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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 351, page id 1815201908:0408
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ELL IPS
Demonstracio es constructio.
Nucneo cllipssmaiore axc BD, describatur diamerro BD circuluS BR F, cui
polysonum inseribatur BF. FO FI, Aimile illi, quod A circulo inseripeum cAt po.
IrGonos sececque FG lacus; exem BD in 9; dein ductis ex P. F, C, FI ad axem
BD normalibus F I, FR, GL, FIMI, gua elliplim sccenein C, NY, O, P. ducatur rectx
BC, CN, NO, O9;OP, PB. dico factum esse quod pericur. Duoniam GL
F K suncparallela, crunceriangula C7L. 9, K FiO limilia, adeoquereoT. ad KF,
hoc est ve OE ad RN, sic P. 1 ad OR. lunevero ex anguli OL9. FR 9 rectii
erporriongula OLO. R FO sunc similia. ergo 09, O F. lunc in directums tigura
isicur B C, N O, PB est polrsonum elliph inlcripeum. ve LF. linea est ad lineam L C, , EX et:
sic IBF criangulu est ad criangulum IBC Scd. est ve TB ad TC, hc ID. F. O crapexium menrir.
ad crapexium ICNO; ixicur cocatigura BF. FO eA ad hgura BCNO. vel P linca
2d lineam IC, id estb segmencum IB F ad seomentui IB C, id est ve circuluS B F F B1 81. 
ed ellipsim BCD. eodem modo octendicur Agura BFIC9 ese ad siguram
BFOO vE circulus BF. C ad ellipsim BCD. Quare cric torum polysonum
BF FC:HI ad polygonum BCNOP, vecirculus BE F ad elliplm BCD, _ per-
mucando, veBLFCHI polrgonum ad circulum B F. F, hoc cAex const. ve polygo.
num circulo A inscripcum ad suum circulum, sic B C N OP polroonum ad elliplm
BCD: Duod cracprimum.
Rursum cum eam sexmencum IB F. SC ad sermencum LB C, quam TB F criangu-
lum ad criangulum IBC, ve est circulus B F. D ad clliplim BC D, erie ee Segmen-
cum BF ad segmencum BC ve B F D circulus ad elliplim BCD: de permucan-
do vescomentum BFi ad circulum BF. D, SCB C segmencum est ad ellipsim BCDS
idem similirer de reliquis segmentis ostenditur: isitur daca cllips BCD Polygo-
num inCcripsimus, ec. Duod erac Faciendum.
PEOPOSIIIO CCII.
83. huiur.
Seo ABC Mllibipu Guaaterum lesulale AbC.l. ad-
ecaec pel la Cehherum vri cdiamerris coniugaris aequalibus P. l; ee
qualis lumatur recta FII: qua diamerro circulus describacur HIIK, cui
in Ccribatur quadraTUM IE L MI N.
Dicoquadrata R L, L. N, NM, MK Cimul Cumpra x quari quadraris
AB, BC, CD, D A Cimul Cumpris.
De