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

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            quodque in parallelis Parabolis, ac ſimilibus concentricis Hyperbolis in 42.
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            <s xml:id="echoid-s6779" xml:space="preserve">& </s>
            <s xml:id="echoid-s6780" xml:space="preserve">47. </s>
            <s xml:id="echoid-s6781" xml:space="preserve">primi huius, ſed alijs aggreſſionibus oſtenſum fuit.</s>
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        <div xml:id="echoid-div711" type="section" level="1" n="284">
          <head xml:id="echoid-head293" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s6783" xml:space="preserve">HInc eſt, quod in parallelis Parabolis, vel concentricis, ac ſimilibus
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            Hyperbolis, aut Ellipſibus, applicata in interiori ſectione hinc inde
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            producta exteriori neceſſariò occurrit, totaque ab illius diametro bifariam
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            ſecatur, & </s>
            <s xml:id="echoid-s6784" xml:space="preserve">quod huius applicatæ intercepta ſegmenta inter ſe ſunt æqualia.</s>
            <s xml:id="echoid-s6785" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6786" xml:space="preserve">Demonſtratum eſt enim applicatas D E, D F in interiori ſectioni D E F
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            exteriori A B C occurrere in L, M, & </s>
            <s xml:id="echoid-s6787" xml:space="preserve">in G, H, & </s>
            <s xml:id="echoid-s6788" xml:space="preserve">diametros O N, F I,
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            quæ bifariam ſecant D E, D F in N, I, bifariam quoque diuidere totas L
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            M, G H, atque interceptas portiones L D, E M inter ſe æquales eſſe, item-
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            que G D, F H æquales.</s>
            <s xml:id="echoid-s6789" xml:space="preserve"/>
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        <div xml:id="echoid-div712" type="section" level="1" n="285">
          <head xml:id="echoid-head294" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s6790" xml:space="preserve">COnſtat etiam ex vltima parte huius Theorematis, quod, ſi in quacunq;
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            <s xml:id="echoid-s6791" xml:space="preserve">coni-ſectione, vel circulo duæ rectæ lineæ applicatæ fuerint inter ſe
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            æquidiſtantes, ad vtranque partem ſectioni occurrentes, quæ à tertia qua-
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            dam applicata vtcunque ſecentur, rectangula ſub ſegmentis æquidiſtantium
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            eandem inter ſe habere rationem, quam rectangula ſub ſegmentis tertiæ ſe-
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            cantis homologè ſumpta.</s>
            <s xml:id="echoid-s6792" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6793" xml:space="preserve">Ibi enim oſtenſum fuit tùm in Parabola, tùm in Hyperbola, aut Ellipſi,
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            vel circulo A B C, in quibus duę æquidiſtanter applicatæ A C, G H ſecan-
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            tur à tertia applicata L M in punctis E, D, rectangulum G D H ad A E C,
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            eſſe vt rectangulum L D M ad L E M.</s>
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        <div xml:id="echoid-div713" type="section" level="1" n="286">
          <head xml:id="echoid-head295" xml:space="preserve">THEOR. XXVIII. PROP. XLVII.</head>
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            <s xml:id="echoid-s6795" xml:space="preserve">In Hyperbola intra angulum aſymptotalem deſcripta, vel in
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            æquidiſtantibus Parabolis, aut ſimilibus concentricis Hyperbolis,
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            aut Ellipſibus, rectarum in exteriori applicatarum, ac interiorem
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            ſectionem contingentium, MINIMA eſt ea, quæ ad verticem
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            maioris axis ducitur. </s>
            <s xml:id="echoid-s6796" xml:space="preserve">At in Ellipſibus, MAXIMA eſt quæ ad ver-
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            ticem minoris axis.</s>
            <s xml:id="echoid-s6797" xml:space="preserve"/>
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            <s xml:id="echoid-s6798" xml:space="preserve">ESto, in prima figura, in angulo aſymptotali A B C deſcripta Hyperbole
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            D E F, cuius axis B E G, vel in ſecunda, ſint duæ Parabolæ æquidi-
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            ſtantes, vel duæ ſimiles concentricæ Hyperbolæ A B C, D E F circa axim
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            B E; </s>
            <s xml:id="echoid-s6799" xml:space="preserve">aut in tertia, duæ ſimiles concentricæ Ellipſes A B C, D E F, ſitque
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            exterioris ſectionis axis maior B P N, minor O P Q, & </s>
            <s xml:id="echoid-s6800" xml:space="preserve">in interiori ſit </s>
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