml:space="preserve">SInt quatuor quantitates eiuſdem generis A, B, C, D, & </s>
            <s xml:id="echoid-s5172" xml:space="preserve">prima A ſu-
              <lb/>
            peret ſecundam B, maiori exceſſu, quo tertia C ſuperat quartam D.
              <lb/>
            </s>
            <s xml:id="echoid-s5173" xml:space="preserve">Dico aggregatum extremarum A, D maius eſſe aggregato mediarum B, C.</s>
            <s xml:id="echoid-s5174" xml:space="preserve"/>
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