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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135	111
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Scan	Original
131	107
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135	111
136	112
137	113
138	114
139	115
140	116
141	117
142	118
143	119
144	120
145	121
146	122
147	123
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149	125
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151	127
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153	129
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155	131
156	132
157	133
158	134
159	135
160	136

Scan	Original
131	107
132	108
133	109
134	110
135	111
136	112
137	113
138	114
139	115
140	116
141	117
142	118
143	119
144	120
145	121
146	122
147	123
148	124
149	125
150	126
151	127
152	128
153	129
154	130
155	131
156	132
157	133
158	134
159	135
160	136