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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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E. L. L L+ 3L5.
Fad 6.
eROPOSITIO, GXLV
Lecidem ad angulos rectos  ad F. D, datam obtincac rationem
11
Constructio e demonstratio.
Hro de circulorum proprietaribus proposui-
mus hoc problema: sed quoniam ejus demon-
stratio ab elliprica proprietate dependet; idcireo in
hunc locum eam distulimus constructio vero est. Du-
cacur diamerer HII normalis ad AB secans
AB, in L. Fiacque vE F ad G, SIC HR ad
KI. Cumpca deinde IM aequali iph FTR, di-
uidatur diamerer HIP, in O puncto rediuidi-
TUF RM in L: deinde rectangulo NOP, Aac
xequale quadracum L F; tandem ducaeur per
E, rectanormalis CF D. DicO C F D, divi-
sam in F, secundum rationem F ad G. Quo-
niam Cunc linex NP, RM ad angulosrectos
bitariam divile; isitur descripea ponacur eirca
illas cam quam axes cllipsiS NR P, crunc ita-
que OO, I. F, ordinacim police ad singulos
axes: _ quia axes similicer dinisx (unE in O et
L, eltque rectangulum DOP aequale qua-
Ectam A. B, subrensam cuiusuis arcus circuli A B C, alFer Z SCCarEC D,
174. hains. deatO L. F, PareE a punctum F. esse ad ellipsim per puncta N, K, P, M de
esde
(criptam. ergo eAVE TIK ad RI, hoc CA VE F ad C7, SC C F ad R D, Pacec rectam
D applicacam elle in circulonormaliter ad CD, VE C E. ad F. D dacam rarionem
obrineat F ad C. ubuun demoau.
PROPOSITIO CRLVI
Aca recta A C. e alcicudinc DD, elliplim delcribere cuus pou
Constructio es demonstratio.
Filac super AC linea in alcicudine
BD criangulum ilosceles ABC.
dein AC linca verimque xequaliter
produCacuF In F _ F: VEEOTA R F SII
aequalis duabus AB, BC, tum per
F, B, F, puncta ellipsis delcribacur:di
coillam esse guxpecieur. Duoniam
F F linea dinila est bitariam in D e
hon bitariam in A: CrIE F A P B recta
Sulus vita Cu Guactaco AD, a.
(INE A, _ C.
quale quaratO F D hoC CAE Pet COMMTACLIONEM Qu2AEACO A B; IC a CCIAM quaded-
manet LAt rectansulum a uale qud aato BDIa ee quarta Palc tsurx. codem
E0 AB aequalia sunE quadraTA AD, BD: dempro isitur communi quadraco AD,
∞I2
suius.
upa pe E. B L. Cald lulinea de alcirudine, ec. Quod etat l
ciendum.
modoostenditur quadeato BD aequari rectangulum F CP: quare CA _ C, Foci
Corol
ostus      s   p te  e e t   e    te e  at   t ut      t   p  a 1 e    . 1   1 a e   i  1  11