Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">IAM oporteat datæ Hyperbolæ GEN, cuius aſymptoti ſint FI, FO per da-
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tum extra ipſam punctum B (quod tamen ſit, vel in agulo aſymptotali
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IFO, vt in prima figura, velin eo, qui ipſi eſt ad verticem, vt in ſecunda, ob
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id quod in 53. </
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<
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">huius monuimus, cum dato ſemi- tranſuerſo latere BD (quod
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in primo caſu excedat diſtantiam BF, in ſecundo verò ſit cuiuslibet longitu-
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dinis) _MINIMAM_ Hyperbolen circumſcribere.</
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">Iungatur F B,
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0122-01
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quę protracta da-
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tæ ſectioni GEN
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occurrat in E, & </
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producta E B ad
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partes oppoſitæ
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ſectionis, ſuma-
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tur B D æqualis
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dato ſemi-tranſ-
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uerſo; </
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<
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">quę ex hy-
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poteſi vtrobique
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cadet in angulo
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aſymptotali, ſiue
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vltra centrum F, & </
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<
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">per verticem B, datæ Hyperbolæ GEN, adſcribatur
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milis Hyperbole ABC, cum ſemi-tranſuerſo dato BD, quæ ipſi GEN
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">48. h.</
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circumſcripta: </
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">Dico hanc eſſe _MINIMAM_ quæſitam. </
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<
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">Quoniam quælibet
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alia per B ei adſcripta cum recto, quod maius ſit eius recto latere, maior
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">2. Co-
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roll. 19. h.</
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ipſa GEN, quæ verò cum recto, quod prædicto ſit minus, qualis eſt PBQ,
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eſt quidem minor eadem GEN, ſed omnino ſecat inſcriptam GEN. </
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<
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<
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">ibidem.</
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enim DH, DR, FI, quæ ſint aſymptoti ſectionum ABC, PBQ, GEN: </
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DH ipſi FI parallela, & </
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<
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">huius, ſed
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ei occurrit in H, quare DR producta ſecabit alteram parallelam F I,
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nempe aſymptoton ſectionis GEN, & </
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<
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">vlteriùs producta, ipſam,
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& </
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<
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">ſectionem GEN ſecabit ſed ipſa DR tota cadit
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PBQ, cum ſit eius aſymptotos, quapropter occurſus
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rectæ DR cum ſectione GEN cadet extra ſectio-
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nem PBQ, ac ideò inſcripta ſectio GEN, ſe-
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ctionem PBQ priùs ſecabit: </
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<
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erit _MINIMA_ circumſcripta quę-
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ſita. </
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dum, ac demonſtran-
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dum erat.</
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