Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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nor eſt; </
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<
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">quæ verò cum maioribus eſt quidem maior, ſed omnino ſecat
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roll. 19. h.</
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">ibidem.</
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rabolen ABC, vti oſtenſum fuit in præcedentibus. </
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<
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AECH, datæ Parabolæ per datum intra ipſam punctum E eſt _MAXIMA_ in-
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ſcripta quæſita. </
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<
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<
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">IAM ſit data Ellipſis AECH, cuius centrum N, & </
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<
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">datum extra ipſam pun-
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ctum ſit B, per quod oporteat _MINIMAM_ Parabolen circumſcribere.</
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<
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">Iungatur BN ſecans Ellipſim in E, & </
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">poſita NE media geometrica, & </
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media arithmetica inter eaſdem ignotas extremas, reperiantur ipſæ
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mę, quę ſint ND, NL, & </
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<
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">per Dad Ellipſis diametrum EH applicetur ADC,
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& </
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<
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">per verticem B, circa diametri ſegmentum BD, & </
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<
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">per terminos A, C de-
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ſcribatur Parabole ABC. </
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<
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">Dico hanc eſſe _MINIMAM_ quæſitam.</
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<
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">Cum enim ſit NE media geometrica inter LN, ND, erit rectangulum
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LND æquale quadrato NE; </
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">& </
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">per D applicata eſt in Ellipſi recta ADC, ſi
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iungantur LA, LC ipſæ Ellipſim contingent in A, C; </
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dia arithmetica inter eaſdem LN, ND, erunt ipſarum differentiæ LB, BD
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inter ſe æquales; </
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<
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">vnde eædem LA, LC Parabolen contingent,
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37. primi
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conic. ex
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Comand.</
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hæc datæ Ellipſi erit circumſcripta. </
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eidem Ellipſi adſcribitur cum recto maiori, maior eſt ABC, quæ verò
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minori eſt quidem minor, ſed omnino ſecat Ellipſim, vti ex
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roll. 19. h.</
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& </
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">Quapropter Parabole ABC eſt _MINIMA_ circumſcri-
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pta quæſita. </
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<
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bolæ, & </
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circulus; </
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<
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AD æquabitur rectangulo HDE; </
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<
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bebitur, quo pacto per punctum E in axe Parabolæ, _MAXIMVS_ circulus in-
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ſcribatur: </
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<
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">applicata enim EF, cui ſumpta æquali ED, iunctaque FD, & </
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ducta in G, & </
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<
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">applicata GH, ipſa dabit EH diametrum quæſiti circuli.</
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">PAtet etiam ſemi-applicatas in Parabola, ex terminis diametri _MAXIMI_
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inſcripti circuli, ęquari contiguis ſegmentis eiuſdem diametri, ab appli-
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cata ex contactu circuli cum ſectione abſciſſis. </
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<
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ob ſimilitudinem triangulorum, crit etiam GH æqualis HD.</
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<
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">SI quis in vigeſimo nono, ac trigeſimo antecedenti Problemate, a
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ſeueritate geometricæ demonſtrationis expeteret, nontantum El-
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lipſes, per datum punctum ibi contingenter inſcriptas, ad par-
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tes verticis, tum anguli, tum Parabolæ oppoſitas, MAXI-
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MAS eſſe ſibi ipſis ſimilium per idem punctum, adeaſdem partes </
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