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

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          <head xml:id="echoid-head298" xml:space="preserve">THEOR. XXXI. PROP. L.</head>
          <p>
            <s xml:id="echoid-s6886" xml:space="preserve">MAXIMA portionum eiuſdem anguli rectilinei, vel cuiuſcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s6887" xml:space="preserve">coni-ſectionis, quarum baſes ſint æquales, eſt ea, cuius diameter
              <lb/>
            ſit ſegmentum axis, vel maioris ſemi- axis (reſpectiuè ad Ellipſim)
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            datæ ſectionis. </s>
            <s xml:id="echoid-s6888" xml:space="preserve">MINIMA verò in Ellipſi eſt, cuius diameter ſit ſe-
              <lb/>
            gmentum minoris ſemi- axis.</s>
            <s xml:id="echoid-s6889" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6890" xml:space="preserve">ESto A B C angulus rectilineus, vt in prima figura; </s>
            <s xml:id="echoid-s6891" xml:space="preserve">vel Parabole, aut
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            Hyperbole, vt in ſecunda; </s>
            <s xml:id="echoid-s6892" xml:space="preserve">vel Ellipſis, vt in tertia, quarum axes ſint B
              <lb/>
            D, & </s>
            <s xml:id="echoid-s6893" xml:space="preserve">in Ellipſi axis maior ſit B D N, minor L K M, centrum E, atque ma-
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            iori axi in quauis figura applicata ſit quęcunque A D C. </s>
            <s xml:id="echoid-s6894" xml:space="preserve">Dico primùm por-
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            tionem A B C, quæ tamen in tertia figura ſit minor ſemi-Ellipſi L B M, eſſe
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            _MAXIMAM_ omnium portionum eiuſdem anguli, vel coni-ſectionis, qua-
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            rum baſes æquales ſint baſi A C.</s>
            <s xml:id="echoid-s6895" xml:space="preserve"/>
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          <figure number="205">
            <image file="0249-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0249-01"/>
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            <s xml:id="echoid-s6896" xml:space="preserve">Nam, in prima figura, deſcribatur per D in angulo aſymptotali A B C
              <lb/>
            Hyperbole F D G, in ſecunda verò, ſi A B C fuerit Parabole, deſcribatur per
              <lb/>
            D congruens Parabole F D G, vel ſi fuerit Hyperbole, deſcribatur item per
              <lb/>
            D, vti etiam in tertia, eiuſdem nominis ſectio F D G ſimilis, & </s>
            <s xml:id="echoid-s6897" xml:space="preserve">concentri-
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            ca ipſi A B C, & </s>
            <s xml:id="echoid-s6898" xml:space="preserve">tunc recta A D C continget omnino ſectionem F D G in
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            D; </s>
            <s xml:id="echoid-s6899" xml:space="preserve">ſumptoque in interiori ſectione F D G quolibet puncto F, per ipſum
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            ducatur ſectionem contingens H F I exteriori occurrens in H I, deque ipſa
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            abſcindens portionem H O I, cuius diameter ſit O F.</s>
            <s xml:id="echoid-s6900" xml:space="preserve"/>
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            <s xml:id="echoid-s6901" xml:space="preserve">Iam, in ſingulis ſiguris, baſis A C minor eſt baſi H I, cum ſit
              <note symbol="a" position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">47. h.</note>
            contingentium ſectionem F D G, quare, & </s>
            <s xml:id="echoid-s6902" xml:space="preserve">dimidium D C dimidio F I mi-
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            nus erit. </s>
            <s xml:id="echoid-s6903" xml:space="preserve">Fiat ergo F P æqualis D C, & </s>
            <s xml:id="echoid-s6904" xml:space="preserve">ex P agatur P R diametro F O
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            æquidiſtans, cui ex R applicetur R Q S: </s>
            <s xml:id="echoid-s6905" xml:space="preserve">patet ipſam R Q S ęquari baſi A </s>
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