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

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        <div xml:id="echoid-div579" type="section" level="1" n="234">
          <head xml:id="echoid-head242" xml:space="preserve">THEOR. XI. PROP. XV.</head>
          <p>
            <s xml:id="echoid-s5592" xml:space="preserve">Si à puncto, quod eſt intra Hyperbolen, ductæ ſint duæ re-
              <lb/>
            ctæ lineæ aſymptotis æquidiſtantes, & </s>
            <s xml:id="echoid-s5593" xml:space="preserve">Hyperbolæ in duobus
              <lb/>
            punctis occurrentes, è quorum altero ducta ſit recta linea vtran-
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            que aſymptoton ſecans, à qua, producta in angulo, qui aſym-
              <lb/>
            ptotalis eſt ad verticem, à puncto alteram aſymptoton ſecans
              <lb/>
            dematur æqualis ei, quę inter eductæ occurſum cum alia aſym-
              <lb/>
            ptoto intercipitur: </s>
            <s xml:id="echoid-s5594" xml:space="preserve">recta linea hoc idem occurſum iungens cum
              <lb/>
            dato puncto, æquidiſtabit rectæ, ſumptæ terminum iungenti, & </s>
            <s xml:id="echoid-s5595" xml:space="preserve">
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            ſectionis punctum, in quo conuenit recta alteri aſymptoto ęqui-
              <lb/>
            diſtanter ducta.</s>
            <s xml:id="echoid-s5596" xml:space="preserve"/>
          </p>
          <figure number="160">
            <image file="0200-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0200-01"/>
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          <p>
            <s xml:id="echoid-s5597" xml:space="preserve">ESto intra Hyperbolen A B, cuius centrum C, & </s>
            <s xml:id="echoid-s5598" xml:space="preserve">aſymptoti C D,
              <lb/>
            C E vltra centrum productæ, ſumptum quodcunque punctum F, à
              <lb/>
            quo ductæ ſint F A D, F B E aſymptotis æquidiſtantes, quæ Hyperbolen
              <lb/>
            ſecent in punctis A, B, è quorum altero, vt ex B, ducta ſit quæcunque
              <lb/>
            B I aſymptoton C E ſecans in G, & </s>
            <s xml:id="echoid-s5599" xml:space="preserve">C D in H, ſumptaque H I æquali,
              <lb/>
            & </s>
            <s xml:id="echoid-s5600" xml:space="preserve">in directum ipſi B G, iungantur rectæ I A, G F. </s>
            <s xml:id="echoid-s5601" xml:space="preserve">Dico has inter ſe eſſe
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            parallelas.</s>
            <s xml:id="echoid-s5602" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5603" xml:space="preserve">Nam cum recta G H ſecet vtranque linearum C G, C H continentium
              <lb/>
            angulum H C G, qui deinceps eſt angulo D C E Hyperbolen A B conti-
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            nenti, ſitque ea (per conſtructionem) hinc inde æqualiter producta in.
              <lb/>
            </s>
            <s xml:id="echoid-s5604" xml:space="preserve">B, I, & </s>
            <s xml:id="echoid-s5605" xml:space="preserve">punctum B ſit ad Hyperbolen A B, erit etiam punctum I ad ei
              <lb/>
            oppoſitam ſectionem. </s>
            <s xml:id="echoid-s5606" xml:space="preserve">Si enim oppoſita ſectio in alio puncto, pręter I, </s>
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