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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 74, page id 1815201908:0131
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# Lines: 55 recognised, mean confidence 0.78
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e  . s.  nipeni.
PR O GR E SSIO N L S
(Sinempe ip(S A, FI, M incetIamuS quartam B, X ipsiS A, F, N quarFaM Y, d iptis
4
de omnes quatuor A, F M, Q; A,BPI,R; _C. eAC concinuaS. Quod erac demon.
Arandum.
A, K, Oquartam d. _ iplis A, L, l gcartam es denique ipls A, E, F quartam E) de-
monstrabimus esse ve pis sspliS O, R. SiI, C+ equales: AC PFOI-
tKO. D5I L 1 I L2.
eet d
iES
B l a C ID. FFOTII
umHtma Ni AO P, D. R5
Eneurbina Peries conrinue proporcionalium in diversis racionibus,
 B, C, D, ec. IL, L, M, N, _C. ita camen ve A IE, L. B sine criam
concinux popooales.
1
Dicoomnes A, IE, L, B, N, O: C, Q, R, D, d Sic deinceps, (omisso
in serie IEL. cerrio quoque tertmino M, P, S) esse in concinur analogia.
Demonstratio.
i
VIa A, R, P, B PONIINEHFCONTIHUE, CFBOVE R ad L, sC L. ad B: sed eriam est
Lextrpochesi ve K ad L, siC L ad M, ergO F. ad B, de M candem habCE La
7. Einsac. rionem; xquales aigitur sune B e M. ideoquerationes B ad C, M ad C aequales
TUnE. OVOnIAM AUEEM A, K, Z, B sunic quaruor continue proporcionales, cric rario A
ad B, id est exhypochesiracio B ad C, id est ex demonstracione rario Mad C; cripii-
cata racionis A ad K: Sed rario A ad K, exhypothes et rario R ad L, id est racio
M ad NI: ergo ratio M ad C, criplicata est racionis M ad NV: est auremrario M ad
P. criplicaca rarionis MI ad N, (sunc enim M, NV, O, P concinux) igitur ve Mad C
SICMI ad P: vnde de aequales sunc C et P. quare cum loco M, in serie Ratuatur illi
aequalis B, e loco P, illi x qualis C. crune A, K, I, B, PY, O, C concinue proporcio-
nales. Similicer ostendemus seriem hanc per rerminos 9. RR, D, erc. concinuari in in-
finicum. Ouod crac demonstrandum.
Corollarium.
Tnesequitur: racionem A ad B, criplicatam eRlerarionis, R ad P: _ B ad C, eri-
plicaram ipsius L ad M: irem C ad D, criplicatam ipsius M. 2d N. e Sic de cc-
ceris. nam racio A ad B concinuatur, est que illa criplicara rarionis R ad L, que DeF
TElIGUOSFERINOS CONFIHUAEUT.
elOOoeeiOana
Veriangulo quovis ABN GMRTOFPONANEUEPATAIICIA AB, C. D, L1
LO FI, in concinua analoslaracinter AB, C FI, media sic. LK; inFCF P F
plicaram elle FatIOMIS L. M al
+II
Dcolactonem AB ad IR et
Demonsitata.
AB ad C+FI, duplicaca est ex
pochesi, racionis AB adTK: &
racio F. P ad CrTI, duplicaca racionis
T Mt a C LL. CrSocumiterum, ex hy-
oche. catio AB ad erF criplicata lcLallous LL dc Ct crultatio AB 2d LL
DuIX
.. l 5
vero ae Citl, meclalit L LML.
5. Ouins
   i  e  u  n   1 . e     t t t        eu  ue ue pu e n ue u u m