Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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[411.] THEOREMA V. PROPOS. V.
Page: 311 (291)
[412.] COROLLARIV M.
Page: 312 (292)
[413.] THEOREMA VI. PROPOS. VI.
Page: 313 (293)
[414.] COROLLARIV M.
Page: 315 (295)
[415.] THEOREMA VII. PROPOS. VII.
Page: 315 (295)
[416.] THEOREMA VIII. PROPOS. VIII.
Page: 316 (296)
[417.] SCHOLIV M.
Page: 316 (296)
[418.] PROBLEMA I. PROPOS. IX.
Page: 316 (296)
[419.] THEOREMAIX. PROPOS. X.
Page: 317 (297)
[420.] COROLLARIV M.
Page: 318 (298)
[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
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456436GEOMETRIÆ
THEOREMA VIII. PROPOS. VIII.
SI in ſpirales in alijs reuolutionibus genitas, quam in
314[Figure 314] 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.
Hę duę Propoſitiones oſtenduntur ab Archimede lib. de pir.
Prop. 14. & 15.
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.
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,

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