Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Præterea ſit data Ellipſis, vel circulus GHB, cuius diameter BG, rectum
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BE, regula EG, & </
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">oporteat per verticem B, _MINIMAM_ Parabolen in pri-
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ma figura, vel cum dato quocunque tranſuerſo BF, _MINIMAM_ Hyperbo-
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len in ſecunda figura, ſiue cum dato tranſuerſo BF, quod in tertia, & </
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<
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figura excedat tranſuerſum BG datæ Ellipſis, vel circuli, _MINIMAM_ Elli-
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pſin circumſcribere.</
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<
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">Adſcribatur Ellipſi GHB per verticem B in prima figura parabole
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& </
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<
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">in ſecunda Hyperbole ABC, cum dato tranſuerſo BF, & </
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<
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">in tertia, & </
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ta Ellipſis ABC cum dato tranſuerſo BF; </
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">& </
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<
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xml:space
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">harum omnium ſectionum re-
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ctum latus idem ſit cum recto BE datæ Ellipſis. </
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ABC datæ GHB circumſcriptam eſſe. </
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">Inſuper dico talem ſectionem
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roll. prop.
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19. huius.</
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eſſe _MINIMAM_ quæſitam.</
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<
s
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">Nam, in prima figura, quælibet parabola, vel in reliquis, quæcunque eiuſ-
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dem nominis ſectio adſcripta ſectioni ABC per verticem B, cum eodem
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tranſuerſo BF, ſed cum recto BL, quod excedat rectum BE ſectionis ABC
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eadem ſectione eſt maior, quælibet verò adſcripta ſectio cum recto BI,
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roll. prop.
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19. huius.</
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minus ſit recto BE minor eſt ſectione ABC, ſed Ellipſim GHB omninò
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roll. prop.
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19. huius.</
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">1. Co-
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roll. prop.
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19. huius.</
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cat cum ipſarum regulæ IN, GE infra contingentem ex vertice ſe mutuò ſe-
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cent. </
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<
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">Quare ſectio Parabolæ, vel Hyperbole, aut Ellipſis ABC eſt _MINI_-
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_MA_ circumſcriptibilium datæ Ellipſi, vel circulo GHB. </
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<
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rem axem, per eius verticem _MAXIMVM_ circulum inſcribere.</
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<
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">Item datæ Ellipſi circa minorem axem, per eius verticem _MIMIMVM_ cir-
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culum circumſcribere.</
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<
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">Si enim in tribus primis ſuperioribus figuris concipiatur diametrum BD
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datæ Parabolæ, vel Hyperbolæ, aut Ellipſis ABC eſſe propriæ ſectionis
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maiorem axem, eiuſque ſegmentum BG æquari recto lateri BE, circa quod
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adſcripta ſit Ellipſis GHB cũ recto BE: </
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<
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huius.</
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_XIMA_ inſcriptibilium, eritque Ellipſis æqualium laterum circa axim, quam
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in Monito poſt primam huius, animaduerſum fuit circulum eſſe. </
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<
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tæ coni-ſectioni circa maiorem axim inſcriptus erit _MAXIMVS_ circulus per
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verticem ſectionis. </
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<
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<
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">Siverò, vt in quarta figura, datæ Ellipſi GHB circa minorem axim BG, & </
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cuius rectum latus BE _MINIMVS_ circulorum ſit circumſcribendus; </
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<
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BF æquali recto BE, ipſa excedet tranſuerſum latus BG datæ Ellipſis GHB
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(nam ſemper in Ellipſi minor axis ad maiorem, eſt vt maior axis ad latus re-
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ctum) itaque ſi circa BF Ellipſis adſcribatur ABC, cum recto BE datæ Elli-
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pſis, ipſa, per ſecundam partem propoſitionis huius, erit _MINIMA_ datæ
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Ellipſi circumſcriptibilium, ſed talis Ellipſis ABC per Monitũ poſt 1. </
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<
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cum ſit æqualium laterum, & </
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<
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tæ Ellipſi circa minorem axem per eius verticem _MINIMVS_ circulus circũ-
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ſcriptus erit. </
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<
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