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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 949, page id 1815201908:1006
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EEOH FTRIC A
Demonstratio
GIaeve G ad B, sic T ad M. eric ergo aratio D+ Ad Lactonem B C vE D ad MI. ar3 huiu
Jam verorario D ad M, Componitue ex rattonC IB hoc esto criplicara rarionis
BG, _ exratione IM, hoc eHt per constructionem raltore CB. Acqui rariones
BC, CB, componune livc producunecrarionem a Gaaals. SLatio DML COM- C76. huius.
ficaris in racionum compolicione nihil addic. CtSLaTIO DM CA duplicara rario. buins
ponitur ex ratione duplicaca racionis B C, ex racione xqualitatis. Ccddracio aequa- dCrroll. 91
nis BC. CcdveD adM, ita racio DI ad lattonem B. C. ergo rario DI adrationem
BC. duplicacam haberpropothtoe latlonis bli. lari modo reliquas Lheore.
maris parres demonstrabimus.
Scholion
Elucet in praesenti Theoremate digna observarione diversitas inter rationes simplices, 
rationum proportiones. Nam per 27. libri proere sionum Ceometricarum ratio D l Tripli
cata est rationis BC. De proporrio rationum DI, B C. Vti iam demonstraulitus; som ratio
nis BC est duplicata. similler rario F. K per 27. proeres). est Quadruplicata rationis B Ci: pro-
porrio autem rationum P. R, B C tansum triplicatd est rationis BC. Arque ita deinceps in
infinitum proportiones rationum sempet dmitale minus rationum, BC multiplicant quam
rationes simplices.
e
CB: Preportionem vero ructe LLC, lB, cAe Sepcuplicacam propor
cionisracionum DI, HC, acque ira in infinieum.
PROPOSITIOICLXIV.
amas A e L.
Dico proportionem rationis CHI ad rationem CDCpricatam cile
propdicionis quam haber rario BC acactenent L. H; ae proportionem
racionum DI, HI C, quincuplicaram elte proportionis rarionum CHI,
Ulne dux series continue proporrionalium, quxe ae quales tabeantpri-
ila
vE A 2d Z, GC C adt ME, e vE B ad G, SC H ad N; _ ve C 2g FE, siC l a
D, ee sic deinceps. ratio isitur BM ett.proPorrio racionum BC, A L  cacio c 13 huius
CN eltproporrioracionum CHL, EB; ex rario DY est provorrio eacionum 
ETC, X sic deinceps. Jam vero quia A eA aequalis L, eAtque vE A ad L BC C ad M
eric C aequalis ip(i M, ac proinde rario BM aqualis rationi B G. Deinde rario C
compolita est exratione CFI, (hoc est duplicaca Fracionis B G) ex exrationCLLL 127. 110
hoc est per constructionem icerum rarione B G. ergo rario CNV, hoc cA, ve iam sress.
octendi, proporrio racionum C HI, CFB criplicaca eAt racionis B C, hoc es racionis
BM hoc Cst. ve ostensum supra, proporrionis rarionu BG, Z A. Pralel TaoDC.
componieur exratione DE, quae criplicat    a LG 27. Cro
Aerc
e i ee  su  t pi pi ei a . et  e e pti  ut  e et u pt u e  si ute  e t e    t e et s  i  s t  t . 1   1     t  t a  e t pli