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

222202GEOMETRIÆ lum ſub, DR, & ſub compoſita ex, {1/2}, RM, & ex, MA, vna cum
rectangulo ſub, RM, & ſub compoſita ex, {1/6}, RM, & , {1/2}, MA. Su-
matur in, MR, vtcunque punctum, T, per quod agatur ipſi, CF,
parallela, TX, fecans curuam, SF, in, V, erit ergo quadratum, R
F, vel quadratum, TV, ad quadratum, TX, vt rectangulum, D
RA, ad rectangulum, DTA; & quoniam, MF, eſt parallelogram-
mum in eadem baſi, RF, & altitudine cum ſemiportione, MRFX

135[Figure 135] S, & , TX, ducta fuit vtcunque parallela
ipſi, RF, repertumque eſt quadratum, T
V, ad quadratum, TX, eſſe vt rectangu-
lum, DRA, ad rectangulum, DTA, con-
11Coroll. 3.
26. Lib.2. ſtructis quatuor magnitudinum ordinibus,
vt in antecedente, cocludemus omnia qua-
drata parallelogrammi, MF, ad omnia
quadrata ſemiportionis, MRFS, eſſe vt
rectangula, DRA, tot, quotſunt omnes
abſciſſæ ipſius, MR, ad rectangula ſub re-
ſiduis omnium abſciſſarum, MR, ad@un-
cta, RD, & ſub omnibus abſciſſis, MR, adiuncta, MA; quia ve-
22Cor. 32.
lib. 2. rò, DA, diuiſa eſt vtcumque in duobus punctis, R, M, rectangula
ſub, DRA, tot, quot ſunt omnes abſciſſę, RM, ad rectangula ſub
refiduis omnium abſciſſarum, MR, adiuncta, RD, & ſub omnibus
33@ Lib. 2. abſciſſis, MR, adiuncta, MA, ſunt vt rectangulum, DRA, ad re-
ctangulum ſub, DR, & ſub compoſita ex, {1/2}, RM, & , MA, vna
cum rectangulo ſub, RM, & ſub compoſita ex, {1/6}, RM, & , {1/2}, M
A, ergo omnia quadrata parallelogramini, MF, ad omnia quadrata
ſemiportionis, MRFS, vel omnia quadrata parallelogrammi, BF,
ad omnia quadrata portionis, ICFS, erunt vt rectangulum, DR
A, ad rectangulum ſub, DR, & ſub compoſita ex, {1/2}, MR, & ex,
MA, vna cum rectangulo ſub, RM, & ſub compoſita ex, {1/6}, RM,
& , {1/2}, MA.

Iungantur nunc, CM, MF. Dico inſuperomnia quadrata por-
tionis, ICFS, ad omnia quadrata trianguli, MCF, eſſe vt rectan-
gulum ſub compoſita ex, MD, DR, & ſub ſexquialtera, MA, vna
cum rectangulo ſub compoſita ex, MD, & dupla, DR, & ſub, {1/2},
MR, ad rectangulum, DRA; omnia . n. quadrata parallelogram-
mi, BF, ad omnia quadrata portionis, ICFS, oſtenſa ſunt eſſe vt
rectangulum, DRA, ad rectangulum ſub, DR, & ſub compoſita
ex, {1/2}, RM, & ex, MA, vna cum rectangulo ſub, RM, & ſub com-
poſita ex, {1/6}, RM, & , {1/2}, MA, ergo eorum tertia pars ad eadem con-
ſequentia erunt vt tertia pars rectanguli, DRA, ad eadem conſe-
quentia rectangula . ſ. vt integrum rectangulum, DRA, ad illa

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