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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 317, page id 1815201908:0374
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b
EL L IDSIS
permutando ve O B ad B HOCCH H KD ad DR, ita 9O ad OR. crBO vi
quadrarum RD ad guactallta DR, ita quadracum 10 ad quadracum OR, hoc
sulum FIOMt adquadracum AB, ita rectangulum HOM ad quadracum DK.
Acqui supra demonstracum est rectangulu FIOM (illud nempe quod est verlus C
aequari quadrato RD, ergorectangulum quoque FIKM quod elt verlus A, aequa-
cur quadraco D K. Ommiaixicus rectansula FLK M, e C. O uod erat demonstrandum.
CoroarB.
o tetioue
esta rectangulum FTOM ad rectangulum FTO M. permurando igicur ve rectan. 2 nas
x discurtu demon AraS iam allaEX LICEL COMSCLC G CMCS
LL. Guacacto C A ee aecacta.
eR OPOSITIO CXXXIZ.
aca Cic elliplis cuius an  Pont D, Hl, ex polo D ducta lic 2a
Ducarte aurem quorcunque normales axi GF F, iunGAnEuTG DF, DF.
Colineas omnes Dh, lincis omnibus C F. aequales ese.
perimetrum DP normalis axt, ce la c’episucansar linca 6PC.
Demonstratio.
ouadrato DF. dao rotor Communt quadraco L. b, aequaneur quadraca De
LF, hoc estquadearum DF, rectangulo FGM cum quadraco R F, hoc est, b qua-
draco OF. Ouia igitur quadratum D F aquarur quadraro CF, eriam recta DF
rectX CF. equalis eAt. F. odem discurlu reliquae omnes D F, reliquis omnibus C F.
equales sunt. Duod erac demonstrandum.
In libro de hyperbola, eria sequencia cheoremata licet sine demonstranda quod
abhyperbole propriccaribus dependeane, ob miram camen cum ellipricis affectio
mibus connexionem visum eAnon alienum HOCIOCOPEOPOHCFC.
PR OIOSITIOCZI.
Ademmanente txura, si rectis D F. c volo ductis aqueneur lInCA
06. octitialo
DROdRCALUEVA RECtarUM C Z In M. PEF PEXCCd. rECtanGUIUM FCM EquaTuE
SE FO normales au aXeM AC.
IM P.
Dicolineam per puncta C ductam esse rectam quae ellip (Im ContinGAE
Dentomao ea e ex propoltione praecedenti.