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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 107, page id 1815201908:0164
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# Lines: 68 recognised, mean confidence 0.83
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AUSTer
abens
dPF.
P ad
acionis
CE qua
ri
Fiac en
Balor et
 habet
quo p
liama
dC
nempe
D, qu
In Ita
E sI
0C1
alter.
C, et
C. al
plicae
suplio
EEOMETRLC
ercottates u ra.
onc duplicaca LL alc B. late ane en Torics racionis duplicacae; ra-
cionis A ad B. deinde quia B, C, D sunc continua proporcionales, cric ra-
cio B ad D, acpbala cacoo B ad C. similicer octendemus, rationem D ad F,
duplicacam cMe raciols B dd C. concinux proporcionales (une ipitur B, D, F.
ad F ejul
S,F ErC
duplicaEA AnE,
vndeleries BN, cAseries dupliaca Lactes  a C, Id el CX dacis, A ad B. MMMCS a6+. Mns
eestune A_ ec BN. quare lunc aincer sc, ve primi cermini AaV. Quoi
exal deontrandum.
PROPOE
Montinuecur rario AB dd BC, HaBCIquC CCMMM S. AcMMdC HaC
Dico IIK agnicudinem maiorem esse quam (IE L N.
Demonstratio.
ria HK est series AB, C D, A  L N est series AB, D R, REC. SUMAnEE
LCL HR, Parces HII, IP aGualeS ipIS AB, CD: CX L N vCTO pATECS LMI, MO
aequales ipsis AB, D F. Ouoniam isitur serici TTF, IP terminus cst R, Cric LLK
bad TK, Ve HI ad. IP: e quia serici LM, MO, _c. terminus cM N, CrIE L N c 2 8 b 8L. huivs.
MH. ve Y. M ad M O. sed HIY ad IP minorem habec rationem, quam L M, id est
TIIadMO ErgO HIK ad IR, minorem habec, quam L I ad L. MI, 8 per conver-
sionem racionis RFT ad FTT, maiorem haber quam L N ad LMI. croopermucando
TTKad E N, maiorem habet, quam FTF ad L M. Ouare cum ex const. FII, L. MI sinE
aequales, necese est HIK maiorem esse quam L. NV. (Duod orde demonsttandumsi
pece
OStT1O
EC
Ecesrationis AB ad B C, terminetur in M; assumatur aurem ex lerie
Dicorationis AB ad DL leriem, una cum lcricrarionis BC. ad L. L
ae serie rationis C. D ad L, xquari Coricirationis AB ad BC.
nust
F. F DO FT TKF cirilc M
lcricirarionis AB ad C D, aequalis magnicudo LIIE: Seriei auremta-
tionis A B ad D E, aqualis L N.
AM, cerminus quicum que DF.
Demonstratio.
Vandoquidem omnes AB, BC, CD, DF, ecc. in continua sine analogiz, BaceF
militer B C, LL, HlL, _c. icenique C D, FC, TK osse concinue proporcionalesi eteo
Cerieserium rarionum AB, D F, BC, F F, CD, F C, concinuantur perpecuo; in
cra leriem AB, BC, CD, _C. ita ve inhiscribus seriebus simul sumpris, nec plures,
nec pauciorescermim reperianeur, quam lincin serie A B, B C, C D, ec. manifestum
igirur esthaseres series, seriei AB, B C, X c. xquales eMte. Quoderat demonstrandu.
R O
exclemencis AB, D F, C TI ex Sic in infinicum esse coneinue peoporcionales, Si-