Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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4121LIBER I. Dico, RO, eſſe parallelam lateri cylindrici, FG. Iungantur, CE.
1133. p. Pri-
mi Elem.
p. 16. Vn-
dec. Elem.
10. Vnde-
cimi Ele. MN, quoniam ergo, CE, MN, coniungunt extrema laterum cy

15[Figure 15] lindrici, CM, EN, quæ ſunt æqualia, &
parallela, erunt & ipſæ æquales, & paralle-
læ, ſunt etiam parallelę ipſæ, CR, MO, er-
goangulus, ECR, erit æqualis angulo, N
MO, eodem pacto oſtendemus angulum, C
ER, eſſe æqualem angulo, MNO, vnde
2226. Primi
Elem. etiam, CR, MO, erunt æquales, & funt pa-
rallelæ, ergo eas iungentes, quæ ſunt, RO,
CM, erunt ęquales, & parallelę, eſt autem,
CM, latus cylindrici, FG, ergo, RO, com-
munis ſectio duorum planorum dictum cy-
lindricum ſecantium, erit eiuſdem lateribus
parallela. Idem oſtendemus, ſi ſectio contingat fieri intra cylindri
cum, ſiautem fiat in ſuperficie, patet non poſſe fieri, niſi in latere
cylindrici, nam plana ſecantia ducuntur per latera, quodfibet autem
latus eſt cęteris eiuſdem cylindrici lateribus æquidiſtans, & ideò vbi-
cumq; contingat ſectionem fieri ſemper communis ſectio planorum
perlatera cylindrici ductorum ſe inuicem ſecantium, eſt parallela la-
teribus cylindrici. Idem ſequetur de tangentibus planis, quod erat
oſtendendum.

THEOREMA V. PROPOS. VIII.

SI quilibet cylindricus ſecetur planis parallelis perlatera
ductis conceptæ in cylindrico figuræ erunt parallelo-
gramma æquiangula.

Sit quilibet cylindricus, BF, planis ſectus

16[Figure 16] parallelis per latera ductis, ſit autem vnius
in cylindrico, AF, concepta figuræ paral-
lelogrammum, BH, alterius autem paral-
lelogramma, AN, QF. Dico hæc eſſe
ęquiangula, quod enim ſint parallelogram-
33ExCor. 6.
huius. ma, patet, quia plana ſecantia ducuntur per
latera, quod verò fint æquiangula patet e-
tiam, nam in parallelogrammo, AN, la-
tus, AD, æquidiſtat lateri, BO, & , AP,
ipſi, BC, nam ſunt communes fectiones pla-
ni, ABCR, & æquidiftantium planorum,
AN, BH, & ideo angulus, PAD, æqua-
4410. Vnde-
cimi Ele. tur angulo, CBO, ergo parallelogramma, AN, BH, erunt

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