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

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3919LIBER I. lela ipſi, HM, quæ ſit regula lateris cylindrici. Dico eam eſſe la-
tus huius cylindrici: Intelligatur per punctum, F, ductum latus cy-

13[Figure 13] lindrici, quod ſit, FE, veligitur du-
cta ab, F, parallela ipſi, HM, ca-
dit ſuper, FE, & ſic erit, & ipſa la-
tus cylindrici, vel non, nempè ſi ca-
deret, vt, FG, tunc quia, FE, eſt
parallela ipſi, HM, & etiam, FG,
eſt ipſi, HM, parallela ſequitur, F
E, ipſi, FG, eſſe parallelam, & ſunt
FE, FG, eductæ ab eodem pun-
cto, F, In quo ſunt concurrentes,
quod eſt abſurdum, igitur quæ du-
citur à puncto, F, parallela ipſi, H
M, cadet ſuper, FE, latus cylindri-
ci, igitur erit latus huius cylindrici, quod erat oſtendendum.

THEOREMA III. PROPOS. VI.

SVperficies, quæ clauditur ambitu deſcripto ab extremo
puncto lateris cylindrici, quod per circuitum eiuſdem
baſis non properat, eſt ſuperficies plana, & æquidiſtans bafi;
ſi ea ſumatur, in qua iacent iungentes duo quæuis puncta de-
ſcripti ambitus.

Sit quilibet cylindricus, AE, cuius baſis, CDEV, latus, MV,
cuius punctum extremum, M, quod non properat per ambitum ba-

14[Figure 14] ſis, in reuolutione deſeribat circuitum, MANH.
Dico figuram hoc circuitu comprehenſam, in qua
iacent iungentes duo quęuis puncta deſcripti am-
bitus eſſe ſuperficiem planam, ęquidiſtantem baſi,
CDEV, & ideò ſingula puncta huius circuitusre-
periri in tali plano. Sumatur ergo in tali circuitu
vtcumq; punctum, M, & per, M, ducatur baſi,
CE, æquidiſtans planum, MBOF. Dico om-
nia puncta deſcripti circuitus eſſe in hoc, plano: ſi
enim non ſint, aliquod erit extra, ſit hoc pun-
ctum, N, & per, N, ſit ductum latus cylindrici,
quod ſit, ND, ſecans circuitum figuræ planæ, B
F, in, O, & circuitum baſis in, D, deinde per, N
D, MV, quæ ſunt æquidiſtantes, cum fint cylindrici latera,

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