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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 349, page id 1815201908:0406
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E L L. IP 5TS
tiabeneis latera quor xe quales perebancur sectores. quoniam auce pereban sellores
aequales lex, erir AF lacus hexagoni. ponacur ergo P. P C normalis ad A Cdiunsancur
icE vE F F ad F Citacriangulu L. De ad criansulu GD F: ergo vecirculus ad elliplin
ica cAlector F. D. A. ad scctorem DA: led loctor LD A es parscerria lemicie
culi, cum linea AP. ic lacus hexasoni; ergo e sector CD A cerria pars semiellip-
sCOSCrIT. Cum aucem EB ips AHI aquidistCE, CFUNE SCGMCNCA AG, BH: adcoqi
_ sectores ED A, P D HI aequales inter se: hoc elE (exTa parS CMipseOS EOTIUS. AaNE L 57. BHE
modolesmenco BHI aequalia lesmenca LIP, TK iunsancurque DHI, DL, DK ins.
sectoresisicur D BFI. D TTI, D TK aequaneur adeoque linguli sinc sexrapars ellip.
(co5. ex simul sumpri lemiclliplim consticuune B C R, reliquam isicur lemiellipsm
B AK seca vedinila est BC K, ericque cora olliplis in sex x quales sectores divita.
Duodtacere oporcebat.
PROPOSITIO CZCLA.
Scocirculo ABC Cus cenerum F. inscripeum porssonum quod-
Sus regulare AB C D: ductaque diamerer FC secer lacus quoduis
AD bitariam in II: IE alrem _ P R L ellipleos diameter quae cunque IL.
divisa in M siCuE FC CA diuila in HI, agacurq. per M ordinarim linca
NO ad diamerrum IL.
Dicorectam N O, esernum e laceribus polygoni regularis inscriben-
dielliplicoclacetum, quoc est polygonum circulo ABC inscriprum.
Polrsonum aurem ellipticum regulare roco, cuius singula larera ab(cin-
dunc elliprica segmentaa qualia.
Demonstratio.
n
que E D, CD, BD, CB. a aequidister A HI: dico Factu eNe quod petitur. re cir-
culus ad clliplin ica est leomoncu FF A ad legmencu C F A id elt vE F C+ ad F B: CAq:
VCatuT EK O linea O P auFerenS sesmentum a qualC SeGI eHEO NY F O ,  ex
P recta PK quesesmencum auferac xe quale Segmenco NL O, dein ex R II.
nea KO auterens legmenrum equale legCHEO NLO, eric O punctumidem
cum puncto N. Junctis enim in circulo AB C punctis R A, E B, R C, S D dueancue
in cllipsi Semidiameeri, R R, R NI, R O, RP. Ouoniam diamerri F G, TF CuHEinHI
_ MI. Proporcionalicet dinilas se AD, NVO linex per II _ MI; acte ordinarim ad
diameeros F C: TL. erit B VESeCFOT A F D ad circulum A B C, SIC NR O scctor ad b iso. M
ellipsIM TR P: SUINEAUEEM CAM A E D, DF C. C F B, BF A SCCtOTCS, qUaM CNR O, ins
ORP, PRK, K R O sectores incer sC aequales, (quIA NO, OP, P R, K O sCg
ta luncaequalia) igieur re sectores quacuor circulares ad tuum circulum sc cllipeiet
Sectoresquatuor ad suam ellipsm: Sed tori circulo x quantur sectores cirluates, st
cur e ellipsi (unc aequales sectores elliprici. quare punctum 1 idem est citi punle
N; _ RNO P polygonum est regulare roc larerum fadt en polssouum circulo in-
Ccrixcum. Ouoderat.
X
hat-