Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER VII. parallelogrammum, & , F℟& , eſt angulus rectus, eſt enim exterior
parallelarum, F℟, XT, & ideòipſi interiori, XT& , æqualis, erit,
E℟, etiam rectangulum, & quia, & ℟, æquatur ipſi, TV, ſunt. n. ΔΜ, OI, figuræ homologæ,
ſicut etiam, F℟, æquatur ip-
ſi, YV, ideò rectangulum, E
℟, erit æquale rectangulo, X
V. Eadem ratione oſtende-
mus, quæcunq; alia duo re-
ctangula ab eodem dictorum
ęquidiſtantium plano in ipſis
ſolidis producta ęqualia eſie,
ergo cum ſolida, CM, PI, ſint
in eadem altitudine ſumpta
regulis eiſdem æqualibus re-
ctangulis, cõcluduntur enim
inter extrema plana parallela, quorum contactus eſt in planis, N
M, RI; Cλ, PB, ideò dicta ſolida erunt æqualiter analoga iuxta di-
ctas regulas, ergo inter ſe æqualia erunt; & cum ſuperficies, ΔΜ,
ſit homologa ipſi, OI, & , DM, ipſi, QI, regula plano, RI, propte-
rea & erit, CM, ſolidum rectangulum æquale ipſi, PI, & ſub eiſdẽ
ſuperficiebus, QI, IO, continebitur, & eius regulæ erunt pariter
ipſæ, HI, IS. Cum verò in ſuperficie, OI, indefinitè producta, in-
definitæ numero figuræ ipſi, OI, homologæ, regula plano, RI,
ſupponi poſſint, vt facillimè apparet, ideò ſupradicta methodo tot
ſolida rectangula ijſdem ſuperexſtrui poterunt, regulis eiſdẽ, quot
erunt figuræ ipſi, HP, homologæ, iuxta dictas regulas, ideſt nu-
mero indefinita, quorum vnumquodq; ipſi, PI, adæquari, ac ſub
eiſdem ſuperficiebus, QI, IO, contineri, vt ſupra oſtendemus. Quemadmodũ ſi etiã indefinitè ſuperficies, PH, HS, SB, BP, ſupra,
vel infra producerentur, alia indefinita numero ſolida rectangula
inueniri eodem modo poſſent, quorum vnumquodque ipſi, PI,
adæquari, ac ſub eiſdem ſuperficiebus, QI, IO, contineri, regulis
eiſdem, HI, IS, pari ratione probaremus. Hæc autem oſtenden-
da proponebantur.

710.1.

11. huius.
0537-01
1. huius.

711. COROLL ARIVM I.

_E_X ſupra demonſtratis manifeſtum eſt, quomodo ſolidum rectan-
gulum ſub duabus datis ſuperficiebus contentum, iuxta datas
regulas, in data ſuperficie cylindracea, quæ continentium altera fit

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