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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 288, page id 1815201908:0345
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.87
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BFX ele-
denris.
mentis.
isituE C F H muleo minor est angulosLB C. Duod crac demonstrandum:
DA
PR OPOSITIO LXXXVII.
 el
Demonstratio.
Vn e FI linea minoE sIC aXC AC.
producacur verimque equalicer inK
e L VE LK, Sc aqualis axi AC, iun-
BaIuEque punCta F K, F. L; _ CX P de
nICEaTuE F M normalis ad L R. cric igi.
CUF K P. L. criangulum maius criangulo
GE FI id est criangulo a A B C: quare
cum inxqualium criansuloru bales AC
LK Sinc xquales, cric L. MI b alcicudo
cranguli K F L, maior IB alticudine
trianguli ABC: adeoque c angulus
AF L maior angulo ABC: angulus
Demonstratio.
Voniam tam A C quam P F paral.
Cleloprammum eAt, CrunE caIn ABC.
BCD anguli, quam R GF, GFFT duo.
busrectis xquales: quare de ansuli ABC.
BCD, simul sumpri aequantur angulis
E. O F, O F II simul sumpeis: est aurem
angulus AB C, ostensus s maior angulo
E C F, igitur _ GFHI maior est angulo
BCD: _x quia, veiam octendis al  B, ex C simul sumpei aequancur angulis C.
_ F, Cimul lumpris quo excellu AB C. angulus superac angulum P C F, codem ne.
cesC csre angulus C F H superet angulum BCD. Quoderat demonstrandum.
Corollarium.
TIncpacecansulum B C. D qui circa axem maiore existie, minimum esse omnium
Lanculorum qui hunc a lincis diamerrorum coniugacarum exerema coniungen.
tibus.
PROPOSITIO LXAAMIII.
Lliplim ABC cuiUSaXES AC, E. G contingat in B reCIA Qualau
DE conveniens cum veroque axc in D de P: excenero vero C recta
demiceatur C F parallela linca DF.
Dico DB, CF, BF. lineas eAc in continua proporrione.
273. huin5.
InE AB C ellip(eOS AXeS AC, BD: iunganturque illOFUM exFremd
B, BC, C D, D A: Sic aurem _ alia quae cunque di2MCEEOrUM CON
iusatio EF, CFI, quarum extrema quoque coniunganeur.
Dico ansulos ABC, FO F, HIF G, BC D arichmecice CAC prOpOr.
tionales.
186. bol 1115.
Denon-
 u qui ete ut e e e  u e ee e te   .   e e ne t   a           t  (     iti a  t      e e   e at   putett