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

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            <s xml:id="echoid-s614" xml:space="preserve">Ex dato puncto A ordinatim applicetur A D, occurrens diametro in
              <lb/>
            D, & </s>
            <s xml:id="echoid-s615" xml:space="preserve">fiat vt C D ad D B, ita C E ad E B, iungaturque E A: </s>
            <s xml:id="echoid-s616" xml:space="preserve">dico ipſam
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            E A ſectionem contingere.</s>
            <s xml:id="echoid-s617" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s618" xml:space="preserve">Etenim ſumpto in ea quocunque puncto F, vel ſupra, vel infra A,
              <lb/>
            ordinatim agatur F H G, ſectionem ſecans in H, diametrum in G, & </s>
            <s xml:id="echoid-s619" xml:space="preserve">ſu-
              <lb/>
            per tranſuerſo B C deſcribatur ſemicirculus B L C, cuius diametto B C
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            in Ellipſi ex puncto D erigatur perpendicularis D L, iungaturque E L,
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            quæ, per Lemma antecedens, erit ipſi circulo contingens in L. </s>
            <s xml:id="echoid-s620" xml:space="preserve">At in
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            Hyperbola ex E puncto ducta ſit diametro C B perpendicularis E L, iun-
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            gaturque D L, quæ item, ob præmiſſum Lemma, ſemi-circulum B L C
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            continget in L, & </s>
            <s xml:id="echoid-s621" xml:space="preserve">ex G ipſi D L æquidiſtans ducatur G I ſemi-circulum
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              <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a" number="10">
                <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0034-01"/>
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            primæ figuræ ſecans in M, in qua cum ſit E L I contingens in L, erit ap-
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            plicata G I maior G M, ſiue quadratum G I maius quadrato G M, vel
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            maius rectangulo C G B, ſed eſt quoque, per idem Lemma, quadratum
              <lb/>
            G I (in ſecunda figura) maius rectangulo C G B, quare in vtraque figu-
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            ra quadratum G I ad quadratum D L, vel quadratum G E ad quadratum
              <lb/>
            E D, vel quadratnm G F ad quadratum D A, maiorem habebit rationem
              <lb/>
            quàm rectangulum C G B ad idem quadratum D L, vel ad rectangulum
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            C D B, ſed vt rectangulum C G B ad rectangulum C D B, ita
              <note symbol="a" position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">21. pri-
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              mi conic.</note>
            tum G H ad quadratum D A, ergo quadratum G F ad quadratum D A
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            maiorem habet rationem quàm quadratum G H ad idem quadratum D
              <lb/>
            A; </s>
            <s xml:id="echoid-s622" xml:space="preserve">quare quadratum G F maius eſt quadrato G H: </s>
            <s xml:id="echoid-s623" xml:space="preserve">vnde punctum F ca-
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            dit extra ſectionem, & </s>
            <s xml:id="echoid-s624" xml:space="preserve">ſic de quibuslibet alijs punctis rectæ E A F, præ-
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            ter A. </s>
            <s xml:id="echoid-s625" xml:space="preserve">Ducta eſt ergo E A ſectionem contingens in A. </s>
            <s xml:id="echoid-s626" xml:space="preserve">Quod erat fa-
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            ciendum.</s>
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