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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