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

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            <s xml:id="echoid-s2478" xml:space="preserve">
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            in ipſa DEF, quocunque puncto D, per ipſum ordinatim applicetur ODS,
              <lb/>
            alteram ſectionem ſecans in S: </s>
            <s xml:id="echoid-s2479" xml:space="preserve">erit quadratum SO æquale rectãgulo
              <note symbol="a" position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">1. huius.</note>
            & </s>
            <s xml:id="echoid-s2480" xml:space="preserve">quadratum DO rectangulo OEH, ſed rectangulum OBG maius eſt rectã-
              <lb/>
            gulo OEH, cum latitudo BG æqualis ſit EH, altitudo verò BO maior EO,
              <lb/>
            quare SO quadratum, maius eſt quadrato DO; </s>
            <s xml:id="echoid-s2481" xml:space="preserve">vnde punctum D cadit intra
              <lb/>
            Parabolen BA, & </s>
            <s xml:id="echoid-s2482" xml:space="preserve">ſic de quibuslibet alijs pũctis Parabolæ DEF; </s>
            <s xml:id="echoid-s2483" xml:space="preserve">ergo huiuſ-
              <lb/>
            modi ſectiones inter ſe nunquam conueniunt. </s>
            <s xml:id="echoid-s2484" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2485" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2487" xml:space="preserve">Has tamen dico, licet in infinitum productas, infra contingentem EA ad
              <lb/>
            ſe propiùs accedere: </s>
            <s xml:id="echoid-s2488" xml:space="preserve">Ducta enim DM parallela ad ON, & </s>
            <s xml:id="echoid-s2489" xml:space="preserve">per M applicata
              <lb/>
            MN, fiet parallelogrammum DN, cuius oppoſita latera MN, DO æqualia
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s2490" xml:space="preserve">Iam quadratum MN, ſiue rectangulum NBG æquatur
              <note symbol="b" position="left" xlink:label="note-0096-02" xlink:href="note-0096-02a" xml:space="preserve">ibidem.</note>
            DO, ſiue rectangulo OEH, ſed horum latera BG, EH æqualia ſunt,
              <note symbol="c" position="left" xlink:label="note-0096-03" xlink:href="note-0096-03a" xml:space="preserve">ibidem.</note>
            & </s>
            <s xml:id="echoid-s2491" xml:space="preserve">latera BN, EO æqualia erunt: </s>
            <s xml:id="echoid-s2492" xml:space="preserve">itaque per proſtaphereſim, erit BE æqualis
              <lb/>
            NO, ſed eſt quoque MD æqualis eidem NO, igitur BE, & </s>
            <s xml:id="echoid-s2493" xml:space="preserve">MD inter ſe ſunt
              <lb/>
              <figure xlink:label="fig-0096-01" xlink:href="fig-0096-01a" number="65">
                <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0096-01"/>
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            æquales, at ſunt quoque parallelæ, igitur coniunctæ BM, & </s>
            <s xml:id="echoid-s2494" xml:space="preserve">ED æquales
              <lb/>
            erunt, & </s>
            <s xml:id="echoid-s2495" xml:space="preserve">parallelæ, ſed BM ſecat NM, quare producta ſecabit quoque alte-
              <lb/>
            ram parallelarum OD, ſed extra ſectionem BMA (cum ſit BM intra ſectio-
              <lb/>
            nem, producta verò, tota cadat extra) ſit ergo occurſus cum ODS in P, & </s>
            <s xml:id="echoid-s2496" xml:space="preserve">
              <lb/>
            cum contingente EA in T; </s>
            <s xml:id="echoid-s2497" xml:space="preserve">& </s>
            <s xml:id="echoid-s2498" xml:space="preserve">in ſecunda figura, in qua contingens EA cadit
              <lb/>
            inter applicatas MN, OS, iungatur SM ſecans EA in V.</s>
            <s xml:id="echoid-s2499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2500" xml:space="preserve">Iam in prima figura, cum in parallelogrammo PE latera ET, DP, ſint æ-
              <lb/>
            qualia, ſitque EA maius ET, erit EA quoque maius DP, eſtque DP maius
              <lb/>
            intercepto ſegmento DS, quare AE, eò maius erit ipſo DS. </s>
            <s xml:id="echoid-s2501" xml:space="preserve">In ſecunda au-
              <lb/>
            tem figura, cum pariter ET, DP ſint æquales, ſitque ablata TV minor abla-
              <lb/>
            ta PS, erit reliqua EV maior reliqua DS, & </s>
            <s xml:id="echoid-s2502" xml:space="preserve">eò magis EA maior eadem DS.
              <lb/>
            </s>
            <s xml:id="echoid-s2503" xml:space="preserve">Non abſimili modò oſtendetur quamcunque interceptam XY infra SD, mi-
              <lb/>
            norem eſſe ipſa SD; </s>
            <s xml:id="echoid-s2504" xml:space="preserve">ducta enim YZ æquidiſtanter EB, demonſtrabitur item
              <lb/>
            YZ æqualis eidem BE, ideoque YZ, & </s>
            <s xml:id="echoid-s2505" xml:space="preserve">DM inter ſe æquales erunt, & </s>
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