Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ cta demon tratione propoſitum oſtendemus; vnde patebit pariter quadra-
ta maxim trum abſciſſarum propoſitæ rectæ lineæ, vt ipſius, EM, adiun-
cta quædam, vt, EF, ad quadrata omnium abſciſſarum eiuſdem adiuncta
eadem, eſſe vt quadratum vnius maximarum abſciſſarum adiuncta iam
dicta . i. vt quadratum compoſitæ ex propoſita, & adiuncta, adrectangu-
lum ſub hac compoſita, & ſub adiuncta, vnacum, {1/3}, quadrati differen-
tiæhuius compoſitæ, & adiunctæ . ſ. vt quadratum, MF, ad rectangu-
lum ſub, MF, FE, vnacum, {1/3}, quadrati, EM, quæ eſt differentia ea-
rundem, & eſt etiam propoſita linea.

256. THEOREMA XXIX. PROPOS. XXIX.

CViuſcunque parallelogrammi omnia quadrata regula
vno laterum ad omnia quadrata eiuſdem regula altero
laterum cum prædicto angulum continentium, erunt vt pri-
ma regula ad ſecundam.

Sit quodcunq; parallelogrammum, AD. Dico omnia quadrata
eiuſdem, regula, DB, eſſe vt, CD, ad, DB: Omnia enim quadra-
ta, AD, regula, CD, ad omnia quadrata, AD, regula, DB, ha-
bent rationem compoſitam ex ea, quam habet quadratum, CD, ad
quadratum, DB, & ex ea,
quam habet, BD, ad, DC,
(quia, BD, & ae; qualiter inclina-
tur baſi, CD, ac, CD, ipſi
baſi, DB, nam ſunt circa eun-
dem angulum) . i. ex ea, quam
habet quadratum, BD, ad re-
ctangulum ſub, BD, DC, duæ autem rationes, nempè quadrati, C
D, ad quadratum, BD, & quadrati, BD, ad rectangulum ſub, B
D, DC, componunt rationem quadrati, CD, ad rectangulum ſub,
BD, DC, quę eſt eadem ei, quam habet, CD, ad, DB, ergo om-
nia quadrata, AD, regula, CD, ad omnia quadrata eiuſdem, AD,
regula, DB, erunt vt, CD, prima regula ad, DB, ſecundam, quod
oſtendere opus erat.

256.1.

11. huius.
0190-01
5. huius.
Diffin. 12.
lib. 1.
5. huius.

257. COROLLARIVM.

_H_Inc patet, ſi iungamus, CB, omnia quadrata trianguli, CBD,
regula, CD, ad omnia quadratratrianguli eiuſdem, regula, DB,
eſſe vt, CD, primam regulam ad, D B, ſecundam, nam omnia quadrata

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