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

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136112 recto FDG, minor eſt ipſa FDG, quæ verò cum recto maiori, eſt 112. Co-
roll. 19. h. maior FDG, qualis eſt HDI, ſed omnino ſecat latera dati anguli ABC: 22ibidem. quoniam ducta BL aſymptoto ſectionis HDI, ipſa cadet extra BA, ſed 3337. h. eſt aſymptotos inſcriptæ FDG, quare ipſa BH producta ſecabit Hyperbolen
circumſcriptam DH, eadem ratione BC ſecabit DI: quapropter Hyperbole
FDG eſt dato angulo _MAXIMA_ inſcripta quæſita. Quod, & c.

Siverò data magni-

102[Figure 102] tudo E, vel ei æqualis
DO, minor fuerit di-
ſtantia DB inter datum
punctum, & dati angu-
li ABC verticem, vt in
ſecunda figura; ducan-
tur ex O, rectæ OP, OH,
aſymptotis BA, BC æ-
quidiſtantes, & intra
aſymptotos OP, OH
444. ſec.
conic. deſcribatur per D Hy perbole FDG: & hæc
erit _MAXIMA_ inſcripta quæſita.

Quoniam, quæ cum eodem tranſuerſo, ſed cum recto minori adſcribitur
per D, minor eſt FDG, quæ verò cum recto maiori, qualis eſt IDL, eſt 552. Co-
roll. 19. h. dem maior, ſed omnino ſecat latera dati anguli BA, BC: quoniam 66ibidem. OM aſymptoto circumſcriptæ IDL, cadet extra OP aſymptoton 77ex 37. h. FDG, & producta ſecabit BA, cum ſecet in O alteram parallelam OP; qua-
re BA producta ſecabit quidem Hyperbolen DIL: vnde FDG eſt 8835. h. _MA_ quæſita. Quod, & c.

Sitandem DO, quæ ipſi E æqualis eſt, excedat DB. Fiat vt OB ad OD,
ita OD ad OF, & per F applicetur in angulo ABC ordinata AFC, & cũ 99Schol.
66. h. mi-tranſuerſo OD, per puncta A,D,C, deſcribatur Hyperbole ADC, 101057. h. ca diametri ſegmentum DF, & applicatam AC. Dico hanc eſſe _MAXIMAM_
quęſitam.

Quoniam, cum ſit FO ad OD, vt DO ad OB, erit rectangulum FOB æqua-
le quadrato OD, quare BA, BC Hyperbolen contingent; ſiue 1111cõuerſ.
37. primi
conic. à
Comand. le ADC dato angulo ABC erit inſcripta; eritque _MAXIMA_; quoniam, quæ
cumrecto minori cadit intra, quæ verò cum maiori cadit quidem 12122. Co-
roll. 19. h. ADC, ſed neceſſariò ſecat dati anguli latera BA, BC, cum ſectio Hyper-
bole in infinitum produci poſſit, & ſpacium ABCDA ſit vndique clauſum:
1313ibidem. quare ipſa ADC eſt _MAXIMA_ inſcripta quæſita, per datum punctum D.
Quod primò faciendum, ac demonſtrandum erat.

IAM oporteat (in quarta figura) datæ Hyperbolæ ABC, cuius aſymptoti
ED, EF, per datum extra ipſam punctum G, _MINIMV M_ angulum circũ-
ſcribere.

Itaque, vel datum punctum G congruit cum centro E, vel cadit in angu-
lo aſymptotali, vel in eo, qui huic eſt ad verticem; ſic enim ſemper, quę per
G, & centrum E ducitur, tum Hyperbolæ, tum anguli eſt communis diame-
ter, non autem ſi datum punctum alibi cadat. Si primùm; ipſæ angulus

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160	136

Scan	Original
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Scan	Original
131	107
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