Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

627. THEOREMA VIII. PROPOS. VIII.

SI in ſpirales in alijs reuolutionibus genitas, quam in
prima incidant duę
lineæ ab initio ſpira-
lis, habebunt illæ in-
ter ſe eandem rationẽ,
quam arcus circuli pri-
mi, intercepti, veluti
dicitur in anteceden-
te, cum integra circũ-
ferentia toties aſſum-
pta, quotus eſt vnitate
minor reuolut ionum
numerus.

627.1.

0456-01

Hę duę Propoſitiones oſtenduntur ab Archimede lib. de pir. Prop. 14. & 15.

628. SCOLIVM.

_I_N prima reuolutione orta ſit ſpiralis, ACER, & RTV MG, in ſe-
cunda, & , AC, AE, pertingant ad primam, AV, AM, ad ſecun-
dam, erit, AC, ad, AE, vt circumferentia, RSO, ad, RSN, AV, verò
ad, AM, erit vt circumferentia tota, RNOS, cum, RSO, ad, RNOS,
totam, cum, RSON, & , ſic in cæteris.

629. THEOREMA IX. PROPOS. IX.

SPatium compręhenſum à ſpirali ex prima reuolutione
orta, & prima linea, quæ initium eſt reuolutionis, eſt
tertia pars primi circuli.

Sit ſpiralis in prima reuolutione genita ipſa, AIE, AE, verò re-
uolutionis initium, & centro, A, interuallo, AE, ſit primus circu-
lus deſcriptus, ESM. Dico ſpatium, AIE, tertiam partem eſſe cir-
culi, EMS. Sumpto itaq; vtcunq; puncto, vt, V, in, AE, centro,
A, interuallo, AV, circulus deſcribatur, VIT, & iuncta, AI, prò-

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