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

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4727LIBER I.

LEMMA PRO ANTECED. PROP.

DEſiderari tantum videtur huius euidentia, quod ſcilicet planum
inter oppoſita tangentia plana eiſdem a quidiſtanter ductum
tranſeat perlatera cylindrici, quod aſſumpra eiuſdem figura nunc

20[Figure 20] fiet manifeſtum; intelliga-
tur ergo in ambitu vtriuſuis
oppoſitarum baſium cylin-
drici, PN, ſumptum pun-
ctum, vt, O, in ambitu fi-
guræ, ZON. Dico pla-
num, quod tranſit per, O,
æquidiſtans planis tangen-
tibus, AG, VL, tranſire
per latera cylindrici, PN.
Ducatur ergo à puncto, O,
latus cylindrici, PO, & ab
eodem pundo, O, in baſi,
ZON, recta, ON, paral-
lela ipſi, XL, igitur pla-
num, quod tranſit per, P
O, ON, æquidiſtat plano,
1115. Vnde-
cimi Ele. VL, nam, PO, ipſi, VX,
lateri cylindrici, & , ON,
ipſi, XL, ęquidiſtat, quod
ergo ducitur per, O, eidem plano tangenti æquidiſtans tranſit per
ipſas, PO, ON, ſi. n. non, erunt duo plana eidem plano, VL,
æquidiſtantia, & ideò inter ſe æquidiſtantia, quibus communis erit
punctus, O, igitur in eo concurrent, quod eſt abſurdum, non ergo
illa ſunt duo plana, ſed vnum tantum, illud nempè, quod ducitur
per punctum, O, ipſi plano, VL, æquidiſtans, tranſitque per, P
O, ON, neceſſariò: Siverò à punctis, I, M, N, erigantur latera
cylindrici, CI, ME, NK, erunt cuncta in plano per, PO, ON,
tranſeunte, ergo planum, quod ducitur per punctum, O, æquidi-
ſtans plano, VL, cylindricum tangenti tranſit per latera, PO, CI,
EM, KN, quod oſtendendum erat.

THEOREMA IX. PROPOS. XII.

SI cylindricus planis ſecetur quomodocumque pet latera
ductis, eiuſdem oppoſitę baſes in figuras ſimiles, ęqua-
les, & ſimiliter poſitas diuiduntur, tales autem erunt,

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