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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 660, page id 1815201908:0717
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i.
ps.
660
11
YP E R
Demonstratio
on
dis Oe C FIMBC
LEPEF D EECtA FK Armali ad A. B, POHAHENEPErF e H corins ences cIlIptim.
LTCCtXF L, KL, occustences rectis (C: FI, in N de M: convenientigitur LL, RL
inpuncto aquodam I, quod in AB producca cAt, quonium recris D Faequales po.
sIC CunCF, CTI, _ V. CB igicur quadraca F C, C D aequalia sunc quadraris FIC hoc
eA recrangulis HIF I, rna cum quadraris F C. unde ablaco communi quadraro PC
remaneE FIF P reccangulum aequale quadraro CD, quare ve cA quadracum CD.
ad CD quadracum id est N. P. quadracum ad quadrarum N F, hcrecrangulum IFI
Ad FIFI, reccangulum. est aurem oltensum MIEM, recrangulum esse ad rectangu,
Ium NFML ve NE, quactracum ad quadracum N P.; residuum igicur reccangulum
IINL ad YINLCA, vE quadracum N P 2d N P. quadracum. igieux per converlam
36. huius exunc HIFI, YI sectiones oppoCEX. D goddemonstrandum tuit.
PROPOSITIO CCXLVI
AC MMMPICOS ABC, Locus D; astumpro aurem in adC pancto P. inter
Focum e verricem ellipleos A, ducaneur ex P. ad perimerrum ellipleos
quorcunque FF, et per F rectae ponanturF, C H, normales ad AC e
aequales F F.
Dico BHIH, esC ad eandem hyperbolam.
Demonstratio.
iX Foco D, erigatur ordinacim ad axem DFN _ per F _ N, concingens
LPONANEUE FML, NYO. divisa deinde bitariam F D in P, ponatur TR parallela
B10 D. DF. OeCMens Comingenti FM in L. quoniam igitur D FacuS CA clliplcOS, d
TK, L. Buormales ad AC, reCEX DK aequalis b cA IL, prour concinsenci occurrit:
sed DK recrx aequalis est, F K, (quia P. D in Y bisecca C() FCCEX iBITUEP R, IL
aequaleslune: se d perhyporhelimrecex P R aequalis eM IL, Prour occurric fipurae
ABFI. Punctmmigicur LCommunis iheerseccio est Agure BHTI _ lincam IR.
quadracis pt e, una cum redrangulis, fl AI C: quia verorecce ff. Pet s perenm
xquales iunc C H et D, F. X4dCd P  57 t. Guaalq F L fL quanta t Gua
oel1)C draris
FM: hane deinde OIr lineis, aequales GY: cruncigicur FIC quadrara xqualia
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