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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 950, page id 1815201908:1007
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950
DR ODOR THOEALEFA FES
EA PeF CONTERHCL. CKTALISHC C It, quae duplicaca est racionis a B G. Fr∞O rario DO
hoc est, ve ostentum supra, proporcio racionum DI, FIC, guincuplicaca est rationis
BC. Eodem raciocinandi modo procedetur in intinitum. Constac erso propolicum.
PROPOSTLIO CLAI.
DOnancur dux series quinque continue proportionalium A, B, C, D, E.
_ F, C, LL, L,R.
Dicoproportionem rationum AF _ F. H duplicatam esse proporeio.
nis rarionum BG, DI.
a 2bid.
Demonstratio
Lciores AF; CTI, FK crunc in Comua, rei Facile exhypocheli e 49. huius de-
monstrabicur. Proporeio igitur actonum AB, F. K duplicaca est proporcionis ra-
cionum AF. CH. Led ex hypothelis permurando, ve AP rario est ad racionem
CTI, Sic racio BC estad racionem DI. ergo proporciorarionum AF, P. R, dupli
caca etiam est proporrionis rationum BC, D I. Ouod erac demonstrandum.
Iuita sE AB in punctis C et D, velint proportionales AC, CD,
Dicorectangulum D C ad C BD rectangulum, criplicatam habe.
rerationem eius quam habet AC ad C. D.
Demonstratio.
roniam rationes A F, BG, CFI, DF, FK sunc in concinua analogia, exiam r2.
PROPOSITIO CLXVI.
DVoniam igITUE PTOPOLCOIALESIMMLHHCX AC, CD, DB; eric componendo et
Lpermurando AD ad C B, DE CD ad DB, hOC CA AC ad CD, rectangulum
aurem D AC ad C BD rectangulum compolicam habec racionem ex D A ad C B,
hoc est, veiamostendi, AC ad CD, d ex ratione AC ad BD. Scd ratio AC ad
BD. duplicaca estrarionis AC ad C D. isicurracio rectanguli D A C ad CBD,
rectangulum eriplicara eA racions AC ad C D. Quod erar demonstrandum.
Corollarium.
DAC a+C BD ECcca a dacam Womeac racionem, vix aliud ab eo di-
vexsum exiseret qui duasmediasrequirerex altisuari incer duas dacas.
7Nde s quis postularet daram lineam AB diuidi in C et D, ve rectangulum
O.