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

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4222GEOMETRIÆ angula, eodem pacto oſtendemus parallelogramma, QF, BH, eſſe
æquiangula, vnde concludetur etiam parallelogramma, AN, QF,
eſſeinter ſe æquiangula, quod oſtendere opus erat.

COROLLARIV M.

_S_I autem intelligamus oppoſitarum baſium cylindrici, AF, ita pra-
ducta plana, vt ſecentur à plano per latera, AD, PN, QM, RF,
ducto in rectis, AR, DF, quarum portiones extra cylindricum manen-
tes ſint, PQ, NM, manifeſtum eſt etiam parallelogrammum, PM,
quod extra cylindricum conſtituitur, & quod integratur ex parallelo-
grammis, AN, PM, QF, . i. AF, eſſe prædictis æquiangulum.

THEOREMA VI. PROPOS. IX.

SI planum æquidiſtans plano perlatera cylindrici ducto
tangat cylindricum, contactus fiet in recta linea, velre-
ctis lineis, quæ erunt latera eiuſdem cylindrici: Vel ſi tan-
gat in plano, aut planis, plana contactus erunt parallelo-
gramma, æquiangula perlatera ducto.

Sit cylindricus, AC, per cuius latera ducatur planum in eo pro-
ducens parallelogrammum, AC, ſit autem ductum aliud plannm

17[Figure 17] huic æquidiſtans, quod tangat cy-
lindricum, AC. Dico eiuſdem con-
tactum fieri in recta linea, vel rectis
lineis, quę erunt latera cylindrici, A
C, vel ſi tangat in plano, aut planis,
plana contactus eſſe parallelogram-
ma, æquiangula ipſi, AC. Primò
igitur non tangat ipſum in plano,
quia ergo tangit cylindricum, ali-
quid ſuperficiei cylindrici commune
eſt ipſi, & plano tangenti, ſit is pun-
ctus, O, exiſtens, & in plano tangen-
te, & in ſuperficie cylindracea, &
per, O, ſit ductum latus cylindrici,
quod ſit, EM. Dico totum, EM,
reperiri in plano tangente cylindri-
cumin, O, ęquidiſtante ipſi, AC. Ducatur per, M, ipſi, BC, pa-
rallela, XR, quia ergo, XR, ęquidiſtatipſi, BC, & EM, ipſi,

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