Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

298. THEOR. XXXVII. PROP. LVI.

Si coni-ſectio, vel circulus coni-ſectionem, vel circulum intus,
vel extra, in vno, aut in duobus punctis contingat, & harum ſectio-
num axes, vel ſibi mutuò congruant, vel æquidiſtent, vtraque au-
tem figura, altera immota, circa proprium axem conuertatur. So-
lidum factum ab vna ſectionum nunquam ſecabit ſolidum ab altera
genitum, ſed omnino ſe mutuò contingent, velin vnico puncto, ſi
figurarum planarum contactus fuerit tantùm in puncto, ſiue axes
congruant, ſiue æquidiſtent; vel in duobus tantùm, ſi ad duo pun-
cta ſe mutuò contingant, dum axes ſint paralleli; vel denique ad
integram circuli peripheriam à contactibus genitam, ſi ad duo
puncta ſectiones ſimul occurrant, dum axes ſimul congruant.

SInt duæ coni-ſectiones A B C, D E F, quarum axes ſint B G, E H, & vel ſimul congruant, vt in prima, quinta, & ſexta figura, vel inter ſe æ-
quidiſtent, vt in ſecunda, tertia, & quarta, atque ſe mutuò contingant, vel
in vnico puncto I, vt in prima, ſecunda, & tertia, vel in duobus tantùm I
L, vt in quarta, quinta, & ſexta; & concipiatur modò figura A B C, ma-
nente alia D E F, circa axim B G conuerti; modò figura D E F, manente
altera, ita vt ab ipſis ſolida conoidalia, ſphærica, aut ſphæroidalia deſcri-
bantur. Dico talia ſolida nunquam ſimul ſecari, ſed vel in vnico puncto I,
in quo plana ſe contingunt, ſe quoque mutuò contingere in prima, ſecun-
da, & tertia, vel in duobus tantùm I, L, in quarta vbi axes B G, E H inter

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