Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

137. 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.

138. 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.

139. 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
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 ſectio CAD, cuius ordinatim du-
ctæ ad angulum ABD ap-

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