Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">MINIMA linearum, ad peripheriam cuiulibet coni - ſectio-
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nis ducibilium à puncto axis (quod
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in Ellipſi ſit axis maior) di-
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ſtante
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à vertice per interuallum non maius dimidio recti lateris,
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eſt idem axis ſegmentum inter aſſignatum punctum, & </
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interceptum. </
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<
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ioris axis ſegmentum, in quo centrum reperitur.</
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<
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">In Ellipſi verò circa minorem axim; </
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<
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à puncto eiuſdem axis, quod diſtet à vertice per interuallum non
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minus dimidio recti, eſt ipſum axis ſegmentum, inter aſſumptum
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punctum, & </
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<
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<
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minoris axis ſegmentum, in quo centrum non reperitur.</
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<
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<
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in prima figura, vel Ellipſis, vt in ſecunda, circa maiorem axim
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B D, in quo ſumptum ſit pun-
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ctum E, quod primò diſtet à
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vertice B per interuallum ęqua-
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le dimidio recti lateris axis BD,
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quodq; </
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<
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">in Ellipſi omnino minus
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erit ſemi - axe B H (eſt enim ſe-
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mi - axis maior ad ſemi - axim
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minorem, vt ſemi - axis minor
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ad ſemi-rectum.) </
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<
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xml:space
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tum axis E B eſſe _MINIMAM_
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linearum ex E ducibilium ad
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ſectionis peripheriam ABC, & </
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reliquam B D, in qua eſt cen-
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trum, eſſe _MAXIMAM._</
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<
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E, interuallo E B circulo B F,
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ipſe cadet totus intra
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roll. 20. 1.
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huius.</
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A B C: </
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ad ſectionis peripheriam ducẽ-
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tur, præter ad B, omnino maio-
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res erunt, quàm ductæ ex eo-
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dem centro ad circuli periphe-
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riam, quibus æqualis eſt E B.
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</
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<
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<
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eſt G B: </
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">cum ad peripheriam circuli B F ipſa G B ſit _MINIMA_, eò magis
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_MINIMA_ erit ad Ellipſis circumſcriptam peripheriam A B C D.</
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