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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 901, page id 1815201908:0958
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G F O M F Y R I C A
PROPOSITIO L
AEX (INEB. quaMItates A, B, C, D, L, F, C, tI.
Or
co proporrionem rationum A l. B L elle de propoltionem
cult a ie li 2 L2 e adProporrio-
nemlalioru , Ct.
Demonstratio.
nem B F, erit proporciorarionum AF,
BF eadem cum proportione racionum
AB, EF. Similicer quoniam rario C C
es ad rationem DFI, ve racio C D ad racionem C: FI, eric proporclorationum CC
DEI eadem cum proporrione racionum CD, CFI. Ergo proporcio rarionum AF,
BF est ad proporcionem racionum AB, F F, ve proporcioracionum C CF, D HI est ad
proporcionem rarionum CD, GFI. ergo bpermurando proporcio eationum AR, B ++. hu-
BF, est ad proporrionem rarionum C C, D II ve proporcio racionum AB, R F ad ius.
proporcionem rationum CD, C FI. Ouod erac demonstrandum.
ROPOSITIO LX.
Trracio AB ad rarionem CD, veratio F F ad G HI racionem.
Dicoquod racio AB ad rarionem (IO, (cveratio L. F ad DC FA-
Demonstratio.
hatus.
)Voniam a racio AF est ad rario: 59. A
nem BF, re racio AB ad rario-
coCI.
rm rario AB Sc ac LaOnem 24, 5, 10,
CD, veratio L.L ad racionem 2
adrarionem P L, ve racio CD 24
racionem CFlihoc eAverariodFIO
ad rationem DC. Rursum igieur
permucando rario AB est adrario.
A3
10
nem FIO, verario F F ad rarionem D C. Ouod exar demonstrandum.
Vod uerie racio  ad racionem HC, veratio F. P ad racionem
orarionem Aene adC Drarionem, reratio L L adaloet1
1.sst SSL e B 32CIC. FE I BCCBEMLIE
Demonstratio il
Voniam estratio AB ad YF C LatIOnEM, vEFarIO E F ad rationem DC; criI
permucandoratio AB, ad rationem R F, ve rario FTG ad rationem DC, hoc
est pec hoticiuo, velalie D mllationem c il; poruntando re tue palee pcopose
11
GFI, eric cpermutando rario AB
clbao
C 4 4. bolitar.
a3 D. litin.
u s uet 1  1  n  pe p t i e n tit