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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 450, page id 1815201908:0507
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e A R A BO L A:
PROPOSITIO CCIV.
Arabolam ABC subrendat recta A C normalis ad dianieerum BD:
turque FL Puralcta spit AC, de lD linex ponantur x quidiltances F. D,
occurcenres parabolae in C, ellipsi vel semicirculo in H, F1 linea inl, e
ip(I AC in D.
Dico DE, DHI, D Ilineas esse continue proportionales.
Demonstratio.
Emittatur ex F diame
TeF FR, ICCAnS AC li-
neam in R. VE AKC cC-
ctangulum ad rectanguluin
ADC, AC FR cst ad =F. D,
sed vi AK C rectangulum
ad rectangulum ADC, AC
FK quadracum quoque elt
ad quadtarum HID, igieur
ve FK linca est ad lincam
F. D, SC quadratum F K est
2d quadracum FID; recta
igicue FR, Id eA ID, ad BD.
duplicacam habet racio-
nem ejus; quam habet II
adFTD : quATEDF, DII,
DElinea in concinua Cune
analosia. Ouod crac de-
monstrandum.
SupeF AC vero re axe describatur lemiellivsis vel semicirculus AP.
GC occurrens parabolx in F _ C, vel eandem contingens in B, duca:
LACOtOSITIOCEN
Anencelecunda Fgura, ducatur BC, occurrens ID lineis in L. L;
Diot ad L aupilcata habere laltone ciuo Gllat ua
2+7. hwins.
bCETL ad FID.
Demonpratio.
667. huius. () Voniam eam +D, BTL, TE linex, quam FD, CFID, ED in continua lnE
204. bn. looia, ex ID prima verique serici ck communis, racio IF ad F D, WIIa
d27. De u celm, C CL LL. al LFD, L aeta. Quoderat
propressioni demonctrandum.
seo6 o oroir 2sraeieo Eo E 2Ehas