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

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          <p>
            <s xml:id="echoid-s3302" xml:space="preserve">IAM oporteat datæ Hyperbolæ GEN, cuius aſymptoti ſint FI, FO per da-
              <lb/>
            tum extra ipſam punctum B (quod tamen ſit, vel in agulo aſymptotali
              <lb/>
            IFO, vt in prima figura, velin eo, qui ipſi eſt ad verticem, vt in ſecunda, ob
              <lb/>
            id quod in 53. </s>
            <s xml:id="echoid-s3303" xml:space="preserve">huius monuimus, cum dato ſemi- tranſuerſo latere BD (quod
              <lb/>
            in primo caſu excedat diſtantiam BF, in ſecundo verò ſit cuiuslibet longitu-
              <lb/>
            dinis) _MINIMAM_ Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s3304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3305" xml:space="preserve">Iungatur F B,
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="87">
                <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0122-01"/>
              </figure>
            quę protracta da-
              <lb/>
            tæ ſectioni GEN
              <lb/>
            occurrat in E, & </s>
            <s xml:id="echoid-s3306" xml:space="preserve">
              <lb/>
            producta E B ad
              <lb/>
            partes oppoſitæ
              <lb/>
            ſectionis, ſuma-
              <lb/>
            tur B D æqualis
              <lb/>
            dato ſemi-tranſ-
              <lb/>
            uerſo; </s>
            <s xml:id="echoid-s3307" xml:space="preserve">quę ex hy-
              <lb/>
            poteſi vtrobique
              <lb/>
            cadet in angulo
              <lb/>
            aſymptotali, ſiue
              <lb/>
            vltra centrum F, & </s>
            <s xml:id="echoid-s3308" xml:space="preserve">per verticem B, datæ Hyperbolæ GEN, adſcribatur
              <note symbol="a" position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">6. huius.</note>
            milis Hyperbole ABC, cum ſemi-tranſuerſo dato BD, quæ ipſi GEN
              <note symbol="b" position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">48. h.</note>
            circumſcripta: </s>
            <s xml:id="echoid-s3309" xml:space="preserve">Dico hanc eſſe _MINIMAM_ quæſitam. </s>
            <s xml:id="echoid-s3310" xml:space="preserve">Quoniam quælibet
              <lb/>
            alia per B ei adſcripta cum recto, quod maius ſit eius recto latere, maior
              <note symbol="c" position="left" xlink:label="note-0122-03" xlink:href="note-0122-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            ipſa GEN, quæ verò cum recto, quod prædicto ſit minus, qualis eſt PBQ,
              <lb/>
            eſt quidem minor eadem GEN, ſed omnino ſecat inſcriptam GEN. </s>
            <s xml:id="echoid-s3311" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-0122-04" xlink:href="note-0122-04a" xml:space="preserve">ibidem.</note>
            enim DH, DR, FI, quæ ſint aſymptoti ſectionum ABC, PBQ, GEN: </s>
            <s xml:id="echoid-s3312" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-0122-05" xlink:href="note-0122-05a" xml:space="preserve">48. h.</note>
            DH ipſi FI parallela, & </s>
            <s xml:id="echoid-s3313" xml:space="preserve">DR cadet infra DH, ex vltima parte 37. </s>
            <s xml:id="echoid-s3314" xml:space="preserve">huius, ſed
              <lb/>
            ei occurrit in H, quare DR producta ſecabit alteram parallelam F I,
              <lb/>
            nempe aſymptoton ſectionis GEN, & </s>
            <s xml:id="echoid-s3315" xml:space="preserve">vlteriùs producta, ipſam,
              <lb/>
            & </s>
            <s xml:id="echoid-s3316" xml:space="preserve">ſectionem GEN ſecabit ſed ipſa DR tota cadit
              <note symbol="f" position="left" xlink:label="note-0122-06" xlink:href="note-0122-06a" xml:space="preserve">35. h</note>
            PBQ, cum ſit eius aſymptotos, quapropter occurſus
              <lb/>
            rectæ DR cum ſectione GEN cadet extra ſectio-
              <lb/>
            nem PBQ, ac ideò inſcripta ſectio GEN, ſe-
              <lb/>
            ctionem PBQ priùs ſecabit: </s>
            <s xml:id="echoid-s3317" xml:space="preserve">vnde ABC
              <lb/>
            erit _MINIMA_ circumſcripta quę-
              <lb/>
            ſita. </s>
            <s xml:id="echoid-s3318" xml:space="preserve">Quod ſecundò facien-
              <lb/>
            dum, ac demonſtran-
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s3319" xml:space="preserve"/>
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