Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſecat Elli pſim datam GBL, _a_ cum & </
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">iuncta regula EN ſecet regulam FD.
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<
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xml:space
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">Quare Ellipſis ABC, erit _MINIMA_ quæſita circumſcripta, cum dato recto
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BE. </
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">Datæ Ellipſi circa minorem axim, per eius verticem MAXI-
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MVM circulum inſcribere. </
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<
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">Datæ Ellipſi circa maiorem axim, per eius verticem MINI-
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MVM circulum circumſcribere.</
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<
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">data Ellipſis ABC, circa minorem axim BD, cuius rectũ ſit BE,
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regula DE, & </
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">oporteat per verticem B _MAXIMVM_ circulum inſcribere.</
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_XIMVM_ quæſitum.</
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">Sumpta enim BF æquali BD, erit ipſa rectum latus deſcripti circuli: </
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ctaque DF eius regula cum ſit axis minor BD, minor recto latere BE, erit
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etiam BF minor BE, vnde regula DF cadet intra regulam DE, ideoque cir-
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culus GBH inſcriptus erit Ellipſi ABC, eritque _MAXIMVS_: </
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roll. prop.
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19. huius.</
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alius per B adſcriptus, cuius diameter, minor ſit ipſa BD, minor eſt circulo GBH, & </
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">cuius diameter BI ſit maior BD eſt quidem maior circulo
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rol. prop.
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19. huius.</
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ſed vel ſecat, vel cadit extra Ellipſim ABC, cum punctum I quoque cadat
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extra. </
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<
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tæ Ellipſi ABC inſcriptus. </
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regula DE. </
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hunc eſſe _MINIMVM_ quæſitum.</
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<
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">Cum ſit enim axis BD maior recto latere BE, ſumpta BF æquali BD, ipſa
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erit latus rectum circuli GBH, & </
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roll. prop.
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19. huius.</
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tota extra Ellipſis regulam DE, ac ideò circulus erit Ellipſi circumſcriptus, eritque _MINIMVS_; </
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<
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19. huius.</
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cuius diameter ſit maior BD, eſt maior ipſo GBH, & </
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