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

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            <s xml:id="echoid-s3757" xml:space="preserve">
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            recto FDG, minor eſt ipſa FDG, quæ verò cum recto maiori, eſt
              <note symbol="a" position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            maior FDG, qualis eſt HDI, ſed omnino ſecat latera dati anguli ABC:</s>
            <s xml:id="echoid-s3758" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">ibidem.</note>
            quoniam ducta BL aſymptoto ſectionis HDI, ipſa cadet extra BA, ſed
              <note symbol="c" position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">37. h.</note>
            eſt aſymptotos inſcriptæ FDG, quare ipſa BH producta ſecabit Hyperbolen
              <lb/>
            circumſcriptam DH, eadem ratione BC ſecabit DI: </s>
            <s xml:id="echoid-s3759" xml:space="preserve">quapropter Hyperbole
              <lb/>
            FDG eſt dato angulo _MAXIMA_ inſcripta quæſita. </s>
            <s xml:id="echoid-s3760" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s3761" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3762" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3763" xml:space="preserve">Siverò data magni-
              <lb/>
              <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a" number="102">
                <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0136-01"/>
              </figure>
            tudo E, vel ei æqualis
              <lb/>
            DO, minor fuerit di-
              <lb/>
            ſtantia DB inter datum
              <lb/>
            punctum, & </s>
            <s xml:id="echoid-s3764" xml:space="preserve">dati angu-
              <lb/>
            li ABC verticem, vt in
              <lb/>
            ſecunda figura; </s>
            <s xml:id="echoid-s3765" xml:space="preserve">ducan-
              <lb/>
            tur ex O, rectæ OP, OH,
              <lb/>
            aſymptotis BA, BC æ-
              <lb/>
            quidiſtantes, & </s>
            <s xml:id="echoid-s3766" xml:space="preserve">intra
              <lb/>
            aſymptotos OP, OH
              <lb/>
              <note symbol="d" position="left" xlink:label="note-0136-04" xlink:href="note-0136-04a" xml:space="preserve">4. ſec.
                <lb/>
              conic.</note>
            deſcribatur per D Hy perbole FDG: </s>
            <s xml:id="echoid-s3767" xml:space="preserve">& </s>
            <s xml:id="echoid-s3768" xml:space="preserve">hæc
              <lb/>
            erit _MAXIMA_ inſcripta quæſita.</s>
            <s xml:id="echoid-s3769" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3770" xml:space="preserve">Quoniam, quæ cum eodem tranſuerſo, ſed cum recto minori adſcribitur
              <lb/>
            per D, minor eſt FDG, quæ verò cum recto maiori, qualis eſt IDL, eſt
              <note symbol="e" position="left" xlink:label="note-0136-05" xlink:href="note-0136-05a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            dem maior, ſed omnino ſecat latera dati anguli BA, BC: </s>
            <s xml:id="echoid-s3771" xml:space="preserve">quoniam
              <note symbol="f" position="left" xlink:label="note-0136-06" xlink:href="note-0136-06a" xml:space="preserve">ibidem.</note>
            OM aſymptoto circumſcriptæ IDL, cadet extra OP aſymptoton
              <note symbol="g" position="left" xlink:label="note-0136-07" xlink:href="note-0136-07a" xml:space="preserve">ex 37. h.</note>
            FDG, & </s>
            <s xml:id="echoid-s3772" xml:space="preserve">producta ſecabit BA, cum ſecet in O alteram parallelam OP; </s>
            <s xml:id="echoid-s3773" xml:space="preserve">qua-
              <lb/>
            re BA producta ſecabit quidem Hyperbolen DIL: </s>
            <s xml:id="echoid-s3774" xml:space="preserve">vnde FDG eſt
              <note symbol="h" position="left" xlink:label="note-0136-08" xlink:href="note-0136-08a" xml:space="preserve">35. h.</note>
            _MA_ quæſita. </s>
            <s xml:id="echoid-s3775" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s3776" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3778" xml:space="preserve">Sitandem DO, quæ ipſi E æqualis eſt, excedat DB. </s>
            <s xml:id="echoid-s3779" xml:space="preserve">Fiat vt OB ad OD,
              <lb/>
            ita OD ad OF, & </s>
            <s xml:id="echoid-s3780" xml:space="preserve">per F applicetur in angulo ABC ordinata AFC, & </s>
            <s xml:id="echoid-s3781" xml:space="preserve">cũ
              <note symbol="i" position="left" xlink:label="note-0136-09" xlink:href="note-0136-09a" xml:space="preserve">Schol.
