Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

715. THEOREMA XIII. PROPOS. XIII.

SI, expoſitis duabus quibuſcumq; ſolidorum rectangu-
lorum deſcriptibilium regulis, ad vnum punctum cõ-
poſitis, iuxta eaſdem ſolidum rectangulum contineatur
ſub parallelogrammo, & alia quacumq; figura plana in
ambitu contenti ſolidi exiſtente, ipſum ſolidum rectangu-
lum erit cylindricus, & figura plana ſuperius dicta erit il-
lius baſis. Quod ſi etiam prædicta figura fuerit parallelo-
grammum, & ambo in illius ambitu, contentum ijſdem
ſolidum rectangulum erit parallelepipedum.

Exponantur duæ inuicem perpendiculares regulæ, BC, CD, ſo-
lidorũ deſcriptib liũ ſub parallelogrammo, AC, & figura plana qua
cumque, HDC, ſit autem deſcriptum ſolidum rectangulum ſub eiſ-
dem contentum, AG
CH, iuxta regulas, B
C, CD, ita tamen vt
figura plana, HDC,
ſit in ambitu ipſius
contenti ſolidi. Di-
co, AGCH, eſſe cy-
lindricum. Quod. n. AC, CG, GH, ſint
ſuperficies cylindra-
ceæ, quarum regula,
BC, manifeſtum eſt,
quod verò latera per
ſecantia para lela plana in ipſis deſignata ſint æqualia ipſi, BC, la-
teri parallelogrammi, AC, ex dictis etiam cõſtare poteſt, ſed maio-
ris dilucidationis gratia ſit ab aliquo dictorum ſecantium planorũ,
in ſolido, AGHC, productum rectangulum, IMON, eſt ergo, IN,
æqualis, MO, hoc eſt ipſi, BC, quo pacto idem de cæteris oſten-
demus, in parallelogrammo autem, GC, eadem verificantur, & in
illi oppoſito, ſi contactus plani ipſi, GC, oppoſiti eſſent in plano,
vt manifeſtum eſt, ergo perinde eſt ac ſi latus æquale, BC, ambitũ
figuræ, HDC, extremo ſui puncto ſemper ipſi, BC, æquidiſtanter
percuriſſet ipſam ſuperficiem, ADBH, deſcribendo, erit ergo, A
GCH, cylindricus, cuius baſis eſt, HDC, figurá. Præfatum qui-
dem ſolidum habet in ambitu figuras ipſum continentes, ſed ſi ve-

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