Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si rectum Conoides Parabolicum, vel Hyperbolicum, aut Sphę-
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ra, aut Sphæroides rectum plano per axem ſecetur, & </
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<
s
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ſectionem plani ſecantis cum ſolidi ſuperficie quædam recta linea
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in puncto contingat, per quam ductum ſit aliud planum, quod re-
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ctum ſit ei per axem ducto: </
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<
s
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">huiuſmodi planum in prædicto tantùm
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puncto ſolidi ſuperficiem continget, ipſaque ſuperficies cadet tota
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ad alteram partem plani contingentis.</
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<
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">ESto rectum Conoides Parabolicum, vel Hyperbolicum, vt in prima fi-
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gura; </
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s
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">vel Sphæra, aut Sphæroides rectum, vt in ſecunda, plano per
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axem B D ſectum efficiente in ſolidi ſuperficie ſectionem A B C, (quæ erit
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genitrix datiſolidi) & </
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<
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">per punctum E in ipſa ſumptum, ſit ei contingens
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ment. Cõ.
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mand. in
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lib. Arch.
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de Conoi.
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& Sphær.</
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nea F E G, per quam concipiatur duci planum H I, quod ſit rectum plano
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per axem A B C: </
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<
s
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">dico huiuſmodi planum H I in ipſo tantùm puncto E con-
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uexam ſolidi ſuperficiem contingere, atque hanc totam cadere infra pla-
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num H I.</
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">Cum enim recta F E G ſe-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0256-01
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ctionem A B C cõtingat, pro-
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ducta conueniet cum axe
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pr. conic.</
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ctionis B D ad partes verticis
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B; </
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">qua propter ſi concipiatur
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planum A B C denuò conuer-
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ti circa axim B D, patet ſectio-
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nem A B C, dati ſolidi, & </
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<
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tingentem F E G, coni ſuper-
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ficiem deſcribere, quæ conue-
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xam ſolidi ſuperficiem per cir-
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culi tantùm peripheriam à pũ-
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cto E deſcriptam continget
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(cum punctum E ſit tum in contingente, tum in ipſa ſectione, & </
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<
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">in reuolu-
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tione peripheriam circuli deſignet, ac reliqua puncta rectæ F G ſint extra
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ſectionem A B C.) </
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<
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">Et quoniam planum H I per contingentem F G du-
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ctum, poſitum fuit rectum ad planum per axem A B C, quod eſt idem, ac
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planum per axem coni â latere F G deſcripti, ergo planum H I ſecundùm
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latus tantùm F G conicam ſuperficiem continget, ſed latus F G
<
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ſolidi ſuperficiem contingit tantùm in puncto E, quare planum H I in vnico
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puncto E ſolidi ſuperficiem contingit, ac ideò hæc cadit tota infra planum
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H I. </
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