Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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_MI_ circuli, erunt, vt quadrata eorumdem numerorum diſparium ab vnita
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te. </
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">Datæ Hyperbolę, per punctum intra ipſam datum MAXIMAM
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Parabolen inſcribere; </
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<
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">Datæ Parabolæ, per punctum extra ipſam datum cum dato ſe-
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mi- tranſuerſo latere MINIMAM Hyperbolen circumſcribere.</
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<
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tum ſit G. </
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<
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arithmeticam, EB verò mediam geometricam inter eaſdem ignotas extre-
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mas, quæ reperiantur, & </
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diametrum GF adſcribatur ipſi Hyperbolæ ABC, Parabole
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quarum communis applicata ſit AC. </
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">Cum enim ſit FE ad EB, vt EB ad EH, erit
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rectangulum FEH æquale quadrato EB, qua-
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re AH Hyperbolen continget. </
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37. primi
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conic.
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Comand.</
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EG media arithmetica inter FE, EH, erunt
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ipſarum diſferentiæ FG, GH æquales, vnde
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eadem AH Parabolen quoque continget:</
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quare Parabole D G M Hyperbolæ ABC erit inſcripta. </
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patet; </
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recto minori, minor eſt AGC, quę verò cum
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maiori, eſt quidem maior, ſed omninò ſecat
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Hyperbolen ABC, cum ſectio Parabole in in-
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finitum abeat, & </
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que ſit clauſa. </
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oporteat, cum dato quolibet ſemi-tranſuerſo D, _MINIMAM_ Hyperbo-
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len circumſcribere.</
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">Ducatur per B diameter Parabolæ DGF, quæ vltra B producatur, ſuma-
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turque BE ipſi D æqualis, & </
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thmetica inter eaſdem ignotas extremas, reperiantur ipſæ extremæ,
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ſint EH, EF; </
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<
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tri ſegmentum BF, cum ſemi- tranſuerſo BE deſcribatur Hyperbole ABC.</
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Dico ipſam eſſe _MINIMAM_ quæſitam.</
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<
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<
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bitur ipſam HA, & </
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ſe mutuò contingent, & </
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<
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eritque _MINIMA_; </
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<
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dem tranſuerſo, ſed cum recto maiori, maior eſt ipſa ABC, quæ verò cum
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minori, eſt quidem minor, ſed cum ipſi ABC ſit inſcripta, & </
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