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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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OEOMETRIC X.
Demonstratio.
monstracione vix indi-
Beac raciones enim esse simi-
les, nihil aliud est quamracio-
nes aquales esse aue caldem
incerle. Duare cum rariones
AB ex C D, similes Ponan-
cur, sibi mucuo equales crunt,
ob candem caulam aquales
cruncraciones FF, G TI. CrgO
racio AB ad racionem CD
est, veracio P. F ad rarionem
GFI.
DEo cum elara est ve de-
R OPOS
O ZLIV.
T
PIEratiO A BaletatiOnem C D, vE FaLIO L F ad racionem C FT.
Oleo pelhutucando rarionem AB else nd Latlone L. L, H tallo
minatores L, K; L, HI. Crie
ergo denominacor Lad de-
nominatorem K, ve racio
ABad rationem C D, hOc
est per hypocholim verario
F F ad racionem C FI, hoc
est ve denominaror L ad
denominatorem M. Cum
isicur sE, ve L ad R, SICF
ad M, eric permurando L
ad L, vE K ad MI. OuarC _
rario AB ad rAEIONEM F. F,
Demonstratio.
est verario CD ad racionem CH uod eratd
R.
5
onstrand
XL
C D ad rationem C FI.
DErB. huius idenianEuE
dacarumm cactonum deno-
Irracio AB adrarionem CB, nta IT ad IK rarionem.
Dicoinumendo rationem C.D ad AB, caltem cum ratione
IK ad 6II.
Demonstratio.
ad CD racionem cA, ve F. ad F, e
racio GFT Cs, ad TK racionem, ve
F 2d M. Sed rario e B est ad CD F2-
cionem, veracio GHIadTK racionem.
ergoracio B ad F, eadem est cum ra-
tione F adM. isitur inverrendo est F
ad B, vE M ad L, ergo es racio C D ad AB, veracio PK ad G: FP rarionem. Ouod
erat demontrandum.
2 25. fuino.
XXXX X 2
NuentaMat denominatores FaL
Lnum F., H, L.S ML. GIEUE FaCIO AF
15
i a         t te  t te     a