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

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        <div xml:id="echoid-div244" type="section" level="1" n="111">
          <head xml:id="echoid-head116" xml:space="preserve">THEOR. XXIII. PROP. XXXXIV.</head>
          <p>
            <s xml:id="echoid-s2580" xml:space="preserve">Hyperbolæ congruentes, per diuerſos vertices ſimul adſcriptæ,
              <lb/>
            ſunt inter ſe nunquam coeuntes, & </s>
            <s xml:id="echoid-s2581" xml:space="preserve">ſemper ſimul accedentes: </s>
            <s xml:id="echoid-s2582" xml:space="preserve">ſed
              <lb/>
            ad interuallum nunquam perueniunt æquale cuidam dato inter-
              <lb/>
            uallo.</s>
            <s xml:id="echoid-s2583" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2584" xml:space="preserve">SInt duæ congruentes Hyperbolæ ABC, DEF per diuerlos vertices B, E
              <lb/>
            ſimul adſcriptæ, quarum recta latera ſint BG, EH (quæ inter ſe æqua-
              <lb/>
            lia erunt) & </s>
            <s xml:id="echoid-s2585" xml:space="preserve">ipſarum tranſuerſa ſint BI, EL (quæ item æqualia erunt
              <note symbol="a" position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            ſectiones ponantur congruentes.) </s>
            <s xml:id="echoid-s2586" xml:space="preserve">Dico primùm has ſectiones nunquam
              <lb/>
            inter ſe conuenire.</s>
            <s xml:id="echoid-s2587" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2588" xml:space="preserve">Nam producta contingente HE donec ſectioni ABC occurrat in A, & </s>
            <s xml:id="echoid-s2589" xml:space="preserve">C,
              <lb/>
            ipſa quoque erit ordinata in ſectione ABC (cum ſint ſectiones ſimul adſcri-
              <lb/>
            ptæ) & </s>
            <s xml:id="echoid-s2590" xml:space="preserve">ſectio DEF tota cadet infra contingentem AEC; </s>
            <s xml:id="echoid-s2591" xml:space="preserve">ſumptoque in ipſa
              <lb/>
            ED quocunque puncto D, applicetur SDO, quæ iunctis regulis IG, LH oc-
              <lb/>
            currat in K, R; </s>
            <s xml:id="echoid-s2592" xml:space="preserve">& </s>
            <s xml:id="echoid-s2593" xml:space="preserve">cum ſit triangulum IBG ſimile triangulo LEH (habent
              <lb/>
            enim circa æquales angulos B, E, æqualia latera, vtrunque vtrique) erit
              <lb/>
            angulus BIG æqualis angulo ELH, vnde regulæ IGK, LHR æquidiſtant,
              <lb/>
            ideoque IK cadit extra LR, cum ſit punctum I ſupra L, ergo OK maior eſt
              <lb/>
            OR, ſed eſt OB maior OE, igitur rectangulum BOK ſiue quadratum
              <note symbol="b" position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">Coroll.
                <lb/>
              1. huius.</note>
            maius eſt rectangulo, EOR ſiue quadrato DO; </s>
            <s xml:id="echoid-s2594" xml:space="preserve">hoc eſt punctum D cadit
              <note symbol="c" position="left" xlink:label="note-0100-03" xlink:href="note-0100-03a" xml:space="preserve">ibidem.</note>
            tra ſectionem ED, & </s>
            <s xml:id="echoid-s2595" xml:space="preserve">ſic de quocunque alio puncto eiuſdem ſectionis infra
              <lb/>
            contingentem EA: </s>
            <s xml:id="echoid-s2596" xml:space="preserve">quapropter huiuſmodi Hyperbolæ inter ſe nunquam
              <lb/>
            conueniunt. </s>
            <s xml:id="echoid-s2597" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2598" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2599" xml:space="preserve"/>
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