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

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            <s xml:id="echoid-s1016" xml:space="preserve">
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            diametro DE deſcribatur Parabole ADG, cuius AE ſit eius ſemi-applicata:
              <lb/>
            </s>
            <s xml:id="echoid-s1017" xml:space="preserve">dico primum Parabolen ADG, etiam ſi in infinitum producatur, totam ca-
              <lb/>
            dere intra ABC, & </s>
            <s xml:id="echoid-s1018" xml:space="preserve">ſi ex A ducatur quæcunque ANMH, ipſam à Parabola
              <lb/>
            ADG ſecari in O, in eadem ratione, ac AC ſecatur in G, & </s>
            <s xml:id="echoid-s1019" xml:space="preserve">AB in D.</s>
            <s xml:id="echoid-s1020" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1021" xml:space="preserve">Ducta enim ex A recta AP contingente Parabolen ABC, erit FB æqualis
              <lb/>
            BP; </s>
            <s xml:id="echoid-s1022" xml:space="preserve">ideoque ED æqualis DR, vnde AR continget Parabolen ADG, & </s>
            <s xml:id="echoid-s1023" xml:space="preserve">AH
              <lb/>
            ſecabit ipſam in O.</s>
            <s xml:id="echoid-s1024" xml:space="preserve"/>
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          <figure number="24">
            <image file="0048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0048-01"/>
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          <p>
            <s xml:id="echoid-s1025" xml:space="preserve">Iam ductis ex H, O, ſemi - applicatis HI, OL, erit, ob Parabolen, FB ad
              <lb/>
            BI, vt quadratum AF ad HI, vel vt quadratum FM ad quadratum MI; </s>
            <s xml:id="echoid-s1026" xml:space="preserve">qua-
              <lb/>
            re per Lemma præcedens, erit FB ad BM, vt BM ad BI, & </s>
            <s xml:id="echoid-s1027" xml:space="preserve">per Coroll. </s>
            <s xml:id="echoid-s1028" xml:space="preserve">eiuſ-
              <lb/>
            dem, in vtraque figura, erit FM ad MI, vt FB ad BM; </s>
            <s xml:id="echoid-s1029" xml:space="preserve">eadem penitus ratio-
              <lb/>
            ne oſtendetur eſſe EN ad NL, vt ED ad DN, ſed eſt FB ad BM, vt ED ad
              <lb/>
            DN, quare & </s>
            <s xml:id="echoid-s1030" xml:space="preserve">FM ad MI erit vt EN ad NL, ſed FM ad MI, eſt vt AM ad MH,
              <lb/>
            & </s>
            <s xml:id="echoid-s1031" xml:space="preserve">EN ad NL, vt AN ad NO, quare AM ad MH erit vt AN ad NO, & </s>
            <s xml:id="echoid-s1032" xml:space="preserve">in pri-
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            ma figura conuertendo, componendo, & </s>
            <s xml:id="echoid-s1033" xml:space="preserve">permutando, HA ad AO, vt MA
              <lb/>
            ad AN; </s>
            <s xml:id="echoid-s1034" xml:space="preserve">in ſecunda verò per conuerſionem rationis, conuertendo, & </s>
            <s xml:id="echoid-s1035" xml:space="preserve">per-
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            mutando HA ad AO erit vt MA ad AN. </s>
            <s xml:id="echoid-s1036" xml:space="preserve">Eſt igitur in vtraque figura HA ad
              <lb/>
            AO, vt MA ad AN, vel vt BA ad AD, ſed eſt BA maior AD ex conſtru-
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            ctione, quare & </s>
            <s xml:id="echoid-s1037" xml:space="preserve">HA erit maior AO, ſed HA tota eſt intra Parabolen ABC,
              <lb/>
            vnde punctum O, quod eſt in Parabola ADG erit intra Parabolen ABC, & </s>
            <s xml:id="echoid-s1038" xml:space="preserve">
              <lb/>
            ſic de quocunque alio puncto Parabolæ ADG, etiam ſi ducta AH cadat in-
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            fra AC; </s>
            <s xml:id="echoid-s1039" xml:space="preserve">quare ipſa cadit tota intra ABC: </s>
            <s xml:id="echoid-s1040" xml:space="preserve">& </s>
            <s xml:id="echoid-s1041" xml:space="preserve">cum ſit HA ad AO, vt BA ad
              <lb/>
            AD, vel vt FA ad AE, vel ſumptis duplis, vt CA ad AG, erit diuidendo
              <lb/>
            HO ad OA, vt CG ad GA. </s>
            <s xml:id="echoid-s1042" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s1043" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1044" xml:space="preserve"/>
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          <figure number="25">
            <image file="0048-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0048-02"/>
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