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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 874, page id 1815201908:0931
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DR OPORTIONALITAEES
reveriemus duplam, quadruplam, et
eriplam, e rario duorum ad vnum du-
etâ in rarione quacuor adrnum, quod
hec per mulciplicarionem denomina
Z. in denominatorem q. exhibebic
veris denominatorem 8. per denoacorem 3. prodibicrario 24. Nullo
nonnum quam id Reri concigesc; illa erenim nomenclatura Colum conve.
nic calibus per similes Lactones mulciplicaris. Ouod (i quis incer duas
quanticares alias, verbi graria, in-
Ter quancicates 36. _c 2. incerpo-
Tueric 12. d 4. vel plures quor-
cunque; Fatio 36. 2d2. dicetur co
Poni ex rationc 36. ad 12. _ CxrA-
idem eria. Tandem rarioni 4. ad 2. denominator 2. denominator 3. du.
ctus in denominatorem se quemtem 3. producac 9. denOminaEorem ra-
cionis nodcupla, que lulciplicarus per denominatorem 2. rationis
4. dd2. exhribeat 18. detminatorem rarionis octodecuplae, eunc ap-
Parebir qualis racre retulter exrribus hilce rationibus, per se invicem
mulciplicacis. nam denominacor 18. Ostendicracionem 26, 2d 12. dc 12.
ad qu X 4. 2d2. incer se mulciplicaras proterre rationem candem quae est
in 36. d 2. 18. enim ad 1. candem habet proporcionem quam 36. ad 2.
Duod aurem pernumerostiuerque est explicarum, prorlus rniverlale c
in omnigenere quancitatum: nam si incer duas lincas a de B, quoruis
12
rum ad vium, ducta inrationem quatuor ad rnum, hoc est rario octupla
rationem cuius denominator erir 8. ac proinde octuplam: ratio vero duo-
Siducatur inrationem Pex ad duo, quod continger quando mulciplica
modocamen dici debebic rario 24. dd3 criplicara, rationis 6. ad 2. neque
ratio 8. ad 4. duplicata rarionis 2. ad r. vel 4. ad 1. quamuis per accidens
tione 12. ad 4. e randem ex ratione 4. ad2. consticuantur enim denomis
natores reiprius factum est, e superponancur singulis racionibus, seili-
cet rationi 36. ad 12. guxe estrripla, Cuperponatur denominacor z. _ ra-
cioni similicer 12. 2d 4. gux etiam cripla cst, superponatur denominator
bus lad C, ducta in racionem C ad D (hol C ex Labiene H al b.
e exlacione A ad D, ducta in rarionem alt L,  MM ex Fatione A
ad P. tandem exratione A F, ducta inrationem F. ad B, Hoc est exra-
cione A ad B. nam si semel admictatur quod ratio A ad C, ductain r2.
tionem C ad D, producarrarionem A ad D, debebit quoque admicii
quodtalio A adD, ducta in rarionem D ad F, producac rarioneh 
ad L, aconequencer quod racio A ad F, ducta in racionem L al b,
protetac rationem Aad B, et lic quod omnes ra , , 
EB, pet
linex incerponantur CDF, racio A ad B, dicicur compolica ex racioni-