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

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          <head xml:id="echoid-head239" xml:space="preserve">THEOR. VIII. PROP. XII.</head>
          <p>
            <s xml:id="echoid-s5526" xml:space="preserve">Si per punctum quodlibet ſumptum in angulo à rectis lineis
              <lb/>
            comprehenſo, quarum altera ſit datæ Parabolæ, vel Hyperbo-
              <lb/>
            læ diameter, aut ipſi æquidiſtans, altera verò ſit quęlibet ſectio-
              <lb/>
            ni ordinatim ducta, vel huic parallela, deſcripta ſit ſectio Hy-
              <lb/>
            perbole, cuius aſymptoti ſint prædicti anguli latera; </s>
            <s xml:id="echoid-s5527" xml:space="preserve">huiuſmodi
              <lb/>
            Hyperbole datam ſectionem in vno tantùm puncto neceſſariò
              <lb/>
            ſecabit.</s>
            <s xml:id="echoid-s5528" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5529" xml:space="preserve">ESto Parabole, vel Hyperbole A B, cuius diameter, vel diametro æ-
              <lb/>
            quidiſtans ſit B C, quàm ad quemcunque angulum D E C ſecet D
              <lb/>
            E, quæ vel ſit vna applicatarum in ſectione, vel ipſis æquidiſtans, & </s>
            <s xml:id="echoid-s5530" xml:space="preserve">in
              <lb/>
            angulo D E C, per datum in eo punctum F, deſcribatur Hyperbole G
              <note symbol="a" position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">4. ſec.
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              conic.</note>
            H, cuius aſymptoti ſint D E, E C. </s>
            <s xml:id="echoid-s5531" xml:space="preserve">Dico hancvltrò, citroque productam,
              <lb/>
            in vno tantùm puncto ſectionem ſecare.</s>
            <s xml:id="echoid-s5532" xml:space="preserve"/>
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            <image file="0197-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0197-01"/>
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          <p>
            <s xml:id="echoid-s5533" xml:space="preserve">Ductis enim, in prima figura, per punctum F, quod eſt in ſectione
              <lb/>
            A B, rectis L F M, I F K aſymptotis D E, E C æquidiſtantibus, eiſque
              <lb/>
            occurrentibus in M, K. </s>
            <s xml:id="echoid-s5534" xml:space="preserve">Patet rectam M F L etiam ſi in infinitum produ-
              <lb/>
            ctam ad partes L, in ipſo tantùm puncto F ſectioni A B occurrere, cum
              <lb/>
            ſit vna applicatarum in data ſectione; </s>
            <s xml:id="echoid-s5535" xml:space="preserve">& </s>
            <s xml:id="echoid-s5536" xml:space="preserve">rectam I F K in eodem tantùm
              <lb/>
              <note symbol="b" position="right" xlink:label="note-0197-02" xlink:href="note-0197-02a" xml:space="preserve">26. pri-
                <lb/>
              mi conic.</note>
            puncto F cum ſectione A B conuenire cum ipſa rectæ B C, vel diame- tro datæ ſectionis æquidiſtet: </s>
            <s xml:id="echoid-s5537" xml:space="preserve">ſed Hyperbole G F H à puncto F ad par-
              <lb/>
            tes G, tota incedit in angulo K F L, & </s>
            <s xml:id="echoid-s5538" xml:space="preserve">inter æquidiſtantes F L, K D; </s>
            <s xml:id="echoid-s5539" xml:space="preserve">& </s>
            <s xml:id="echoid-s5540" xml:space="preserve">
              <lb/>
            à puncto F ad partes H, tota incedit in angulo M F I, ac inter paralle-
              <lb/>
            las F I, M C. </s>
            <s xml:id="echoid-s5541" xml:space="preserve">quare ipſa Hyperbole G F H in nullo alio puncto quàm F
              <lb/>
            ſectioni A B occurret.</s>
            <s xml:id="echoid-s5542" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5543" xml:space="preserve">In ſecunda verò, ac tertia figura, ductis ex dato puncto F (quod ibi
              <lb/>
            extra cadit, hic verò intra ſectionem) rectis F L, F I alteri </s>
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