Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ cumferentiam, CD, eſt
autem circulus, ABCD,
æqualis triang. HOM,
ergo triangulus, HOM,
ad ſectorem, ECD, eſt
vt circumferẽtia, ABCD,
ad circumferentiam, CD,
ideſt vt, OM, ad, MN, id-
eſt vt triangulus, HOM,
ad, HNM, igitur idem
triangulus, HOM, ad ſe-
ctorem, ECD, ad trian-
gulum, HNM, eandem
habet rationem, ergo ſector, ECD, eſt æqualis triangulo,
HNM, quod oſtendere opus erat.

619.1.

33. Sexti
Blem.
Exantec.
0450-01

620. COROLLARIVM I.

_H_Inc patet, ſi ſumpto vtcumque puncto in, ED, vt, X, centro,
E, ad diſtantiam, X, circuferentia, FZX, deſcripta fuerit in-
ſuper abſciſſa, HR, æquali ipſi, EX, per, R, ducta fuerit, SR, parllela
ipſi, OM, ſecans, HN, in, I, trape zium, OSRM, æquari reſiduo circu-
li, ABCD, ab eo dempto circulo, FZX, quod reſiduum dicatur faſcia
circulorum, BD, FX, nam circulus, BD, ad circulum, FX, eſt vt qua-
dratum, DE ad quadratum, EX, ideſt vt quadratum, MH, ad qua-
dratum, HR, ideſt vt triangulus, HOM, ad triangulum, HSR, vnde,
quia circulus, BD, æquatur triangulo, HOM, etiam circulus, FZX,
æquatur triangulo, HSR, vnde faſcia, BF, æquatur trapezio, OSRM; eoden modo colligemns reſiduum ſectoris DEC, ab eo dempto ſectore,
XEZ, quod dicatur eorundem ſectorum faſcia, ſcilicet ipſum, ZXDC,
æquart trapezio, IRMN.

620.1.

_Coroll. 1._
_11. l. 3._
_Coroll. 1._
_19. l. 2._

621. COROLLARIVM II.

_P_Atet inſuper, quia circulus, CDB, æquatur triangulo, HOM, & circulus, FZX, triang. HSR, item circumferentia, ABCD, ipſi
OM, & , FZX, ipſi, SR, (nam, DE, æquatur ipſi, MH, & , EX, ipſi, RH,)
quod veluti, OM, ad, SR, eſt vt, MH, ad, HR ita circumferentia, ABCD,
ad, FZX, erit vt, DE, ad, EX. Sic etiam oſtendemus ſimilium ſectorum,
CED, ZEX, circumferentias, CD, ZX, eſſe vt ſemidiametri, DE EX, & ipſos ſimiles ſectores eſſe vt quadrata ſemidiametrorũ, DE, EX, quoniã

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