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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 234, page id 1815201908:0291
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PROL E GON F N. A
Demonstratio.
N conprectansulo vel acucangulo sic trian-
sulum peraxem BF C de quoduis aliud ex.
Era aXCM IB FI dliameTer aUFCM BasIS CONi BIF
AF C. ex punctis C aC HI AUCANEUECTL, FIK
normales ad BF, FI. Quandoquidem conus
sic rectangulus vel acucangulus, CrIE aXIS BC
veostendi lupra, aequalis semidiametro (FP, auc
aior. Fx quo liquerlesmencum P L non esse
minus SCGIMENEO L F, ac proinde punctum
E caderc vel incer F ex punctum medium recte
FB, vel ad lummum in iplam medium punctum
incidere. Deinde quia angulus BOF, BFI,
rectisine, vepacet ex dictis prop. 1I. _ ab iis nor-
males dimiltae, OL, HIR, crunc a rectangula
LHB, R IB aequalia quadraris F C, FII. Acqui
quadrarum C F maius est quadrato HII, rectan.
sulumigitur I FB maius est rectangulo RIB.
esed cum BE, B B aequales ABE, LR Mor est quam FL. quoniam isicur, ve anee
oltena punctum L Cadicincer fe punctum medium rectae BF, punctum R er
iam cadec incer I ex punctum medium recta BI, id est BF, e quidem propius vec-
65. scundi. su5 F, quam L, verlus F. liquee isitur b rectangulum BK L minus ese rectan-
sulo, BC. F. Aequi quadraca T. C, KFF, aequantur rectangulis BL. Fb B R I, cr80 qua-
ATaCUM K FT minus est quadraco L C, ersonormalis K HIminornormali L C, Oua-
recumbases BI, BF aequales linc, criangulum YB H minus est criangulo B F Cr. (1.
milicer octendam quoduis aliud exrra axem criangulum minus elle criangulo pae
axem FBC, illudigirur maximum est. Ouod Fueras demonstrandum.
LROTOSTIIO ZIII
AEUS (IE COnUS rectus
axem habens BD d ratio
maioris inxequalicacis RL ad L.
Oporcere criangulum extri-
bere exera axem ad quod BE. D
eriangulura per axem datam
habeacrationem R ad L.
Constructio es demonstratio.
iX puncto D ad B F normalem
ducico DI, tiacque reK ad L.
AC DI ad M. Tum quadrato M
aequale fac rectangulum BNF, 8
quoniam quadracum. MI minus est
quadrato DI, hoc eA (quia ex
anoulorecto BD F ad basim ducta
est normalis DI) rectangulo BIF,
cxreguoque B NF rectangulum mi-
nus rectangulo BIF. crigatur de-
inde ex puncto N normalis NO
par rectX M ium g acurGIBO, FO.
Ouo
8. fegti.
e e e ue te t. es 1 . e eis 1. 1e. a e . e  u. . e  e 1 e pe e te  u et ir  e  te     e p  t  1 a  t e   te a p ta pi 1