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

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        <div xml:id="echoid-div291" type="section" level="1" n="128">
          <p>
            <s xml:id="echoid-s3139" xml:space="preserve">
              <pb o="93" file="0117" n="117" rhead=""/>
            diametro vltra centrum 2 in D, quare ſi eadem D 5 producatur, neceſſa-
              <lb/>
            riò ſecabit Hyperbolen SPEQ, ſed ipſa D 5 tota cadit extra
              <note symbol="a" position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">35. h.</note>
            ABC, cum ſit eius aſymptotos, quapropter occurſus rectæ D 5 cum Hyper-
              <lb/>
            bola SPEQ ſiet extra ABC, ideoque ſectio EP ſecabit priùs Hyperbolen
              <lb/>
            ABC, & </s>
            <s xml:id="echoid-s3140" xml:space="preserve">ſic Hyperbole IEL erit _MAXIMA_ inſcripta quæſita. </s>
            <s xml:id="echoid-s3141" xml:space="preserve">Quod facien-
              <lb/>
            dum, ac demonſtrandum erat.</s>
            <s xml:id="echoid-s3142" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="1" n="129">
          <head xml:id="echoid-head134" xml:space="preserve">ALITER breuiùs.</head>
          <p>
            <s xml:id="echoid-s3143" xml:space="preserve">PRoducatur contingens HE vſque ad circumſcriptã ſectionem ABC in K.
              <lb/>
            </s>
            <s xml:id="echoid-s3144" xml:space="preserve">Cum Hyperbolę ABC, IEL ſimiles ſint per diuerſos vertices, & </s>
            <s xml:id="echoid-s3145" xml:space="preserve">ad ean-
              <lb/>
            dem regulam ſimul adſcriptæ erunt infra EK ad ſe propiùs accedentes,
              <note symbol="b" position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">45. h.</note>
            mirum ſectio KAT recedet ab EI per interuallum minus ipſo EK; </s>
            <s xml:id="echoid-s3146" xml:space="preserve">Verùm
              <lb/>
            cum Hyperbolę PEQ, IEL ſint concentricæ, & </s>
            <s xml:id="echoid-s3147" xml:space="preserve">per eundem verticem ſimul
              <lb/>
            adſcriptæ, erunt ſemper magis recedentes, & </s>
            <s xml:id="echoid-s3148" xml:space="preserve">ad interuallũ peruenient maius
              <lb/>
            quocunq; </s>
            <s xml:id="echoid-s3149" xml:space="preserve">dato interuallo, videlicet ſectio EPS recedet ab eadem EI per
              <note symbol="*" position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">37. h.</note>
            teruallũ omnino maius eodẽ EK: </s>
            <s xml:id="echoid-s3150" xml:space="preserve">quapropter ſectiones KAT, EPS neceſſariò
              <lb/>
            ſe mutuò ſecabunt: </s>
            <s xml:id="echoid-s3151" xml:space="preserve">Vnde Hyperbole IEL erit _MAXIMA_ inſcripta quæſita.</s>
            <s xml:id="echoid-s3152" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div296" type="section" level="1" n="130">
          <head xml:id="echoid-head135" xml:space="preserve">PROBL. XIX. PROP. LIII.</head>
          <p>
            <s xml:id="echoid-s3153" xml:space="preserve">Datæ Hyperbolæ per punctum extra ipſam datum MINIMAM
              <lb/>
            Hyperbolen circumſcribere, quarum eadem ſit regula.</s>
            <s xml:id="echoid-s3154" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3155" xml:space="preserve">Oportet autem datum punctum, vel eſſe in angulo aſymptotis
              <lb/>
            contento, vel in eo, quod
              <unsure/>
            eſt ad verticem, dummodo in hoc caſu,
              <lb/>
            ipſius diſtantia à centro datæ ſectionis, minor ſit eius ſemi-tranſ-
              <lb/>
            uerſo latere per datum punctum tranſeunte.</s>
            <s xml:id="echoid-s3156" xml:space="preserve"/>
          </p>
          <figure number="82">
            <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0117-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3157" xml:space="preserve">ESto data Hyperbole ABC, cuius centrum D, aſymptoti DF, DG, & </s>
            <s xml:id="echoid-s3158" xml:space="preserve">da-
              <lb/>
            tum extra ipſam punctum ſit E, quod tamen ſit in angulo aſymptotali
              <lb/>
            FDG, vt in prima figura; </s>
            <s xml:id="echoid-s3159" xml:space="preserve">vel in eò qui ipſi eſt ad verticem, vt in ſecunda,
              <lb/>
            dummodo coniuncta ED, & </s>
            <s xml:id="echoid-s3160" xml:space="preserve">producta vſque ad ſectionem in B, ipſa ED </s>
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