Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si Parabolen, vel Hyperbolen, aut Ellipſim circa maiorem
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axim recta linea, præter ad verticem contingat, cui à tactu ducta
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ſit perpendicularis axi occurrens; </
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<
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">circulus, cuius centrum ſit idem
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occurſus, radius verò ſit ipſa perpẽdicularis erit ſectioni inſcriptus.</
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<
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<
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<
s
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xml:space
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">Si autem Ellipſis fuerit circa minorem axim, cui prædicta per-
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pendicularis occurrat, circulus ex ea tanquam radio, at centro fa-
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cto ipſo occurſu, erit eidem Ellipſi circumſcriptus.</
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<
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">ESto ABC, Parabole, vel Hyperbole, in prima figura, aut Ellipſis in ſe-
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cunda, circa maiorem axim BO; </
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<
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">vel circa minorẽ, vt in tertia, quarum
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vertex B, & </
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<
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">ad aliud punctum quædam contingens EF, cui ducta ſit perpen-
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dicularis ED, quæ axi occurret in D, quo facto centro, & </
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<
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circulus EGHI deſcribatur. </
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<
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ra, datæ ſectioni eſſe inſcriptum.</
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130
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<
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">Applicata enim EH, ſecans
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axim in L, & </
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<
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<
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">Cum in triangulis
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ELD, HLD anguli ad L ſint recti, & </
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">latera EL, LD æqualia lateribus HL,
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LD, erit baſis DE æqualis DH, exquo circulus ex DE tranſibit omnino per
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H, ideoque coni-ſectio, & </
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<
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">circulus, ſunt binæ ſectiones ſimul adſcriptæ
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(cum earum diametri, & </
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<
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">applicatæ ſimul congruant) quæ in ijſdem extre-
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mis communis applicatæ EH ſimul conueniunt, atque ad eorum alterum E,
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eadem recta EF vtranque ſectionem contingit, nempe ſectionem ABC, ex
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ſuppoſitione, & </
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<
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">circulum EGHI, cum EF ſit ad extremum ſemi-diametri
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ED perpendicularis, atque vertex circuli G cadit infra B verticem ſectionis,
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cum ſit DB maior DE, ſiue maior DG, quare circulus ex DE erit
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">ibideni.</
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xml:space
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inſcriptus. </
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<
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">AMpliùs, dico in tertia figura, prædictum circulum EGHI eſſe datæ El-
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lipſi ABCO circumſcriptum.</
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<
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