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

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125101

COROLL. I.

EX quinque proximè præcedentibus problematibus ſatis conſtat, _MAXI-_
_MAM_, vel _MINIMAM_ Hyperbolen, inſcriptam, vel circumſcriptam
cuilibet datæ per punctum intra, vel extra Hyperbolen datũ in locis poſſibili-
bus, ad eandem regulam, aut concentricè adſcriptam, vel cuius centrum pro
inſcripta cadat infra centrum datæ, & pro circumſcripta cadat vltra, ſemper
eidem datæ Hyperbolæ ſimilem eſſe.

COROLL. II.

PAtet quoque, _MAXIMAM_ Hyperbolarum datæ Hyperbolæ ſimilium,
per datum intra ipſam punctum inſcriptarum, eſſe concentricam, cum
hæc, inter ſimiles, ſit _MAXIMORVM_ laterum. Item _MINIMAM_ Hyperbola-
rum datæ Hyperbolæ ſimilium per datum extra ipſam punctum in angulo
aſymptotali, circumſcriptarum, eſſe pariter concentricam, cum eadem, in-
ter ſimiles, ſit _MINIMORV M_ laterum.

PROBL. XXIII. PROP. LVII.

Datis magnitudine, & poſitione cuiuslibet coni- ſectionis dia-
metri ſegmento, & vna applicatarum, & pro Hyperbola, & Ellipſi
dato etiam tranſuerſo latere; imperatam coni-ſectionem deſcri-
bere.

SIt in qualibet ſigura, pro quacunque coni-ſectione, datum magnitudine,
& poſitione diametri ſegmentum AB, & vna applicatarum CD, & pro
Hyperbola, & Ellipſi in ſecunda, & tertia, datum ſit quoque rectum latus
AF, quod pro Hyperbola in ſecunda vltra BA ipſi in directum ponatur, & in
tertia, ex A ad partes B: oportet circa diametrum AB, ſuper applicatam
CD, quæſitam coni-ſectionem deſcribere.

Fiat in ſingulis figuris, vt

90[Figure 90] AB ad BC, ita BC ad BE
ipſi BC in directum poſitã,
& per E, in prima figura,
ducta EG parallela ad BA,
vel in ſecunda, & tertia iun-
cta FE, occurrat AG, (quæ
ipſi CD æquidiſtet) in G, &
per verticem A cum data
diametro AB, datiſque la-
teribus AF, A G deſcriba-
tur quæſiti nominis 115. 6. 7.
huius. CAD, cuius ordinatim du-
ctæ ad angulum ABD

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113	89
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130	106

Scan	Original
101	77
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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
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121	97
122	98
123	99
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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
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125	101
126	102
127	103
128	104
129	105
130	106