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

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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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