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

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          <head xml:id="echoid-head247" xml:space="preserve">THEOR. XIV. PROP. XIX.</head>
          <p>
            <s xml:id="echoid-s5687" xml:space="preserve">Si à puncto, quod eſt in angulo aſymptotali, ductæ ſint re-
              <lb/>
            ctæ lineæ aſymptotis æquidiſtantes, & </s>
            <s xml:id="echoid-s5688" xml:space="preserve">Hyperbolæ occurrentes,
              <lb/>
            atque ex vnius eductarum occurſu agatur recta, quæ ſectionem,
              <lb/>
            vel in ipſo tangens puncto, vel alibi ſecans, producta ſecet
              <lb/>
            quoque eam aſymptoton, cui altera eductarum æqui diſtat; </s>
            <s xml:id="echoid-s5689" xml:space="preserve">re-
              <lb/>
            cta linea iungens hoc idem punctum cum puncto contactus, vel
              <lb/>
            interſectionis nouiter ductæ lineæ cum Hyperbola, æquidiſtabit
              <lb/>
            rectæ, quę ab occurſu eiuſdem lineæ cum prædicta aſymptoto
              <lb/>
            ad datum punctum educitur.</s>
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          <figure number="164">
            <image file="0204-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0204-01"/>
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            <s xml:id="echoid-s5691" xml:space="preserve">SIt Hyperbole A B C, in cuius angulo aſymptotali E D F ſumptum ſit
              <lb/>
            quodlibet punctum G, vel extra Hyperbolen, vt in prima, ſecunda,
              <lb/>
            & </s>
            <s xml:id="echoid-s5692" xml:space="preserve">tertia; </s>
            <s xml:id="echoid-s5693" xml:space="preserve">vel intra, vt in quarta, quinta, & </s>
            <s xml:id="echoid-s5694" xml:space="preserve">ſexta figura, à quo ductæ
              <lb/>
            ſint aſymptotis æquidiſtantes G A, G C, ſectioni occurrentes in A, C;
              <lb/>
            </s>
            <s xml:id="echoid-s5695" xml:space="preserve">& </s>
            <s xml:id="echoid-s5696" xml:space="preserve">ex altero occurſuum C ducta ſit quæcunque alia C B E, quæ, vel ſe-
              <lb/>
            ctionem contingat in C, vt in prima, & </s>
            <s xml:id="echoid-s5697" xml:space="preserve">quarta figura, vel alibi ſecet in
              <lb/>
            B, vt in reliquis, & </s>
            <s xml:id="echoid-s5698" xml:space="preserve">producta conueniat cum aſymptoto D E, quæ rectæ
              <lb/>
            G A ęquidiſtat. </s>
            <s xml:id="echoid-s5699" xml:space="preserve">Dico, ſi iungantur A B, E G ipſas inter ſe æquidiſtare.</s>
            <s xml:id="echoid-s5700" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5701" xml:space="preserve">Nam ducta B H parallela ad F D, productiſque A G, C G vſque ad
              <lb/>
            aſymptotos in F, L; </s>
            <s xml:id="echoid-s5702" xml:space="preserve">& </s>
            <s xml:id="echoid-s5703" xml:space="preserve">E B C ad aliam aſymptoton D F in I. </s>
            <s xml:id="echoid-s5704" xml:space="preserve">Erit iuncta
              <lb/>
            A B iunctæ H F parallela, eſt autem E B æqualis C I; </s>
            <s xml:id="echoid-s5705" xml:space="preserve">quare, ob
              <note symbol="a" position="left" xlink:label="note-0204-01" xlink:href="note-0204-01a" xml:space="preserve">13. h.</note>
            lelas B H, C L, I D, erit quoque E H æqualis ipſi L D, ſiue ęqualis G F;</s>
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