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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 31, page id 834940469:0039
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PROP. XIV. THEOREMA.
Inc duo polysona coin plicats A, B.
eDnempe A incra circuli rel ellipleos
dectorem se Bexeras continuecur series
conversenshorum polreoriorucom-
plicatorum secunduin nostram metho-
dum lubduplam delcripeorum, ita vrpolysona intra circulie
SInEA. C, E; deC; ec exrra circutum B. D, F, aC; dico A  F
minorem esse quam 2C: ex prae dictisinanifeltae lune leque-
ces analosixe s prima: quoniam
A;C, B; LUNE COnFINAC PFOPOr C = A: B - C:: A: C
tionales; ee secunda quoniam. B - C: D - C:: A  C: A
C, D, B. Cuncharmonice peo-
portionaless _ Droinde exce(sus C supra A; hoc eA C A,
est ad excessum D supra C Peu D C inratione copolica CX
proportione A ad C X exproportione A.  C ad A, hoC est
inrarione A F C ad C; dF R  C estmaior quam C, e ideo
excessis C lupra A est maior quim excelsiS I supea C, est
aurem Dinaior quam E, e pioinde excessus C supra A muI
comaior es quain excelsus F Cupea C; CsigItUE A ifft F MI-
nor quam 2C; quod demonstrare opOrtuIto.
PROP XV. THIEOREMA.
IIdem posiis: dico excessum C supra A minorem eNse qua-
 diuplo excessus E lupra C. Cx praedictis maniFest e (uMB
lequencestres analogix, prima quoniam A, C, B, lUNE CO-
tinue proportionales; secunda; quoniam C. D, B. Tunc Mar-
monice proportionales; scerria, quoniam C, E, D, TUINECO-
tinue proportionalesi e idco
exce(SuS C Faipea A(HBC est). C - A: B C: R: C
C A CAad exceHTUM. F (1 - B  C: D C:: A C: A
PraC (euF: = C, ve AC HFC. D C: F C:: F C: C
A AE A CC ad C VinCB Ma
LL.