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

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12298

IAM oporteat datæ Hyperbolæ GEN, cuius aſymptoti ſint FI, FO per da-
tum extra ipſam punctum B (quod tamen ſit, vel in agulo aſymptotali
IFO, vt in prima figura, velin eo, qui ipſi eſt ad verticem, vt in ſecunda, ob
id quod in 53. huius monuimus, cum dato ſemi- tranſuerſo latere BD (quod
in primo caſu excedat diſtantiam BF, in ſecundo verò ſit cuiuslibet longitu-
dinis) _MINIMAM_ Hyperbolen circumſcribere.

Iungatur F B,

87[Figure 87] quę protracta da-
tæ ſectioni GEN
occurrat in E, &
producta E B ad
partes oppoſitæ
ſectionis, ſuma-
tur B D æqualis
dato ſemi-tranſ-
uerſo; quę ex hy-
poteſi vtrobique
cadet in angulo
aſymptotali, ſiue
vltra centrum F, & per verticem B, datæ Hyperbolæ GEN, adſcribatur 116. huius. milis Hyperbole ABC, cum ſemi-tranſuerſo dato BD, quæ ipſi GEN 2248. h. circumſcripta: Dico hanc eſſe _MINIMAM_ quæſitam. Quoniam quælibet
alia per B ei adſcripta cum recto, quod maius ſit eius recto latere, maior 332. Co-
roll. 19. h. ipſa GEN, quæ verò cum recto, quod prædicto ſit minus, qualis eſt PBQ,
eſt quidem minor eadem GEN, ſed omnino ſecat inſcriptam GEN. 44ibidem. enim DH, DR, FI, quæ ſint aſymptoti ſectionum ABC, PBQ, GEN: 5548. h. DH ipſi FI parallela, & DR cadet infra DH, ex vltima parte 37. huius, ſed
ei occurrit in H, quare DR producta ſecabit alteram parallelam F I,
nempe aſymptoton ſectionis GEN, & vlteriùs producta, ipſam,
& ſectionem GEN ſecabit ſed ipſa DR tota cadit 6635. h PBQ, cum ſit eius aſymptotos, quapropter occurſus
rectæ DR cum ſectione GEN cadet extra ſectio-
nem PBQ, ac ideò inſcripta ſectio GEN, ſe-
ctionem PBQ priùs ſecabit: vnde ABC
erit _MINIMA_ circumſcripta quę-
ſita. Quod ſecundò facien-
dum, ac demonſtran-
dum erat.

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Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106