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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 951, page id 1815201908:1008
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GEOHETRICR.
AetOSAEIO CLXVII
Peandem rationem concinuene quatuor quancitates A, B, C, D, ee alix
curtum quinque CL, C. Cl, hhC repelaa k, Lia Porccelua ic lilu
aequales:
Dicoractonem aB Guacpeacae etas Cutus Lacio F. F eA cripli-
cara.
minosseriei P duae medix: de consta-
bic veraque leries eredecim cerminis co
cinue proporrionabus, eltque B quin-
ca in lua lee Lquarca in Tua. Prx
cerca gnonai ma A3 F. e vicima
D, I lunc pares, erunenecessario omnes
cermini veriusque seriei alcer alceri x
quales. Ex quo manifectum est racionem
A ad B, hoc est primxe ad quincam, quadruplicatam esse cius cuiusracio P. Ad F, id est
primae ad quarcam eM criplicaca. Duoderac demonstrandum.
ROPOSITIO CEXVIII
TIeandem rarieme Continuene (ex quancicaces A, B, C, V, L, L, d alie
A seprem quancicacet C, tL, G, K, L, M, N, ita camen ve A e C, aequales
Cinc, quemadmodum _ F N.
Dicorationem Aad B sexcuplicaram ciuIdem esse rariomis, culus tact
C ad HI estquincuplicaca. 
neraoc
demonstrat
Hccx cerminos singulOS KKKT A I.
cerponancur eres medix, de interTer
Demonstratio.
Neerposiris enim incer
cerminos primae Coriet
quinque quancicacibus, qua
cum priotibus candem ra-
cionem concinvene, de simi
licer incel cerminos Ainsu-
los lecundae Periei inceriectis
quaciot quanciracibus, con-
cinue plovoctionalibus, cx.
lincque cam O, quam el lescain illa lete, mannenum quoque ie cactonem e
sexcuplicatu   FACIONIS CUS C ad HL, elt quincupCaa. SO ACUC
monulianduti.
TurgeE numetus quantiracu
ro quamenarum quae in Ce-
cunaa constiturx sune; cum veraque series eriginta e rna constet quancitacibus: R 
cionurem A ad B sexcuplicaca estracionis eius, cuiusracio A ad O (quancicacem
prima serici xqualis nume.
ips B Proximam) Habec quincuplicacam. Isitur cum O quanecas mascm 11
sic xequalis, ex eo quodprimae A d C. Bonancur xquales ex Cimilicer vlcime, F, N,
5e1
Scholion.
( t  e   t su  purtiue.  ei s ie t t u u u p e e  u i  p pite  a a et e  ete  s te    1t     . 1         t   1 (11 . 1