Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ XEZ, ducta, HN, quæ abſcindat, NM, æqualem circumferentię,
CD, facilè oſtendemus, hæc autem erant demonſtranda.

622.1.

0451-01
3. l. 2.

623. THEOREMA V. PROPOS. V.

QVicumque ſectores inter ſe comparati, ſeu quæcum-
que figuræ ex ſectoribus compoſitæ ad ſectores, vel
ad figuras ex ſectoribus compoſitas comparatæ, habent
eandem rationem, quam omnes ipſarum circumferentiæ
ad omnes illarum circumferentias.

Sint quicunque circuli ſuper centro, A, nempè, ECD, maior, & ,
VIO, minor, & in, ECD, fit ſector quicunque, CAD, & ſimiliter
in, VIO, quilibet ſector, OAB. Dico ſectorem, CAD, ad ſectorẽ,
OAB, eſſe vt omnes circumferentias, CAD, ad omnes circumfe-
rentias, OAB. Secent radij, CA, AD, circumferentiam, VIO, in
punctis, I, O; Eſt ergo ſector, CAD, ſi-
milis ſectori, IAO, & ideo eſt ad illum,
vt omnes circumferentiæ ad omnes
circumferentias, ſed & vt ſector, IAO,
ad ſectorem, OAB, ita omnes cir-
cumferentiæ ad omnes circumferen-
tias, nam ſector, IAO, ad, OAB,
eſt vt circumferentia, IO, ad, OB,
vt verò, IO, ab, OB, ſic, deſcripta cir-
cumferentia, STR, vtcumque, ipſa, ST,
ad, TR, eſt enim, IO, ad, ST, vt OA, ad,
AT, ideſt vt, OB, ad, TR, vnde, permu-
tando, vt, IO, 3d, OB, ſic, ST, ad, SR, & vt vnum ad vnum, ita
omnia ad omnia, ideſt vt, IO, ad, OB, ita omnes circumferentiæ,
IAO, ſectoris ad omnes circumferentias ſectoris, OAB, ſed vt, IO,
ad, OB, ſic, vt dectũ eſt, ſe habet ſector, IAO, ad, OAB, ergo, IAO,
ad, OAB, eſt vt omnes circum ferentiæ, IAO, ad omnes circumfe-
rentias, OAB, ſed & ſectorem, CAD, ad, IAO, eſſe oſtenſum eſt,
vt omnes circumferentiæ, CAD, ad omnes circumferentias, IAO,
ergo ex æquali ſector, CAD, ad ſectorem OAB, eſt vt omnes cir-
cumferentiæ, CAD, ad omnes circumferentias, OAB. Et com-
ponendo figura compoſita ex ſectoribus, CAD, OAB, ad ſectorẽ,
OAB, erit vt omnes circumferentiæ figuę eiuſdem, ad omnes cir-
cumferentias ſectoris, OAB, veiuti etiam ſi prædicta figura non

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