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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 401, page id 1815201908:0458
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Demonstratio.
P A R A B C
Vn enim eam rectangulum
EFC ad quadrarum E A, qua
rectangulum LOFI ad, guadra-
cum C A Habeanerationem qua
deaci DB ad quadratum D A,
constacica eNe R F C rectangulum
2d IOTIve quadeacum PA ad
C A. Duod demonctrandum Fuit.
Corollarium.
iT ex A ducacur diamerer AR, Occmerens ordinarim ap pHaciS In R ee L. rect an:
outum C FE ad FFOT, duplicacam habebic rarionem elS quam C K F habee
ad rectangulum FILI. rario enim rectanguli CR F. ad HI L L. eltracio linca R A
2ad F A, hoc est F A ad C: A. Sedrario rectanguli C F F ad FTCI, est racio qua- a +4. hmins.
draci F A ad C A: igicur racio rectanguli CF F ad TICI, duplicara eA eius quam
habec C. KF ad HIL. I, rectangulum.
PROEOSITIO LXXLVIH.
Darabolam AB C cuius diameter BD, ex ordinatim ad illam polica
ADC; continear in A linca A F, conveniens cum diametrO IN F,
erectilque Ex A e C diametris AF, C C ducatur quae cunque HTI, paral-
lela AC, OCCurrenS A F. contingenci in KE, lineae AF in F, diametro BD
in MI, iunctae AB in N, _ rectae CG in 6.
Dico IEFC rectangulum xequa-
ri rectangulo HFI.
a5. I Demonstratio.
1L ccr esp C.
Voniam eam FNB in R, quam
LFC In M bitariam divila est, erie
FR ad FN, VE FM ad FC. vnde re-
ctatigulo FRFG, aeQUaTUE FNFM
rectanculum: sed rectangulo NIM
octensum cest X quari rectans ulum HI P P. igicur etiam rectangulo HIF L aequale est Is. humr
KL Crectangulum. uod erat demonttrandum.
ivODOBT P R, O P, OSAFLO LXXZIX.
IIdem potitis: C
1. 12 4.2 1:
DICOHK HF, FC sineas elle conrinue proporrionales.
5. 115313 1C S1E et
Demonstratio.
E
Voniam rectangulum R F (d ae quale est rectangulo FIFI, VE FHI, ad F R, lIC 188. Buins
LF C est ad FiI: ex congerrendo ve F II ad c FTR, Sic F G eAt ad CT, id eA ad F FT; cPor elo
quadracum isicur F H aequale est rectangulO HRFC; e HIR, HP, F C PEOPOT. Menca.
rionales lunt. Duodtuic demonstrandum;
ninc
35 30