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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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PROPOR TION ALITATFS
PROPOSITIO XLVI
Dico componendo rarionemsB eum ratione C. D ad racionem
CD eandem habere proporeu  lacio C H cum Parione IK ad
Trario A B eAt ad C D racionem, ve rario G FL ad racionem LR.
Demonstratio.
1
Nueniantur  denominatores tarum r2.
cionum esse F, F. L.M is berac
AB 2d C D Tattone ia L 2dF;. _ ve
CHl racio ad racionem lR, IEa L. 2aLL)
quia veroracio AB ad C D rationem Po-
nitur esevEraciO CFI de LLC LaLII
ergo et F a dF, Ve, L ad HI. Deindecum
SIE F Cum F ad F, VE P. Cum NaM
hinc cciam racio AB, cum C D ad ra-
tionem CD, eAt ve racio GHI cum LK
adracionem LX. Duod tui dem oan
dum.
racionem IL.
R
SITIO XLVII.
rodsirario ABcum ractone C. D ad rationem C D, GiE verario C HI
Dicodimachaotatlonem AB, eandem habere proporrionem
adrationem CD quam haber rario C H ad rationem IH.
Demonstratio.
COnstitmancur b AH SOlarum Pationum denOInAEOTES P, E, F, MI. Ononiam ra.
Lseio AB cum CD ad CD, elt verario GiFI cum IK ad TK, igicur denomi-
FOF F CUm F ad F, erie ve denominator L cum M ad HI. igicur diuidendo est
E ad F, DE L ad M. adeogue eriam csracio AB ad C D, VE CB G+ FT ad TK rario.
nem. Ouod erac demonst.
eROeOSITIO ZLVIII
eraco Beracioe CD ad rarionem CD, ve ratio E F cum
Drarione CHI ad rationem C II.
Dico per conversionem rarionis rarionem AB cum racione C DCil a
racionem AB, ve ratio P. F cum ratione C Hadrarionem F. F.
in ratione LH ad lR rarionem:
b Xbid.
Demoni