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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 311, page id 1815201908:0368
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ett
cedt
irct
Et
E L L IP SIS.
3II
guli aequales: sed an gulus C C F. per demonstrata in 121. huius aequalis est angulo
E A. igicur e angulo CTIF aequacur angulus ATIE; addico ergo communian-
b a e  A C tecto agualis angulus AEIC, quare ex iple rectus
l. CllodeFaC demontrandum.
PROPOSITI
CXXVITI.
Elipsim ABC cuius aris A C conrineane in A, C, B, Ma I B
cempolit, e cenerum El ductasueea Lielca fB ad punctum con-
aCLUS aucatur ex FI linea HII parallela rectae FB OCCUErENS F D linex
AI.
Dico Hllineam aequalem linex ITC, d (I FIL OcCurrCNS E: D recta,
C aqualis HlC. dico HI lincam ae quidictare F B.
CE, DE, ac D E quidem occurrat AD, C F lineis in D d F: Cinc
Demonstratio.
tat BI aequalis IR: iungantUrque BG, GK, de rectae dueaneur AF TC: Ouo-
niam TB, LR sunExquales, erir BI ad TR, vE FFI ad FTC: adeoque BF, K C
lince parallela, et angulus BR C xqualis angulo DBF, hoc est a IBCr: Quare ausc huins.
B C, CR linex aequales: sune aurem e duo reliqua lacera BL, IC aequalia
duobuslaceribus RI, TC. Angulus ergo BTC, aequalis angulo RIO: adcoque C I
lineanormalis canrenti DF, e angulus ATC rectus. quare circulus cenerO HI in-
ceruallo TIC descripcus cransibic per Y, crieque FI I linea a qualis linex FIC. Quod
cracprimum.
Reliquis manenribus, sEiam FY Z linCR quX OCCUEEAE tang enti F. D in T, aequalis
linex HC. Dico FII rectam aequidistare linee BF: sin vero; ducacur ex FI linca
ETL, Parallela rectae FB OCCUErCNS F, D tangenti in L;ericigieur FTL linca aqua-
lislinex FT C, hoc es FTT. quare circulus cenero FI interuallo FTC. descriptus eran-
Elic per Id P puncta. Ouod impossibile: isicur HIL non csparallela iphi FB: nCC
Juxenis alia: precer HII lincam. Ouod erat demonstrandum.
PRoedo111 BaatL.
IE ABC ellipleos axis AC, poli aurem
et D _ L rectae inAectaneurDB.
convemences in puncto quodam peri
pheric B.
Dico DB, E. B lincas limul Cumpras
quatdat AC.
Demon.