Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ hyperbolæ, HTN, erunt vt parallelepipedum ſub, LO, & triplo
quadrati, OG, ad reliquum, quod habetur, dempto parallelepipe-
do ter ſub, OT, & quadrato, TL,
cum cubo, TL, à parallelepipedo
ſub, LO, & quadrato, LO, . i. à cu-
bo, LO, & parallelepipedo ſub, LO,
& triplo quadrati, OT, verum, quia
cubus, LO, æquatur parallelepipe-
dis ter ſub, OT, & quadrato, TL,
ter ſub, TL, & quadrato, TO, cum
cubis, OT, TL, ideò ſi à cubo, OL,
dematur parallelepipedum ter ſub,
OT, & quadrato, TL, cum cubo,
TL, remanebit parallelepipedum
ter ſub, LT, & quadrato, TO, cum
cubo, TO, quod iungendum eſt pa-
rallelepipedo ſub, LO, & triplo qua-
drati, TO, habebimus ergo pro
quæſito reſiduo parallelepipedum
ſub, LO, & quadrato, OT, ter . i. ſub, LT, & quadrato, TO,
ter, cum tribus cubis, TO, & adhuc parallelepipedum ſub, LT, & quadrato, TO, ter cum cubo, TO, . i. habebimus parallelepipe-
dum ſub, LT, & quadrato, TO, ſexies, cum quatuor cubis, TO,
pro quæſito reſiduo, igitur omnia quadrata, RC, ad omnia qua-
drata figuræ, DAVC, demptis omnibus quadratis hyperbolæ, HT
N, vel omnia quadrata, FC, ad omnia quadrata figuræ, FADCV
E, demptis omnibus quadratis oppoſitarum hyperbolarum, Y & B, HTN, erunt vt parallelepipedum ſub, LO, & triplo quadrati,
OG, ad parallelepipedum ſexies ſub, LT, & quadrato, TO, cum
quatuor cubis, TO, . i. vt parallelepipedum ſub, LO, vel, ZC, & quadrato, OG, vel, ZS, ad parallelepipedum bis ſub, LT, & qua-
drato, TO, cum cubo, TO, & amplius eiuſdem cubi, TO, nam
hæc ſunt eorundem ſubtripla, vt conſideranti facilè patebit, quod
erat oſtendendum.

568.1.

9. huius.
0426-01
38. l. 2.
3. 6. l. 2,

569. THEOREMA XXVII. PROPOS. XXVIII.

SI, expoſitis ſectionibus coniugatis, parallelogrammũ
deſcribatur, habens latera earundem axibus, vel dia-
metris coniugatis parallela, in earum aſymptotis conue-

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