Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER V. H, NOS, ſit autem, veluti in anteced. Prop. conſſitutum paralle-
logrammum, FC, cuius oppoſita latera, FD, EC, ſint ad axim,
vel diametrum, AV, in eadem productam, órdinatim applica@a,
erunt, DC, FE, ipſi, AV, ęqui
diftantes, ſint earum portiones
inter aſymptotos concluſæ, H
S, NY, regula ſit, AV. Dico
ergo omnia quadrata, FC, ad
omnia quadrata figuræ, FAD
CVE, ideſt figuræ concluſæ in-
ter latera, FE, DC, & oppoſi-
tarum ſectionum portiones in-
ter eadem manentes, quę ſunt,
FAD, EVC, eſſe, vt quadratũ,
DC, vel, FE, ad quadratum,
AV, cum {1/3}. quadrati, HS, vel,
NY. Per puncta ergo, O, V,
ducantur, XL, VP, ad ipſam,
AV, ordinatim applicatæ, erit
igitur, XL, ſecunda diameter,
& , VP, tanget ſectionem, EV
C. Quoniam ergo rectangulum, HCS, æquatur quadrato. OV,
ideſt quadrato, LP, rectangulum verò, HCS, æquatur rectangu-
lo, LSC, bis vna cum quadrato, SC, ideò, rectangulum, LSC, bis
vna cum quadrato, SC, erit æquale quadrato, LP; eodem pacto
ſi intelligamus ipſi, LC, æquidiſſantem vtcunq; ductam intra pa-
rallelogrammum, OP, viq; ad ſectionem, VC, productam, oſten-
demus rectangulum bis ſub eius portionibus inter, OL, OS, & in-
ter, OS, & ſectionem, VC, concluſis, vna cum quadrato eius, quę
inter, OS, & ſectionem, VC, clauditur, æquari quadrato eius, quę
manet inter, OL, VP, & ſic de reliquis conſimihter ſumptis; vnde
patebit tandem rectangula ſub trianguio, LOS, & figura, OVCS,
bis ſumpta, vna cum omnibus quadratis figuræ, CVCS, æquari
omnibus quadratis, OP, regula, AV, iam ſuppoſita, quia ergo
omnia quadrata, CO, ad omnia quadrata, OP, ſunt vt quadratũ,
ZO, ad quadratum, OV, ideò pam [?] teron @ a quadrata, OC, ad
rectangula ſub triangulo, LOS, & figura, OVCS, bis, vna cum om-
nibus quadratis figuræ, OVCS, erunt vt quadratum, ZO, ad qua-
dratum, OV; quod ſerua.

558.1.

0413-01
II. Secun.
Con.
9. lib. 2.

Inſuper omnia quadrata, CO, ad omnia quadrata parallelogrã-
mi, SO, ſi compleretur, eſſent vt quadiatum, CL, ad quadratum,

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