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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 212, page id 1815201908:0269
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
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∞V L V 5.
Demonstratio.
VnGAnEUE AG, AHI: quoniam anguli
ABC, AF C ciuldem scomenci equales lunc,
crunc e reliqui ABC, AF FI quoque inter (0
aquales: vnde cum ex anguli AC C, AHIC
cide insistences arcui sinc x quales, cruc A G B,
AFEF criangulasimilia: _E AF ad AFI; Ve
AB ad AC. est aurem racio rectanguli
ABC, 2d AF C rectangulum compolITa ex
ratione AB ad AF, hoc est GB ad HTF, et
ex BC ad CC, e exiildem quoque compo.
sca est racio rectanguli GB C ad FIF C; igieue
ve rectangulum ABC ad AFC; siC G BC
rectangulum ad ITF C. Quod crac demon-
Atrandum.
Corollarium primum.
Inc consequens est demissis normalibus BD, F F esse G B C, rectangulum ad
rectanoutum FTFC, veelt recta BD, ad F F. CAenim rE AB C rectangulum
ad AF C sic OBC ad rectat lum HIFC; scd ABC ad AF C, rectangulum
Cst, re AB C parallelorrammum in angulo AB C, ad parallelogrammum, AFC
in angulo AF C (quia ex ii(dem racionem habene compolicam) hoc est verectan-
69. bnins. gulum A C BD ad a rectangulum A C F F: igicur ve rectangulum A C B D, cAt ad
rECLAHgUIUM sUPCE A C F F; AIC GB C rectongulum ad rectangulum FTF C: qua-
reve BD ad L F, HC CBC rectansulum ad rectangulum HIF C. Ouod fuit de.
monstranduu.
Corollarium secundum.
TAdemmanenEC Agura, patet AC eNC ad AFF vE A B ad AF, siuc vE G B ad
HE, quia ACB, AFIF criangula ostenla lunc incer se limilia: quod speciarim
ideo volui apponere, quia aliquories postea alumendum est..
eROTOSITIO LZXXD.
Ranlear percirculi A BC centrum, perimeter circuli AGC, iun-
Atisque AC, POnantuT qua cunque BF, D P norrmales ad AC: ex
cnero deinde C, pet D_ D, IBanTTrECtE CBL, CDH.
DicoDE, BF lincis HD, LB, CAEprO.
portionales.
Demonirar.
catiut Det e de B ceclaL 1l L Btdeito
ad BF, sc HIDC b Eccatiouum ad lBC
ctangutum, hoc ettRDC ad L. BCr: led est quoque
VE KD 2d C B; sic RDC rectanoulum ad rectan-
rulum T BC cum DC B C linex sint xqualesiioi.
TUEVE DE adt BF, Eic KD ad L. B. Quod tuie de-
monstrandum.
        1a   1 6  o     se  S