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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 108, page id 1815201908:0165
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12
DROGRESSTONES
5.1111
Demonstratio.
d
dS IT
Friesrarionis AB ad BC cerminetur in C; seriei aucem rarionis AB
100
iadC D aequalis (ILHIR; icem serici rarionis B C ad F P, aequalis (ICL N.
Dico seriem AC7, duabus FTK, L N maiorem esse.
e
BE
rodhuins. GErres BC; L F, _C. 2minor el lerie BC, DL, dC. ergolerieS B C) P F, deC. cum
lerie AB, C D. dC. minorerie, quam sertes BC, DF, Xc. vna cum seric AB,
CD, SC. acqui per praecedencem leries B C  M. cum lerie AB, C D, _c. Con-
FF, _c. cum leric AB, C D, dec. minorem contticur, quamm ACr: C18ILR, LH
series aegnales sericbus AB, C D, _C. B C, P P, ex c. minores lunc, quam series, AO
Duoderae demonttrandum.
Ricne leriem AB, BC, CD, D F, ec. hoc esmagnieudinem A Cr. ergo leries BC
P R
C+ L X
1 C
113 bS, (X (151
(4d
Eries continue proporcionalium AB, B C, C D, dc.
Lcorminetur in L. Vecur aurem proporrio a ad B,
mulciplicata rationis AB ad BC, iuxta darum aliquem
numerum (quacuor exempli caul2) de quor lune rnicares in daco nume.
co coernaminustac magnicudines L.M, OP, RS, aequales dacx scrici
terminis AB BC, GyId.
Dico Ceries, rarionis a ad B, quarum primi termini (InEL, O, R, Cimul
Cumpeas, consticuere eandem magnicudinem, quam series rationis AB
ad BC. 111 11.
et 12 5
Demonstratio.
2 1
TaErea 2dB, sic F NI ad NNY, _ OF ad P O, _ R S ad S YJ CrUCCESO OmneS
haerariones quadruplicaex encicinis AB ad B C: _ quoniam L MI, A B, Xquales
sune, candem habebunerationem 2d MI NI; ergo e racio AB ad MINT quadruplica-
caestrationis AB ad BC; est aurem _ rario AB ad DF, quadruplicaca racionis
AB ad BC. ergO VE A B ad D F, iT2 A B ad NTN. RQUAnEUE igIEUE DF _E MNS
CeriesigieurratIOnIS L MI ad MNV, eA Ceries rationis AB ad D F. Similicer osten-
Jam seriem racionis OP. ad PO, esse seriemrationis B C ad I FS ex Ceriemrarionis
RS ad ST, seriem ese rarionis C D ad F C. acquilx cres b series smul sumpex,
adaquane seriem rarionis AB ad BC; ergo criam e illae candem ad aequabunt.
Duod erar demonttrandum.
CELBILM
riis
2
3 hui
A   ue euu e  e s  te ete s s  p se t ue pet qe ue e eus u  ses  ur ue se  e et s.  e  e te  1 t . s 1. 1)e
(11   spTIII
C
CI.
R