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

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        <div xml:id="echoid-div408" type="section" level="1" n="172">
          <head xml:id="echoid-head177" xml:space="preserve">LEMMA XII. PROP. LXXX.</head>
          <p>
            <s xml:id="echoid-s4221" xml:space="preserve">Si fuerit rectangulum ABC, ęquale rectangulo DEF, ſitque AC
              <lb/>
            maior DF, erit BC minor EF.</s>
            <s xml:id="echoid-s4222" xml:space="preserve"/>
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          <figure number="115">
            <image file="0149-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0149-01"/>
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            <s xml:id="echoid-s4223" xml:space="preserve">SI enim dicatur BC æqualem, vel maiorem
              <lb/>
            eſſe EF, cum ſit data AC maior DF, eſſet
              <lb/>
            omnino AB maior DE, & </s>
            <s xml:id="echoid-s4224" xml:space="preserve">BC dicitur æqualis,
              <lb/>
            vel maior EF, ergo rectangulum ABC eſſet om-
              <lb/>
            nino maius rectangulo DEF, ſed æquale poſi-
              <lb/>
            tum fuit. </s>
            <s xml:id="echoid-s4225" xml:space="preserve">Ergo patet propoſitum.</s>
            <s xml:id="echoid-s4226" xml:space="preserve"/>
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        <div xml:id="echoid-div409" type="section" level="1" n="173">
          <head xml:id="echoid-head178" xml:space="preserve">THEOR. XXXVIII. PROP. LXXXI.</head>
          <p>
            <s xml:id="echoid-s4227" xml:space="preserve">Si recta linea ad alterũ terminũ cuiuſdam applicatæ coni-ſectio-
              <lb/>
            nem, vel circulũ cõtingat, ipſa omnino ſecabit ſibi adſcriptã eiuſdẽ
              <lb/>
            nominis ſectionẽ circa eandẽ applicatam, & </s>
            <s xml:id="echoid-s4228" xml:space="preserve">cum æquali tranſuerſa
              <lb/>
            diametro, ſi ſectiones fuerint Hyperbolæ, vel Ellipſes, aut circuli.</s>
            <s xml:id="echoid-s4229" xml:space="preserve"/>
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            <s xml:id="echoid-s4230" xml:space="preserve">ESto quæcunque coni-ſectio, vel circulus ABC, cuius diameter BD, yo
              <unsure/>
              <lb/>
            vna applicatarum ſit AC. </s>
            <s xml:id="echoid-s4231" xml:space="preserve">& </s>
            <s xml:id="echoid-s4232" xml:space="preserve">ad ipſius terminum A, ſit recta contingens
              <lb/>
            EAF, quæ diametro occurret in F; </s>
            <s xml:id="echoid-s4233" xml:space="preserve">& </s>
            <s xml:id="echoid-s4234" xml:space="preserve">ſumpto in diametri ſegmento
              <note symbol="a" position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">24. 25.
                <lb/>
              pr. conic.</note>
            quolibet puncto G, cum diametro GD, & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">applicata AC in qualibet figura,
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              <figure xlink:label="fig-0149-02" xlink:href="fig-0149-02a" number="116">
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            ſed etiam, pro Hyperbola in ſecunda, & </s>
            <s xml:id="echoid-s4236" xml:space="preserve">pro Ellipſi, vel circulo, in tertia,
              <lb/>
            cum dato tranſuerſo latere GM, quod æquale ſit tranſuerſo BL datæ ſectio-
              <lb/>
            nis, deſcribatur eiuſdem nomin@s ſectio AGC: </s>
            <s xml:id="echoid-s4237" xml:space="preserve">dico hanc omnino
              <note symbol="b" position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">57. h.</note>
            contingente EAF.</s>
            <s xml:id="echoid-s4238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4239" xml:space="preserve">Ducatur enim per A recta IAH, quæ ſectionem continge
              <unsure/>
            t AGC, cum
              <lb/>
            eius diametro conueniat in H.</s>
            <s xml:id="echoid-s4240" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4241" xml:space="preserve">Iam in prima figura exhiben@ Parabolas, cum AF contingat </s>
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