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

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3818GEOMETRIÆ ducamus rectam, VN, parallelam ipſi, AB, tranſibit hæc per
11Vide di-
cta lib 7.
Annot.
Prop. 3. punctum, E, qui eſt etiam vertex rcſpectu ipſius, AB, igitur ſeca-
bit, HM, quod eſt abſurdum, nam vtræque ſunt parallelæ eidem,
AB, & ideò inter ſe ſunt parallelæ, vel, VN, extendetur ſuper, H
M, & ſic, HM, tranſiret per, C, in ipſoq; tangeret figuram con-
tra ſuppoſitum, quod etiam eſt abſurdum, non igitur, HM, tanget
22Ex A. De-
fin. 1. hu-
ius. figuram, CARB, ſed erit tota extra figuram, ſi nullibi concurrat
cum ambitu figuræ, vel, tranſiens per aliquem punctum, eandem
ſecabit, ſi is punctus non ſit ex illis, qui funt vertices ipſius figuræ ex
hac parte, vel ex oppofito reſpectu ipſius, AB; quod ſimiliter in ſo-
lidis oſtendemus pro rectis lineis, AB, HM, VN, plana intelligen-
tes, & ipſam, CARB, eſſe figuram ſolidam ſupponentes, quæ
oſtendere opus erat.

COROLLARIVM I.

_H_Inc patet à quolibet puncto ambitus datæ figuræ planæ, vel ſolidæ
ductam lineam, vel planum æquidiſtans illi, reſpectu cuius ſumi-
tur vertex (ſi ſumptus punctus non ſit vnus ex verticalibus dictis) ſeca-
rè figuram, cum, vt oſtenſum eſt, tangens eſſe non poſſit, & ideò ſem-
per inter duo oppoſita tangentia, reſpectu regulæ, penes quam ſumitur
vertex, aſſumpta linea cadet, licet indefinitè producatur.

COROLLARIVM II.

_E_T quia ſi recta linea, vel planum, ſecat duas parallelas, vel duo
æquidiſtantia plana, ſecat etiam omnia intermedia illis æquidi-
ſtantia; ideò ſi recta linea, vel planum, tranſeat per verticem, & baſim,
ſiue per oppoſitos vertices datæ figuræ planæ, vel ſolidæ, ſecabit etiam om-
nes in figura oppoſitis tangentibus æquidiſtantes intra figuram, vel ea-
ſdem productas extra figuram.

THEOREMA II. PROPOS. V.

SI à quocumque puncto circuitus cylindrici, per quam fit
reuolutio verſus cylindricum ducta fuerit recta linea
33D. fin. 3. paralleìa regulæ lateris cylindrici, hæc eritlatus cylindrici
in talibaſi conſtituti.

Sit cylindricus, CB, In baſi, AFB, in cuius circuitu ſumpto vt-
cumq; puncto, F, ab eo ducta ſit verſus cylindricum quædam

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