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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 292, page id 845634801:0298
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PNEOREMAZA
E Y E Y L C Y M.
In circulo duas circumterentias sumere inratione muleipla data, in qua
etiam se habeane rectarum gux ipsis circumterentiis (uBEENdUNEF qua
drata.
Sit datus circulus qui supra, ABFI, cujus diametex EE AFI, Cemidiameter BI, duCarUE
que re Eca BH _ sinc circum terentia AB, AC inrarione dupla, AB, AD in racione eripla
AB, AE. inrarione quadrupla _C. eric igitur BLad BFI, uc AB ad AC, proprer similicudt
BEI in AB
BI 3 ic2
BII in AB
20
BHg. in AB g. = AB q. in BI4.
ABin BI9.
BEI in AB
B1
aequabitur ips AC. UE aurem AB 2C
BII g. in ABg9.
ABin BIg. quod mulcatum ipta AB, dac
Ld
id ct
BI9.
=equale ip ( AD, ex
Praecedentipropolicione. Psicur uc BI g. 2d BH q. = BI q. ita AB ad AD: vel quoniam ett
AB44. AB4 in AFI 9. -. AB49.
UEAEI ad AB, ita AB ad BK, quadracum igituEBK, erie
AFI9.
AII9.
aquabituE A K quadrato: et ABg. in AFI 9. 4. = AB99. 4. aequabitur A C quadeaco:
AIIg.
ROCauteM ex prxcCdemi Theoremareaquale est ipsis ABg. F AB in AD. Ablaco isicll
BEI in AB
et
11
AFI9.
BBg. in AFl 9. 3. = AB94. 4 aequabirur AB in AD: ee hisce
AFI9.
A B 9. in AH 9. 3. = AB 99. d aquabituE AD, id et
ABin AH g.
=erit iBituEUE AF 9. ad AF9. 3, = AB 9. 4, ica AB ac
BEI in AB
AFZ  aequale ip( AR, et e
BII in AB
BFIg. in AB4. id
et
BIIg. in AB
AI ita hoc 2C
AB in AI9
ALg. : hoc aurem minus AB aequatur ipsi BFI4 in AB - AI 9. in A
AI9.
id cA ex prademonstraris ips AD. CA quoque uE AB ad BFL in P B, iet
BH2 g. in AB - A I g. in AB., EB cub. in ABg. = BFL in ALq. in AB 4. id eMt
AI9.
BE cub. = BIIin AI9
AIcab.
AB in AI. cub.
in AB, quod mulcacum ipta A C, ret BHL in AB id est
BEEcub. in ABin AI =BHin AI cub. in AB2. BEI Cab. in AB -BFL in AIg. inAB2.
AI99.
AI. cub.
aquatur ip ( AE. ur igicur AL cub. ad BFI cub. = BFI in AI. 9. 2, ita AB ad AF. CadeM
que mechodo lumentur et alix, pro ratione mulcipla data. Ouod erat faciendum.
que huc perrinet Analyricum illud arrificium generale quadrandi lunulas, quod acc
Viera Libro rariorum 8o, cap. 9n
P E P O R B NE A V
Si a cermino diamerri sumantur in circulo circum terentix quorcunqua
aequales, e ab altera extremitate cducantur rectxe linex ad sumptarum ct
cumterenciarum aqualium cerminos, eric uc lemidiamerer ac rectamas a
dicta
e
lumr