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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 925, page id 1815201908:0982
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11III.
G F DH EY R IC A.
PROPOSETTO OX
Vlracio AB duplicara estrationIS C D.
Dico rectanguli AC ad BD racioleM criplicatam erus elle quam
habet C ad D.
acio quDecctaBI AC dd BB
rectangulum, compolica eAt exra-
tione A ad B, hoc cAt duplicata C ad
D, ex hypoches insuper ex rarione C
ad D. eroo racio rectanouli A C 2d
BC rectangulum, est eriplicata cario-
nis C ad D. Duod erac demonstran-
dum.
PR OFOSIT
uc proporto actotum AB, CD ad proportoneh corum LL,
aOHI, ve proporciorarionum lK, L. M, a pope lallonum
NO, PC
Dicorarionem rectangulorum AD. LHL elle ad rationem recransu.
lorum (M, NO, veratio recrangulorum BC, FO ad ratIONCM FCCTan-
Sulorum IEL, OP.
lac re DadC, dcBadl
_ ve IIad C, HCF 2d5.
DEVETO M adL, SiC K AaC 2C
T: demum ve O ad P, sic
Aac O ad V. Itaque eacio
AR eAtaproporcioracionum
AB, CD; _ rario F S est
Proporrio ratiOnUIM PF
CFI: racio aurem Il estra-
EIONUM TRS LMproporcIOS
denique rario NV Clt PrO-
porcioracionum iNO, PO.
Acqui daccrationum prapor-
tiones exhrpoches lunE PEo-
porcionales sibi mutuo. ergo
CtiaM PaTIONES AR, F, S Fa.
cionibus PT, NV lunc pro.
porcionales. Jam vero rario
Fecrangulorum AD, BC cA
quemadmodum iam ostendi, verario IL adracionem AV. AEAUI YE FaTIO reCEAn. .M
sulorum AD, B C, est adracionem recrangulorum P HL, P C, AC, est rario Fectan. c 3 huius.
sulorum AD, F.FI, ad rarionem recrangulorum B C, F G. ergocciamratioreeran.
sulorum AB, F. FL, est ad rarionem cectangulorum BC, FC veracio FY, ad pario-
nem NV. Eodem plane discurtu probabimus racionem rectangulorum LM, NO
esse ad racionem reccanoulorum R I, OP, vetacio IY est ad tacionem NV. Crgo
racio rectangulorum AD, E FI, est ad rationem receangulorum B C, E C+, Ve racio
reccansulorum TM, N Q est ad rarionem recrangulorum RP. OP. Isirux permu-
cando dracio rectangulorum A D, F HI est ad rationem recrangulorum LM, NO, ve
cacio reccangulorum B C, F C cA ad racionem secrangulorum RL, OP. Quodetat d ibid.
demonaramdum.
Demonstratio
Demonstratio.
3
ad racionem recrangulorum F FT, I. G vebratio A R est ad racionem ES; hoc CR,
Pt
oooroo2223aS