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

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            <s xml:id="echoid-s3228" xml:space="preserve">
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            ſcriptam HEL, ſed eadem DL eſt aſymptotos ABC, ſiue tota cadit
              <note symbol="a" position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">37. h.</note>
            ABC, quare DL, & </s>
            <s xml:id="echoid-s3229" xml:space="preserve">ſectio EH ſecabunt ſe mutuò extra ſectionem BA, qua-
              <lb/>
            propter EH ſecabit priùs ſectionem BA: </s>
            <s xml:id="echoid-s3230" xml:space="preserve">ex quo ſimilis, & </s>
            <s xml:id="echoid-s3231" xml:space="preserve">concentrica Hy-
              <lb/>
            perbole FEG erit _MAXIMA_ quæſita: </s>
            <s xml:id="echoid-s3232" xml:space="preserve">Quod primò faciendum, & </s>
            <s xml:id="echoid-s3233" xml:space="preserve">demon-
              <lb/>
            ſtrandum erat.</s>
            <s xml:id="echoid-s3234" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div307" type="section" level="1" n="134">
          <head xml:id="echoid-head139" xml:space="preserve">ALITER breuiùs.</head>
          <p>
            <s xml:id="echoid-s3235" xml:space="preserve">DVcatur ex E contingens EM. </s>
            <s xml:id="echoid-s3236" xml:space="preserve">Sectio MA accedit ſectioni EF per
              <note symbol="b" position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">47. h.</note>
            teruallum minus quolibet dato interuallo; </s>
            <s xml:id="echoid-s3237" xml:space="preserve">at ſectio EH quæ cadit ex-
              <lb/>
            tra EF, recedit ab eadem EF per interuallum maius eodem dato interuallo;</s>
            <s xml:id="echoid-s3238" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">37. h.</note>
            quare MA, & </s>
            <s xml:id="echoid-s3239" xml:space="preserve">EH neceſſariò ſe mutuò ſecant: </s>
            <s xml:id="echoid-s3240" xml:space="preserve">Vnde FEG eſt _MAXIMA_ in-
              <lb/>
            ſcripta quæſita. </s>
            <s xml:id="echoid-s3241" xml:space="preserve">Quod iterum, &</s>
            <s xml:id="echoid-s3242" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3243" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3244" xml:space="preserve">IAM ſit data Hyperbole FEG, cuius centrum G, aſymptotos DL, & </s>
            <s xml:id="echoid-s3245" xml:space="preserve">opor-
              <lb/>
            teat per datum extra ipſam punctum B (quod tamen ſit in angulo aſym-
              <lb/>
            ptotali, ob rationem in præcedenti propoſ. </s>
            <s xml:id="echoid-s3246" xml:space="preserve">allatam) _MINIMAM_ Hyperbo-
              <lb/>
            len circumſcribere.</s>
            <s xml:id="echoid-s3247" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3248" xml:space="preserve">Iungatur DB, & </s>
            <s xml:id="echoid-s3249" xml:space="preserve">producatur ſectioni
              <lb/>
              <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a" number="85">
                <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0120-01"/>
              </figure>
            FEG occurrens in E, & </s>
            <s xml:id="echoid-s3250" xml:space="preserve">cum ſemi-tranſ-
              <lb/>
            uerſo BD, per verticem B, adſcribatur
              <lb/>
            ſimilis, & </s>
            <s xml:id="echoid-s3251" xml:space="preserve">concentrica Hyperbole ABC:
              <lb/>
            </s>
            <s xml:id="echoid-s3252" xml:space="preserve">patet hanc eſſe datæ FEG circumſcriptã,
              <lb/>
            cum nunquam ſimul conueniant.</s>
            <s xml:id="echoid-s3253" xml:space="preserve"/>
          </p>
          <note symbol="d" position="left" xml:space="preserve">47. h.</note>
          <p>
            <s xml:id="echoid-s3254" xml:space="preserve">Dico præterea ipſam eſſe _MAXIMAM_
              <lb/>
            quæſitam. </s>
            <s xml:id="echoid-s3255" xml:space="preserve">Quoniam quæcunque alia
              <lb/>
            adſcripta per B ipſi FEG, vel ipſi ABC
              <lb/>
            concentrica, cum recto, quod maius ſit
              <lb/>
            recto ſectionis ABC, maior eſt
              <note symbol="e" position="left" xlink:label="note-0120-05" xlink:href="note-0120-05a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            ABC, quæ verò cum recto, quod præ-
              <lb/>
            dicto ſit minus, qualis eſt Hyperbole
              <lb/>
            NBO, eſt quidem minor eadem ABC, ſed omnino ſecat inſcriptam FEG.</s>
            <s xml:id="echoid-s3256" xml:space="preserve">
              <note symbol="f" position="left" xlink:label="note-0120-06" xlink:href="note-0120-06a" xml:space="preserve">ibidem.</note>
            Quoniam ſectio MA accedit ſectioni EF per interuallum minus
              <note symbol="g" position="left" xlink:label="note-0120-07" xlink:href="note-0120-07a" xml:space="preserve">47. h.</note>
            dato interuallo; </s>
            <s xml:id="echoid-s3257" xml:space="preserve">ſed ſectio PN eſt intra MA, & </s>
            <s xml:id="echoid-s3258" xml:space="preserve">ab ipſa recedit per
              <note symbol="h" position="left" xlink:label="note-0120-08" xlink:href="note-0120-08a" xml:space="preserve">37. h.</note>
            lum maius eodem dato interuallo; </s>
            <s xml:id="echoid-s3259" xml:space="preserve">quare PN, & </s>
            <s xml:id="echoid-s3260" xml:space="preserve">EF neceſſariò ſe mutuò ſe-
              <lb/>
            cant. </s>
            <s xml:id="echoid-s3261" xml:space="preserve">Igitur ſimilis, & </s>
            <s xml:id="echoid-s3262" xml:space="preserve">concentrica Hyperbole ABC eſt _MINIMA_ circum-
              <lb/>
            ſcripta quæſita. </s>
            <s xml:id="echoid-s3263" xml:space="preserve">Quod ſecundò faciendum erat.</s>
            <s xml:id="echoid-s3264" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3265" xml:space="preserve">Quod in hac, & </s>
            <s xml:id="echoid-s3266" xml:space="preserve">in duabus-præcedentibus factum eſt, idem ſimul, ac
              <lb/>
            vmuerſaliùs habebitur in ſequenti.</s>
            <s xml:id="echoid-s3267" xml:space="preserve"/>
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