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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 209, page id 1815201908:0266
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CTR CYL YS.
eROP OSIT1O LXXVIII.
Ecenc teledenuo in C adrectos dux quavis AB, D E, in circulo
ABD, ee luper parcibus, circuli describantur.
Dico illos simul lumpeosxquales esse circulo ABD.
Demonstratio.
eculiinteele cam rationem habene quam
a diamerris a deleripra quadraca: octendi-
nus aucem praecedenci propolicione quadra-
ea AC, CD, CB, C F. aquari quadraco dia-
mecri circuli ADB; igicur de circuli supee
AC, CD, CB, C F, deseripci xquales Cunr cie-
culo ADB. Quodtuic demonctrandum.
PROPOSITIO LXXIZ.
Emicirculo AB C inscripra sine
Periangula quECUnGHC AF C, A DC,
actaque contingente HIK quae A C diametro aequidistet, POnAnEUE L. I,
DK normales concingenti FI R. v1
Dicoquadrarum composiex ex AF, P. C, ad quadracum composicx,
ex AD, DC eam habere rarionem quam concinet E. I ad D R;
Demonstratio.
DOcea HB diametto duearrut ad illaim
normalicer R F, D G iunganeurque P FI
DII E B. D B, quoniam F F normalirer in(I.
Rit rCCtEBHI, CTUNCEHI, HIF, HIB, lincx in
corinua analogia, ve ex elementis pacee. vn-
de rectangulo FTIB, aquatur TIE quadra.
cum; cademqué de czusa quadraco HID,
rectangulum GFTB; quare ve FTIadOTI.
hoc est F I, ad DK, AC F HT quadracum adt
DH quadracum: Rursum cum sIE vE HIF
ad HD, ItA COMPOSICA B CK AF, FC, 2d
COmPOTiTa CX AD, DC, erit re quadra-
um HE, ad HID quadeacum. sc quadra.
um composica Cx AF, F C, ad quadracum
compot ex AD, DC; igicur ve F Lad
OK, ica quadratuM COMPOIILX CX AR, PC.
ad quadratum composiix ex AD, DC.
Quod demonctrandum Fuit.
eKOEOSHIIOEXXK.
uodecr
Emicirculo ABC inlecipea line crlansula duo aBL, Ldi ae
que ex C, ad oppolica larera recte ducantur C F, C. F, vrcunque.
Dico siincra aream circuli occurrane rectis AB, AD, in E, F, quadra-