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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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C
C
R
ESSTO NES
Demonstratio.
Tcenim primxe MaSicudini AB, aequalis qua cumque alia H L _ H A B ad BC.
ica sC MI N ddaliam NO. Jua cum M N, unam maonicudinem concinuam a ho-
mogencam compone: concinuecurque racio M IY ad NVO, in infinicum per plu-
res temper cerminos OP, P 9, dec. qui perperuo cum praecedentibus rerminis vnam
maonicudinem componane. Ouoniam ipieur aequales suInE AB, NTNT, erit AB ad
NO, VE MN ad NO; sCd MN eAt ad NO, ve AB ad BC; ergo AB eA d 
ve AB ad BC: aquales ergo lunt BC, N O; ergo BC est ad OP, ve NO ad OP:
sed NYO est ad OP, ve MN ad NO, id est ve AB ad BC, id est ve BC ad CDS
eroo BC cA ad NTO, Ve BC eA ad CD. aequales ergo lunt CD, OP. Cimilicee
oltendam lingulos veriusque prooresonisterminos incer se aequari in infinicu. Dua-
re _Ccries tora AB, ecc. aequalises eori leriei MNV, ec. repore constans xqualibus
sivc iidem cerminis: aequi qua cumque coro se cundo libro demonstrata lunc de pro-
pressionum propriecacibus, conveniune progressioni MN, NO, _c ergocriam con-
veniuneprogrestioni AB, BC, ec. Ouod crac demonstrandum. Verum re res cla.
rius pareas, idiplum per aliquor consectaria seu corollaria explicabimus.
Corollarium primum.
Xhis igitur (ii (dem poliris) intero primo: progressionem vnivertam maonicudi-
Lnum AB, B C, ec. producere eandem decerminatam magnicudinem seu quanci-
carem quam scries NEI, NO.
Demonstratio.
Eries enim A B, BC, etc. xqualis est seriei ALNY, N O, RC. erBO CAIIICI PTBdVCH
quanticarem: aequi series M N consticuie. finicam de decerminaram guanticarem
(exempli caua M RR) ergo ex series AB producir quancitarem finitam MR.
Corollarium secundum.
IIdem Polts MetoeCuao, leries AR (id est omnes ancecedentes) est ad seriem
BK (id estomnes consequences) re AB ancecedens ad B C rnam consequencem.
Ec series BR eA ad leriem CR VE AB ad BC.
EFEreSSerICS AR, BK. CR, lunc in concinus analogia. de similiter alia interemus
ux prop. octuagesim à se cunda habeneur.
Demonstratio.
(E NTR aequale tori seriei AINI, BY O, e C. Crit erdO de coTa leries, AB, BC, eC et
iam VE OstCMMCa aGa ML. CuMICT a ALB aqualIS SIE MN, crie
quogees BC. CB alaGaiBHR. ColeneS KCnaeeBR
3o2. huus. it le adt le. Agu ee  DMI al HO. eBBleS AR eU Lale.
riem
pt  .  e  e .  1 p e     e      e    t   1  1   e e   e 1   l t  . 1    nt   i ap