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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 121, page id 1815201908:0178
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=178
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_ EDMEFRLC AS
GHT BC REMD E NOPF C
DROpOSIEX SnEeres, auc plures magnicudines AB, CD, E F, et rario O
ad R guacumque, minoris ina qualicaris: Auferantur a lingulis A 6,
CR, E. N ita ve ablaTa AG, CR, L N, Sinc ad lua eoca, inratione O ad
R X incadem ratione  ad R inter se continue proportionalia;
Dicolihoc lemver heri postic, propolicas magnicudines AB, CD, L. F
esse in continua analogia.
Demonstrat.
Via ex hypochesi AG es ad AB, vE GFF ad GB, etic eriam  reliquum G B a 29. uin-
Lad reliquum EIB, vecoca AB ad coram EB, CuncisituIE AB, CB, HIB et co-
dem discurlu eciam IB reliquae que in infinicum continux proportionaless onde ce-
iam b ablaca AC CFI, HIT Xc. Cunc in concinua analogin, de ccerminus huius pro- Br. Huius.
BrecionIS AC, GFI, _C. eA B. Similiter oltendam abIATA CK, RL, L. M, _C, esse C73. huins
in concinua analogia, culus cerminus sIc D. ex quoniam ex hypocheli AC est ad AB,
VE O adR; _ CK ad CD, VE  ad R, CrIC A G ad ABVE CK ad CD; e in-
verrendo ac per convertionem racionis AB ad G B, VE CD ad RD. ACqui AC,,
OF, FII, 8C. Cunc d concinux proporrionales in racione AB, ad GB; hoc est d 6. hminti
reiam ostendi C. D ad RD, e per eandem CK, R L, dec. sunc eriam concinux in
racione CD ad R D: IBIEUE A G, GFI, _C. CR, X L. 80. limilium racionum (0.
riessunE. Ouare AB est ad CC D, vE RC ad C R. Similiprorlus discurtu octendam c8+. huimo.
CD, CNC ad P F vE CK ad F NV. sunc aurem ex datis AO, CR, RNF, eres concinux
proportionales; ergo et A B, CD, P P in concinua sune analogia. Quod cracde.
monstrandum. csic
P R OPOSITIO CXVIII.
det
erati
eROPOSITIO ORIK
1111
11.0e
pe  
ldata qualiberprooato a Gaca  al B, CoMuetur
perperuo; deuenictur  aeea inorem.
Demonstratio.
b: .t. C 22 3e diti Sd E+ BeCBEIEEFFSE E
dOnatur enim magnieudo quaenis F; _ HAE F ad aliam J. ve B ad As continue-
curquerario I ad C donec por lepllasena lopeimam hurusiabeaut K Ma
 llat t llallaniled.de Del colldem cetmnos concinucine raclo L da
e el quatu. el onum vi A ad B, lic C5ad. ti; ecveBadC. Hc
AL ad. Cr, C. ergo exaequo in proportione perturbacas veA ad B, he K ad F, sed A
minor est quam R, ergo _ F. E quam P. Ouod exac demonstranduti LI: 1ICI4. Ruin-
Scholion.
rC etiam pertineret propositio septuaa u  otes=
sionis inveniendum esset necessaria, coacti essemus citeriori loco collocare.