Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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gentem ex vertice ſe mutuò ſecant, (extra tamen circumſcriptam) & </
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ptotos inſcriptæ ſecat Hyperbolen circumſcriptam.</
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">Hyperbolæ concentricæ per eundem verticem ſimul adſcriptæ,
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quarum recta latera ſint inæqualia, ſunt inter ſe nunquam coeuntes,
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& </
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<
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">in infinitum productæ, ad interual-
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lum perueniunt maius quolibet dato interuallo, & </
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<
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ſcriptæ ſecat Hyperbolen circumſcriptam.</
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<
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<
s
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">SInt duę Hyperbolę ABC, DBE per
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0090-01
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eundem verticem B ſimul adſcri-
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pte, quarum idem centrum ſit F, idem-
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que tranſuerſum BFG, ſed tamen Hy-
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perbolæ ABC rectum latus ſit BH, ma-
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ius recto BI Hyperbolæ DBE. </
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<
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primùm eas ſimul eſſe non coeuntes.</
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<
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<
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<
s
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">Cum enim Hyperbolæ DBE, ABC
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ſint per verticem ſimul adſcriptæ cum
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eodem tranſuerſo BG, ipſa DBE, cuius
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rectum minus eſt, inſcripta erit
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roll. 19. h.</
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perbolæ ABC, cuius rectum maius eſt,
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hoc eſt, ſi iſtæ ſimul in infinitum produ-
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cantur, erunt ſimul non coeuntes.</
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<
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<
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<
s
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">Iam dico, has etiam eſſe ſemper in-
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ter ſe recedentes. </
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">Ductis enim, & </
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tractis regulis; </
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duabus vbicunque rectis ADL, MON; </
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<
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">quæ regulas ſecent in Q, S, T, V,
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cum ſit vt quadratum MN ad quadratũ NO, ita recta VN ad NT, vel
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roll. 19. h.</
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SL ad SQ, vel quadratum AL ad LD, erit etiam recta MN ad NO, vt AL ad
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LD, & </
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AD, ſed eſt MN maior AL, quare, & </
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ſtrabitur quamlibet aliam interceptam applicatę portionem inter Hyperbo-
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las infra MO, maiorem eſſe ipſa MO, & </
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perbolæ ſunt ſemper inter ſe recedentes. </
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<
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re, ad interuallum maius quolibet dato interuallo X. </
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penitùs arte, ac in 33. </
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<
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">Tandem ſit FP aſymptotos inſcriptæ DBC, & </
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pte, & </
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<
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<
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ergo quadratum BP ęquale quartę parti figurę GBI, & </
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<
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parti figuræ GBH, ſed rectangulum GBI maius eſt rectangulo GBH, cum ſit
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BI minor BH, ergo BP minor eſt BR; </
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<
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infra FR aſymptoton circumſcriptæ diuidens angulũ ab ipſius aſymptotis fa-
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ctum, ex quo ipſa FP producta ſecabit Hyperbolen circumſcriptam ABC.</
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Quod erat vltimò, &</
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