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

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          <p>
            <s xml:id="echoid-s2506" xml:space="preserve">
              <pb o="73" file="0097" n="97" rhead=""/>
            rallelæ, ex quò ſi iungatur MZ, & </s>
            <s xml:id="echoid-s2507" xml:space="preserve">DY, ipſæ æquales, & </s>
            <s xml:id="echoid-s2508" xml:space="preserve">parallelæ erunt, & </s>
            <s xml:id="echoid-s2509" xml:space="preserve">
              <lb/>
            facta conſtructione vt ſupra, idem omninò demonſtrabitur, nempe interce-
              <lb/>
            ptam YX minorem adhuc eſſe ipſa DS. </s>
            <s xml:id="echoid-s2510" xml:space="preserve">Huiuſmodi igitur Parabolæ con-
              <lb/>
            gruentes, quò magis à tangente EA remouentur ad ſe propiùs accedunt:
              <lb/>
            </s>
            <s xml:id="echoid-s2511" xml:space="preserve">quod ſecundò, &</s>
            <s xml:id="echoid-s2512" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2513" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div237" type="section" level="1" n="107">
          <head xml:id="echoid-head112" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s2514" xml:space="preserve">SEd hoc idem aliter in nouo hoc ſchemate, in quo item oſtendetur inter-
              <lb/>
            ceptam contingentem EA maiorem eſſe intercepta applicata DI, & </s>
            <s xml:id="echoid-s2515" xml:space="preserve">DI
              <lb/>
            maiorem infra intercepta
              <lb/>
              <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a" number="66">
                <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0097-01"/>
              </figure>
            ML, & </s>
            <s xml:id="echoid-s2516" xml:space="preserve">hoc ſemper, ſi ſectio-
              <lb/>
            nes in infinitum producan-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s2517" xml:space="preserve">Ducta enim DN paral-
              <lb/>
            lela ad EB, eadem penitus
              <lb/>
            methodo, qua ſuperiùs vſi
              <lb/>
            ſumus, demonſtrabimus DN
              <lb/>
            ipſi EB æqualem eſſe, & </s>
            <s xml:id="echoid-s2518" xml:space="preserve">pa-
              <lb/>
            rallelam, quare, & </s>
            <s xml:id="echoid-s2519" xml:space="preserve">coniun-
              <lb/>
            ctæ BN, ED æquales erunt,
              <lb/>
            ac parallelæ: </s>
            <s xml:id="echoid-s2520" xml:space="preserve">ſi ergo BN ſe-
              <lb/>
            cetur bifariam in O, duca-
              <lb/>
            turque POT diametro BE
              <lb/>
            æquidiſtans, patet ipſam
              <lb/>
            TOP eſſe vtriuſque
              <note symbol="a" position="right" xlink:label="note-0097-01" xlink:href="note-0097-01a" xml:space="preserve">46. pri-
                <lb/>
              mi conic.</note>
            bolæ diametrum, & </s>
            <s xml:id="echoid-s2521" xml:space="preserve">BN eſſe
              <lb/>
            vnam ei applicatarum in
              <lb/>
            Parabola ABC, vti etiam QDER ipſi NB æquidiſtantem: </s>
            <s xml:id="echoid-s2522" xml:space="preserve">quapropter QP,
              <lb/>
            & </s>
            <s xml:id="echoid-s2523" xml:space="preserve">PR æquales erunt, ſed eſt DP æqualis PE (ob parallelas, & </s>
            <s xml:id="echoid-s2524" xml:space="preserve">quia NO
              <lb/>
            æquatur OB) quare reliquæ QD, ER æquales erunt, ideoque rectangulum
              <lb/>
            QDR æquabitur rectangulo QER. </s>
            <s xml:id="echoid-s2525" xml:space="preserve">Ampliùs ducatur TV æquidiſtans ad
              <lb/>
            QR, vel ad NB: </s>
            <s xml:id="echoid-s2526" xml:space="preserve">patet TV ſectionem contingere in T, & </s>
            <s xml:id="echoid-s2527" xml:space="preserve">contingenti
              <note symbol="b" position="right" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">32. pri-
                <lb/>
              mi conic.</note>
            occurrere in V, (nam hæc, cum ſecet in B alteram parallelarum BN, ſecat
              <lb/>
            quoque reliquam TV.) </s>
            <s xml:id="echoid-s2528" xml:space="preserve">Cumque duæ rectæ TV, BV, ſectionem ABC con-
              <lb/>
            tingentes, in vnum conueniant, ſitque QR ipſi TV, atque IS, & </s>
            <s xml:id="echoid-s2529" xml:space="preserve">AC ipſi BV
              <lb/>
            æquidiſtantes, ac ſe mutuò ſecantes in D, & </s>
            <s xml:id="echoid-s2530" xml:space="preserve">E, erit rectangulum QDR ad
              <lb/>
            IDS, vt quadratum TV ad BV quadratum, itemque rectangulum QER
              <note symbol="c" position="right" xlink:label="note-0097-03" xlink:href="note-0097-03a" xml:space="preserve">17. tertil
                <lb/>
              conic.</note>
            AEC, vt idem quadratum TV ad BV, quare vt rectãgulum QDR ad
              <note symbol="d" position="right" xlink:label="note-0097-04" xlink:href="note-0097-04a" xml:space="preserve">ibidem.</note>
            ita rectangulum QER ad AEC, & </s>
            <s xml:id="echoid-s2531" xml:space="preserve">permutando rectangulum QDR ad QER,
              <lb/>
            vt rectangulum IDS ad AEC, ſed QDR, QER ſunt ęqualia, vt modò oſten-
              <lb/>
            dimus, ergo & </s>
            <s xml:id="echoid-s2532" xml:space="preserve">rectangulum IDS æquatur rectangulo AEC, ſiue quadrato
              <lb/>
            AE, quare vt SD ad EA, ita EA ad DI, ſed SD maior eſt EA, cum ſit
              <note symbol="e" position="right" xlink:label="note-0097-05" xlink:href="note-0097-05a" xml:space="preserve">32. h.</note>
            maior CE ſiue EA, vnde AE quoque, maior erit DI. </s>
            <s xml:id="echoid-s2533" xml:space="preserve">Eadem ratione oſten-
              <lb/>
            detur rectangulum LMX æquale quadrato AE: </s>
            <s xml:id="echoid-s2534" xml:space="preserve">vnde rectangula IDS, LMY
              <lb/>
            inter ſe æqualia erunt, ſed eſt latus MY maius later@ DS, cum eius ſegmen-
              <lb/>
            tum ZY maius ſit huius ſegmento XS, & </s>
            <s xml:id="echoid-s2535" xml:space="preserve">reliquum ſegmentum MZ
              <note symbol="f" position="right" xlink:label="note-0097-06" xlink:href="note-0097-06a" xml:space="preserve">ibidem.</note>
            reliquo ſegmento DX, quare latus LM minus erit latere ID, & </s>
            <s xml:id="echoid-s2536" xml:space="preserve">ſemper, </s>
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