Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ lam, ADC, in puncto, D, quæ indefinitè quoq; producta
occurrat ipſi, XP, in puncto, P, ſuppoſitoque, BD, eſſe
axim, oſtendemus omnia quadrata hyperbolæ, ADC, ad
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,
& baſi quadrato, AC, ad parallelepipedum ſub altitudine
hyperbolæ, OVX, baſi aute m rectangulo ſub, XO, OP.

Nam omnia quadrata hyperbolæ, ADC, regula eadẽ, AC, ad oĩa
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
quadrato, OX; inſuper omnia quadra-
ta hyperbolę, OVX, ad rectangula
omnia eiuſdem hyperbolę ſimilia re-
ctangulo, XOP, regula, XO, ſunt vt
vnum ad vnum, ſcilicet vt quadratũ,
XO, ad rectangulum, XOP, . ſ. ſumpta
communi altitudine eiuſdem hyperbo-
læ, OVX, altitudine, vt parallelepi-
pedum ſub altitudine hyperbolæ, O
VX, baſi quadrato, OX, ad parallele-
pipedum ſub eadem altitudine, baſi
autem rectangulo, XOP, ergo omnia
quadrata hyperbolę, ADC, regula,
AC, ad omnia rectangula hyperbolę,
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
hyperbolę, ADC, & ſub quadrato, AC, ad parallelepipedum ſub
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-
lę, ADC, baſi quadrato, AC, ad parallelepipedum ſub altitudine
hyperbolę, OVX, baſi rectangulo, XOP, ergo omnia quadrata
hyperbolę, ADC, regula, AC, ad omnia rectangula hyperbolę,

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