Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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Dico hanc eſſe _MINIMAM_ circumſcriptam quæſitam.</
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<
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">Cum ſint enim ipſæ Parabolæ congruentes, & </
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ſcriptæ, erunt inter ſe nunquam coeuntes quare ABC datæ GDH erit
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cumſcripta.</
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<
s
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">Præterea, quælibet alia Parabole per B adſcripta cum recto, quod exce-
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dat BF, maior eſt ipſa ABC, quę verò cum recto BO, quod minus ſit ipſo BF,
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qualis eſt PBQ, eſt quidem minor ipſa ABC, ſed omnino ſecat inſcriptam
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GDH. </
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">Quoniam ſi fiat vt FO ad OB, ita BD ad DE, ac per E applicetur
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EGP ſecans DG in G, & </
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">cum ſit BD ad DE, vt FO ad OB, erit com-
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ponendo BE ad ED, vt FB ad BO; </
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roll. 1. h.</
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quadratum applicatæ EP in Parabola PBQ æquale erit rectangulo ſub me-
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dijs ED, & </
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<
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">BF, ſiue DI, hoc eſt quadrato applicatę EG in Parabola GDH:</
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">ibidem.</
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vnde EP, EG ſunt æquales. </
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per diuerſos vertices, in puncto P, quare in eodem occurſu, & </
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partem ſe mutuò ſecant. </
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_NIMA_ circumſcripta quæſita.</
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Hyperbolen inſcribere, quarum eadem ſit regula.</
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tum ſit E. </
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ſed tamen eius regula ſit quoque regula datæ ſectionis.</
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B, & </
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erit FB trãſuerſum ſectionis ABC,
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conic.</
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vertex B, ſitque BG eius rectum latus, & </
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regula FG, quæ producatur, & </
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ducta EH parallela ad BG, & </
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E, circa communem diametrum BE, da-
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tę ſectioni ABC adſcribatur
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IEL, cuius latera ſint FE, EH, hoc eſt
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eadem ſit regula FGH: </
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datæ ABC eſſe inſcriptam, cum in infini-
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tum productæ ſint inter ſe
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coeuntes.</
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<
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_MAM_. </
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per verticem E, cum eodem tranſuerſo
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FE, ſed cum recto, quod minus ſit recto
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EH, minor eſt ipſa IEL; </
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<
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">quæ verò cum recto EO, quod excedat EH,
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roll. 19. h.</
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lis eſt Hyperbole PEQ, eſt quidem maior ipſa IEL; </
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<
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ABC. </
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<
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<
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Hyperbolen PEQ ſecans in P, BA verò in A, & </
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FH, in N, & </
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