                <lb/>
              66. h.</note>
            mi-tranſuerſo OD, per puncta A,D,C, deſcribatur Hyperbole ADC,
              <note symbol="l" position="left" xlink:label="note-0136-10" xlink:href="note-0136-10a" xml:space="preserve">57. h.</note>
            ca diametri ſegmentum DF, & </s>
            <s xml:id="echoid-s3782" xml:space="preserve">applicatam AC. </s>
            <s xml:id="echoid-s3783" xml:space="preserve">Dico hanc eſſe _MAXIMAM_
              <lb/>
            quęſitam.</s>
            <s xml:id="echoid-s3784" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3785" xml:space="preserve">Quoniam, cum ſit FO ad OD, vt DO ad OB, erit rectangulum FOB æqua-
              <lb/>
            le quadrato OD, quare BA, BC Hyperbolen contingent; </s>
            <s xml:id="echoid-s3786" xml:space="preserve">ſiue
              <note symbol="m" position="left" xlink:label="note-0136-11" xlink:href="note-0136-11a" xml:space="preserve">cõuerſ.
                <lb/>
              37. primi
                <lb/>
              conic. à
                <lb/>
              Comand.</note>
            le ADC dato angulo ABC erit inſcripta; </s>
            <s xml:id="echoid-s3787" xml:space="preserve">eritque _MAXIMA_; </s>
            <s xml:id="echoid-s3788" xml:space="preserve">quoniam, quæ
              <lb/>
            cumrecto minori cadit intra, quæ verò cum maiori cadit quidem
              <note symbol="n" position="left" xlink:label="note-0136-12" xlink:href="note-0136-12a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            ADC, ſed neceſſariò ſecat dati anguli latera BA, BC, cum ſectio Hyper-
              <lb/>
            bole in infinitum produci poſſit, & </s>
            <s xml:id="echoid-s3789" xml:space="preserve">ſpacium ABCDA ſit vndique clauſum:
              <lb/>
            </s>
            <s xml:id="echoid-s3790" xml:space="preserve">
              <note symbol="o" position="left" xlink:label="note-0136-13" xlink:href="note-0136-13a" xml:space="preserve">ibidem.</note>
            quare ipſa ADC eſt _MAXIMA_ inſcripta quæſita, per datum punctum D.
              <lb/>
            </s>
            <s xml:id="echoid-s3791" xml:space="preserve">Quod primò faciendum, ac demonſtrandum erat.</s>
            <s xml:id="echoid-s3792" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3793" xml:space="preserve">IAM oporteat (in quarta figura) datæ Hyperbolæ ABC, cuius aſymptoti
              <lb/>
            ED, EF, per datum extra ipſam punctum G, _MINIMV M_ angulum circũ-
              <lb/>
            ſcribere.</s>
            <s xml:id="echoid-s3794" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3795" xml:space="preserve">Itaque, vel datum punctum G congruit cum centro E, vel cadit in angu-
              <lb/>
            lo aſymptotali, vel in eo, qui huic eſt ad verticem; </s>
            <s xml:id="echoid-s3796" xml:space="preserve">ſic enim ſemper, quę per
              <lb/>
            G, & </s>
            <s xml:id="echoid-s3797" xml:space="preserve">centrum E ducitur, tum Hyperbolæ, tum anguli eſt communis diame-
              <lb/>
            ter, non autem ſi datum punctum alibi cadat. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">Si primùm; </s>
            <s xml:id="echoid-s3799" xml:space="preserve">ipſæ angulus </s>
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