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

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        <div xml:id="echoid-div474" type="section" level="1" n="194">
          <head xml:id="echoid-head199" xml:space="preserve">THEOR. XLVI. PROP. XCII.</head>
          <p>
            <s xml:id="echoid-s4724" xml:space="preserve">Si Parabolen, vel Hyperbolen, aut Ellipſim circa maiorem
              <lb/>
            axim recta linea, præter ad verticem contingat, cui à tactu ducta
              <lb/>
            ſit perpendicularis axi occurrens; </s>
            <s xml:id="echoid-s4725" xml:space="preserve">circulus, cuius centrum ſit idem
              <lb/>
            occurſus, radius verò ſit ipſa perpẽdicularis erit ſectioni inſcriptus.</s>
            <s xml:id="echoid-s4726" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4727" xml:space="preserve">Si autem Ellipſis fuerit circa minorem axim, cui prædicta per-
              <lb/>
            pendicularis occurrat, circulus ex ea tanquam radio, at centro fa-
              <lb/>
            cto ipſo occurſu, erit eidem Ellipſi circumſcriptus.</s>
            <s xml:id="echoid-s4728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4729" xml:space="preserve">ESto ABC, Parabole, vel Hyperbole, in prima figura, aut Ellipſis in ſe-
              <lb/>
            cunda, circa maiorem axim BO; </s>
            <s xml:id="echoid-s4730" xml:space="preserve">vel circa minorẽ, vt in tertia, quarum
              <lb/>
            vertex B, & </s>
            <s xml:id="echoid-s4731" xml:space="preserve">ad aliud punctum quædam contingens EF, cui ducta ſit perpen-
              <lb/>
            dicularis ED, quæ axi occurret in D, quo facto centro, & </s>
            <s xml:id="echoid-s4732" xml:space="preserve">interuallo
              <note symbol="a" position="right" xlink:label="note-0165-01" xlink:href="note-0165-01a" xml:space="preserve">88. h.</note>
            circulus EGHI deſcribatur. </s>
            <s xml:id="echoid-s4733" xml:space="preserve">Dico primùmhunc, in prima, & </s>
            <s xml:id="echoid-s4734" xml:space="preserve">ſecunda figu-
              <lb/>
            ra, datæ ſectioni eſſe inſcriptum.</s>
            <s xml:id="echoid-s4735" xml:space="preserve"/>
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          <figure number="130">
            <image file="0165-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0165-01"/>
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          <p>
            <s xml:id="echoid-s4736" xml:space="preserve">Applicata enim EH, ſecans
              <unsure/>
            axim in L, & </s>
            <s xml:id="echoid-s4737" xml:space="preserve">iuncta DH. </s>
            <s xml:id="echoid-s4738" xml:space="preserve">Cum in triangulis
              <lb/>
            ELD, HLD anguli ad L ſint recti, & </s>
            <s xml:id="echoid-s4739" xml:space="preserve">latera EL, LD æqualia lateribus HL,
              <lb/>
            LD, erit baſis DE æqualis DH, exquo circulus ex DE tranſibit omnino per
              <lb/>
            H, ideoque coni-ſectio, & </s>
            <s xml:id="echoid-s4740" xml:space="preserve">circulus, ſunt binæ ſectiones ſimul adſcriptæ
              <lb/>
            (cum earum diametri, & </s>
            <s xml:id="echoid-s4741" xml:space="preserve">applicatæ ſimul congruant) quæ in ijſdem extre-
              <lb/>
            mis communis applicatæ EH ſimul conueniunt, atque ad eorum alterum E,
              <lb/>
            eadem recta EF vtranque ſectionem contingit, nempe ſectionem ABC, ex
              <lb/>
            ſuppoſitione, & </s>
            <s xml:id="echoid-s4742" xml:space="preserve">circulum EGHI, cum EF ſit ad extremum ſemi-diametri
              <lb/>
            ED perpendicularis, atque vertex circuli G cadit infra B verticem ſectionis,
              <lb/>
            cum ſit DB maior DE, ſiue maior DG, quare circulus ex DE erit
              <note symbol="b" position="right" xlink:label="note-0165-02" xlink:href="note-0165-02a" xml:space="preserve">ibideni.</note>
              <note symbol="c" position="right" xlink:label="note-0165-03" xlink:href="note-0165-03a" xml:space="preserve">@ 1. h.</note>
            inſcriptus. </s>
            <s xml:id="echoid-s4743" xml:space="preserve">Quod primò erat, &</s>
            <s xml:id="echoid-s4744" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4745" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4746" xml:space="preserve">AMpliùs, dico in tertia figura, prædictum circulum EGHI eſſe datæ El-
              <lb/>
            lipſi ABCO circumſcriptum.</s>
            <s xml:id="echoid-s4747" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4748" xml:space="preserve">Nam facta eadem conſtructione, ac ſupra oſtendetur pariter </s>
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