Volltext: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ lam, ADC, in puncto, D, quæ indefinitè quoq; producta
occurrat ipſi, XP, in puncto, P, ſuppoſitoque, BD, eſſe
rectangula omnia hyperbolæ, OVX, ſimilia rectangulo
ſub, XO, OP, habere rationem compoſit am ex ratione re-
ctanguli ſub, MB, HI, ad rectangulum ſub, RI, FB, & ex
tatione parallelepipedi ſub altitudine hyperbolæ, ADC,
hyperbolæ, OVX, baſi aute m rectangulo ſub, XO, OP.

quadrata hyperbolę, OVX, regula, OX, oſtenſa ſunt habere ratio-
nẽ cõpoſitam ex ratione rectang. ſub, MB, HI, ad rectang. ſub, RI,
FB, & parallelepipedi ſub altitudine hyperbolę, ADC, baſi quadr. AC, ad parallelepipedũ ſub altitudine hyperbolę, OVX, baſi autẽ
omnia eiuſdem hyperbolę ſimilia re-
ctangulo, XOP, regula, XO, ſunt vt
XO, ad rectangulum, XOP, . ſ. ſumpta
communi altitudine eiuſdem hyperbo-
læ, OVX, altitudine, vt parallelepi-
pedum ſub altitudine hyperbolæ, O
autem rectangulo, XOP, ergo omnia
OVX, ſimilia rectangulo, XOP, regu-
la, OX, erunt in ratione compoſita ex ratione rectanguli ſub, MB,
HI, ad rectangulum ſub, RI, FB, & parallelepipedi ſub altitudine
altitudine hyperbolę, OVX, baſi quadrato, OX, & ex ratione hui-
us parallelepipedi ad parallelepipedum ſub eiuſdem hyperbolę, O
VX, altitudine baſi rectangulo, XOP, quę duę vltimò dictę racio-
nes componunt rationem parallelepipedi ſub altitudine hyperbo-
hyperbolę, OVX, baſi rectangulo, XOP, ergo omnia quadrata