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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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P R O GR F SSLO, N F S
PR OPOSITIO XXVII
Vine duo ordines continue pro-
Lporcionaliuma avee
a A, b, C, D, F, F, e A, 63
Dicoproportionem FI ad C, el-
se duplicatam proporcionis  ad B;
 rationem lad D, rationis C ad B
essecriplicatam: e rationem R ad F
quadruplicaca. ret a Gu
cuplicacam cruldem rationis ( ad B:
. Sexti.
quorcunqe es alia plane methodo demonstrabimus.
10
cC1. L
eet
Llum FTA, QuadraTO G, _CTCCAMBMHI C H, Guadracoa B equale cric. vnde re-
b20. Sexti ciin guadraca G, B, sinc b induplicaca ratione basium C ad B, erie e rectangulo-
rum ploporcio duplicaca, rationis C ad b: led lactoetanguli ITA, ad rectinou-
lum CA, estracio cHI ad Cs ergo proporcio HI ad C est duplicaca racionis Cr2d B.
Deinde quonian cam G, FI, I, quam B, C, D, sunc continux, eric rectangulum LC
quadraco II, et rectangulum DB, quadrato C aequale. icaque rario rectangulorun
16, DB, hoc est racio d compolica ex proporcionibus lacerum L ad D, ec C 2d B.
aequalis est racioni quadraci TI, ad C: aequiracio quadrarorum HI, C, est quadrupli-
cacarationis G, B; (eA enim racio quadrarorum HI, C duplicaca racionis II ad C.
quae octensa modo eA duplicata rationis C ad B:) ergo proporrio compolica exra-
tionibus I ad D, _ C ad B, cA quadruplicaca racionis C ad B. ex quo pacet racio-
nem Iad D Colam, esse criplicaram rationis C 2d B. Simili discursu demonstrabi-
musrationem K ad B, eAe quadruplicatam; de racionem L. ad f. quincuplicacam
rationis C ad B. Constar ergo veritas propolicionis.
PROPOSITIO XXVII
InEduo ordines COHCCALI AI, B, C, D, E; _ A, F, C, FI, P eandem
Mactiprimam A: Penalut aduen tertius ordo continue proporciona-
lium; K, L, M, N, C, lecumoordini similis; ita tameH VE A de IL, Sine in-
aequales. DCieMCL FErTIAS C _ C, Donacur media P; dt InFEF QuaFFaS
D _ HI, ponancur aa ea_ R; candem incer quintas ponantur
CT. SexIi.
a rronni
100
ee su ncum.
Demonstras hanc Zucl. lib. 24. pr. 28. de quaruor concinue proporcionalibus. Noseandem de
demonstratio.
Voniam eam A, C, FI quam A, B, C lunc concinua profbiconales, rectangu.
ctangulum FTA, ad rectangulum C A, eA re quadrarum Cn ad quadracum B: itaque
eres medix S, T, V, _ ita deinccps.
Dicoesse ve a la alL, le alt, t alt , lec
Demon-
oti u i   e .  uu u   .i1    i   1  i  t  i.    t a  a    p  1 a   u g pu