Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRI Æ cta, TX, ſecante curuam, MH, in, I, regula, OH, oſtendemus
quadratum ſolidum, PH, viſa dicta figura, ad quadratum ſo-
lidum, ABHM, eſſe vt, ON, ad compoſitam ex, NR, & @. RO.

Extendantur . n. HO, VR, verſus, OR, & fiant, OC, RA, ſingulæ
æquales ipſi, ON, & , DO, BR, capiantur ſingulæ æquales ipſi, RN
& iungantur, AC, BD, CB, quas extenſſa indefinitè, TX, ſecet in, F’
P, E. Etunt ergo, AO, BO, AD, parallelogramma. Cum verò, CO’
æquetur, ON, & DO, ipſi, RN, erit, CD, æqualis, OR . i. ipſi, DB,
vnde etiam, EP, ipſi, PB, hoc eſt ipſi, RX, & tota, EX, toti, NX, & reliqua, FE, reliquæ, OX, æqualis erit. Quoniam vero quadratum,
OH, ad quadratum, XI, eſt
vt, ON, ad, NX, hoc eſt, FX,
ad, XE, hoc eſt quadratum,
FX, vel quadratum, CO, ad
rectangulum, FXE, ideo per-
mutando quadratum, HO,
ad quadratum, OC, erit vt
quadratum, IX, ad rectangu-
lum, FXE, ex quo conclude-
mus, vt in ſuperioribus rectangulum ſolidum ſub, AO, & trapezio,
BCOR, eſſe proportionaliter analogum quadrato ſolido, RMHO. Similiter oſtendemus quadrata ſolida, AO, OV, eſſe proportionali-
ter analoga, & conſequenter prædictis duobus ſolidis eſſe propor-
tionalia colligemus, vnde permutando quadratum ſolidum, VO,
ad quadratum ſolidum, MORH, ſeu (conſpecta figura prop. 23. lib. 4.) quadratum ſolidum, PH, ad quadratum ſolidum fruſti, ABHM,
erit vt quadratum ſolidum, AO, ad rectangulum ſolidum ſub, AO,
& trapezio, BCOR . i. vt, AO, ad, BCOR . i. vt, CO, ad compoſi-
tam ex, OD, & {1/2}. DC, . i. vt, ON, ad compoſitam ex, NR, & {1/2}. R
O, quod & c.

753.1.

0560-01
Cor. 1. 13.
huius 20.
l. 2.

754. ANNOTATIO.

PEr hanc ſimiliter ſuppletur prop. 23. poſterior . n. pars, cum
Cor. deducetur vt ibi, mutatis nominibus & c. Prop. 24. reſtau-
ratione non indiget, ſicut etiam p. 25. cum Cor. Prop. 26. oſtende-
tur etiam vt ibi, mutatis, & c. ſicut & p. 27. cum Cor. ſimiliter p. 28. cum Cor. p. 29. cum Corollarijs, p. 30. cum Corollarijs, p. 31. 32. cum Cor. p. 33. 34. cum Cor. 35. cum Cor. p. 36. 37. 38. 39. 40. cum Cor. 41. 42. 43. 44. 45. p. 46. autem eſt nobis reſtauranda.

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