Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER II. drata, Τ β, ad omnia quadrata trianguli, & Ζ β, ita non ſunt om-
nia quadrata, AS, ad omnia quadrata trianguli, OES, erunt igi-
tur ita omnia quadrata, AS, ad maius, vel ad minus omnibus qua-
dratis trianguli, OES, ſint exceſſus, vel defectus, omnia quadrata
figuræ planæ, Ω, diuidatur autem latus, OS, bifariam, in, Q, & ,
OQ, QS, bifariam in, P, R, & ſic deinceps fiat, ita vt ductis per
puncta diuiſionum parallelis ipſi, ES, DR, CQ, BP, tandem de-
uentum ſit ad parallelogrammum, DS, cuius omnia quadrata, re-
gula, ES, ſint minora omnibus quadratis figurę, Ω, per puncta au-
tem, in quibus dictæ parallelę ipſam, OE, ſecant, ducantur vſque
ad proximas parallelas æquidiſtantes lateribus, AE, OS, ipſę, LN,
GK, EM, erit igitur triangulo, OES, circumſcripta figura quæ-
dam cõpoſita ex
parallelogrãmo,
LP, GQ, FR,
DS, & alia in-
ſcripta compoſi-
ta ex parallelo-
grammis, 9 Q, I
R, HS, ita vt
omnia quadrata
figuræ circũſcri-
ptę, regula, ES,
excedant omnia
quadrata inſcri-
ptæ, regula ea-
dẽ, minori quan-
titate, quam ſint
omnia quadrata figuræ, Ω; nam in parallelogrammo, DS, recta,
HM, diuidit omnia quadrata, DS, in omnia quadrata, DM, in
omnia quadrata, HS, & in rectangula bis ſub, DM, MR, veluti
punctum, H, diuidit quadratum, DR, in quadrat. DH, quad at-
HR, & rectangulum bis ſub, DHR, ſiue ex 23. ſeq. ab hac inde-
pendente, & ideò omnia quadrat. DS, excedunt omnia quadrata,
HS, omnibus quadratis, DM, & rectangulis bis ſub, DM, MR,
eodem pacto oſtendemus omnia quadrata, FR, excedere omnia
quadrata, IR, omnibus quadratis, FK, & rectangulis bis ſub, FK,
KQ, & ſic omnia quadrata, GQ, excedere omnia quadrata, 9 Q,
omnibus quadratis, GN, cum rectangulis bis ſub, GN, NP, & in
figura circumſcripta ſuperſunt adhuc omnia quadrata, LP, porro ſi
hos exceſſus ſimul colligamus fient omnia quadrata, DS, nam ſi
omnia quadrata, LP, vel, 9 Q, iunxeris omnibus quadratis, GN,

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