Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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218198GEOMETRIÆ ergo intra, EB, vtcumque punctum, C, & per, C, ducaturipſi, D
P, parallela, CM, ſecans curuam circuli, vel ellipſis, EDRP, in,
N;
Eſt igitur quadratum, BP, vel, MC, ad quadratum, CN, vt
rectangulum, RBE, ad rectangulum, RCE;
eſt autem, EP, pa-
132[Figure 132] rallelogrammum in eadem baſi, &
alti-
tudine, cum ſemiportione, EBP, regu-
la eſt ipſa baſis, &
, CM, ducta vtcum-
que parallela ipſi baſi, repertumque eſt
quadratum, CM, ad quadratum, CN,
eſſe vt rectangulum, RBE, ad rectan
gulum, RCE, ergo magnitudines ho-
rum quatuor ordinum erunt proportio-
nales.
ſ. omnia quadrata parallelogram-
11Coroll.3.
26.lib. 2.
mi, EP, magnitudines primi ordinis col-
lectæ, iuxta primam, nempè iuxta qua-
dratum, CM, ad omnia quadrata ſemi-
portionis, EBP, magnitudines ſecundi
ordinis collectas, iuxta ſecundam.
ſ. iux-
ta quadratum, CN, erunt vt rectangu-
la ſub maximis abſciſſarum, EB, &
ſub
adiunctis, BR, magnitudines tertij or-
dinis collectæ, iuxta tertiam .
ſ. iuxta re-
ctangulum, RBE, ad rectangula ſub
omnibus abſciſſis, EB, &
reſiduis earun-
dem, adiuncta, BR, (recti, vel obliqui
tranſitus ſupradictis exiſtentibus) quæ
ſunt magnitudines quarti ordinis colle-
ctæ, iuxta quartam.
ſ. iuxta rectangulum,
R CE;
quoniam verò rectangula ſub
maximis abſciſſarum, EB, &
ſub adiun-
ctis, BR, ad rectangula ſub omnibus ab-
ſciſſis, EB, adiuncta, BR, &
ſub earum
reſiduis, ſunt vt, BR, ad compoſitam ex
22Cor. 30.
lib.2.
dimidia, BR, &
ſexta parte, EB, ergo conuertendo omnia quadrata
ſemiportionis, BEP, ad omnia quadrata parallelogrammi, EP, vel
338. lib. 2. iſtorum quadrupla .
ſ. omnia quadrata portionis, DEP, ad omnia
quadrata parallelogrammi, FP, erunt vt compoſita ex, {1/6}, BE, &
,
{1/2}, BR, ad eandem, BR;
Iungantur nunc, DE, EP.
Dico vlterius omnia quadrata portionis, EDP, ad omnia qua-
drata trianguli, DEP, eſſe vt compoſita ex dimidia totius, ER, &

ipſa, BR, ad eandem, BR.
Cum enim oſtenderimus omnia qua-
drata parallelogrammi, FP, ad omnia quadrata portionis,

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