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

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        <div xml:id="echoid-div237" type="section" level="1" n="107">
          <p>
            <s xml:id="echoid-s2536" xml:space="preserve">
              <pb o="74" file="0098" n="98" rhead=""/>
            interceptæ applicatarum portiones à contingente AE magis remouentur eò
              <lb/>
            ſunt minores, vnde tales ſectiones ad ſe propiùs accedunt. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">Sed quod de
              <lb/>
            congruentibus, ſiue æqualibus parabolis hactenus expoſuimus, & </s>
            <s xml:id="echoid-s2538" xml:space="preserve">iam olim
              <lb/>
            demonſtrauimus (dum Aſymptoton doctrina promoueri poſſe animaduer-
              <lb/>
            timus) maximos poſtea Geometras, Torricellium nempe, ac Gregorium à
              <lb/>
            S. </s>
            <s xml:id="echoid-s2539" xml:space="preserve">Vincentio aliter quoque oſtendiſſe reperimus, quorum edita opera ad
              <lb/>
            vberiorem de hac re eruditionem conſulere ſuademus.</s>
            <s xml:id="echoid-s2540" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2541" xml:space="preserve">Dico tandem has con-
              <lb/>
              <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a" number="67">
                <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0098-01"/>
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            gruentes Parabolas ad in-
              <lb/>
            teruallum ſimul peruenire
              <lb/>
            minus quocunque dato in-
              <lb/>
            teruallo 1 2. </s>
            <s xml:id="echoid-s2542" xml:space="preserve">Fiat enim vt
              <lb/>
            1 2 ad AE, ita AE ad 2 3
              <lb/>
            quæ ipſi 1 2 indirectum po-
              <lb/>
            natur, & </s>
            <s xml:id="echoid-s2543" xml:space="preserve">tota 1 3 bifariam
              <lb/>
            ſecetur in 4, & </s>
            <s xml:id="echoid-s2544" xml:space="preserve">per B appli-
              <lb/>
            cetur BK ęqualis 1 4; </s>
            <s xml:id="echoid-s2545" xml:space="preserve">aga-
              <lb/>
            turque KI parallela ad BX,
              <lb/>
            & </s>
            <s xml:id="echoid-s2546" xml:space="preserve">per I recta IDS contingẽti
              <lb/>
            BK æquidiſtans, erit ergo
              <lb/>
            IX æqualis KB, ſiue 4 1;
              <lb/>
            </s>
            <s xml:id="echoid-s2547" xml:space="preserve">eſtque IX dimidium IS, & </s>
            <s xml:id="echoid-s2548" xml:space="preserve">
              <lb/>
            4 1 dimidium 1 3; </s>
            <s xml:id="echoid-s2549" xml:space="preserve">quare
              <lb/>
            IS, 1 3 ſunt æquales; </s>
            <s xml:id="echoid-s2550" xml:space="preserve">ſed
              <lb/>
            factum eſt rectangulum 1 2 3 æquale quadrato AE, & </s>
            <s xml:id="echoid-s2551" xml:space="preserve">rectangulum IDS
              <lb/>
            oſtenſum eſt æquale eidem quadrato AE, ergo rectangula IDS, 1 2 3 in-
              <lb/>
            ter ſe ſunt æqualia; </s>
            <s xml:id="echoid-s2552" xml:space="preserve">ſed rectæ IS, 1 3, ſunt æquales, quare ſegmentum ID
              <lb/>
            æquatur dato interuallo 1 2; </s>
            <s xml:id="echoid-s2553" xml:space="preserve">interceptæ verò infra ID ſunt minores ipſa
              <lb/>
            intercepta ID, quapropter huiuſmodi congruentes Parabolę ad interuallum
              <lb/>
            perueniunt minus dato interuallo 1 2. </s>
            <s xml:id="echoid-s2554" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s2555" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div240" type="section" level="1" n="108">
          <head xml:id="echoid-head113" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s2556" xml:space="preserve">EXhac patet, in congruentibus Parabolis per diuerſos vertices ſimul ad-
              <lb/>
            ſcriptis, omnes, inter eas, interceptas lineas communi diametro ęqui-
              <lb/>
            diſtanter ductas, eſſe inter ſe æquales, quales ſunt EB, DN, &</s>
            <s xml:id="echoid-s2557" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2558" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div241" type="section" level="1" n="109">
          <head xml:id="echoid-head114" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s2559" xml:space="preserve">PAtet quoque, ex penultima parte huius, rectangula ſegmentorum ap-
              <lb/>
            plicatarum vtranque Parabolen ſecantium omnia inter ſe æqualia eſſe,
              <lb/>
            qualia ſunt rectangula LMY, IDS, &</s>
            <s xml:id="echoid-s2560" xml:space="preserve">c.</s>
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