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

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page |< < (66) of 347 > >|
THEOR. XIII. PROP. XXXVII.
Tandem ſit FP aſymptotos inſcriptæ DBC, & FR aſymptotos circumſcri-
pte
, &
contingens HB producatur, vtranque aſymptoton ſecans in P, R: erit
ergo
quadratum BP ęquale quartę parti figurę GBI, &
quadratũ BR 448. huius. parti figuræ GBH, ſed rectangulum GBI maius eſt rectangulo GBH, cum ſit
BI
minor BH, ergo BP minor eſt BR;
hoc eſt FP aſymptoton inſcriptæ cadit
infra
FR aſymptoton circumſcriptæ diuidens angulũ ab ipſius aſymptotis fa-
ctum
, ex quo ipſa FP producta ſecabit Hyperbolen circumſcriptam ABC.
55ibidem. Quod erat vltimò, & c.

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