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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 30, page id 1815201908:0087
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.87
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

L IN L A R V M
crianguli AB C. quadrata, sune aGualia quadrato AD semel, quadrato D Bbis, e
C.D quadraco cer sumped. Quodcrac demonttrandum.
EROPOSITIO XLI.
Sco ABC criangulum rectangulum, _ ex B
srecta demitratur quanis BD, ad oppolicum
latuS AC.
Dico AD, BC quadraca simul sumpra, xquari
quadratis AC, BD simul Cumpris.
Demonstratio.
Voniam angulus B A C rectus ponitur, eric B C quadra-
Ccum, vua cum quadraco AD, xquale cribus quadeacis
AB, A C; AD: lediiidem aequale est quadearum BD vna
cum qua drato AC, ixitur LD; BC quadraca; aequalia lunc quadraris AC BD.
ABC ertangulum, _ ex singulis angulis du-
ctx lincae BB, AF, C E SecenE latera oppOlica
DicOAF, FC, BD, quadrata, ad quadracatria la-
cerumerianguli ABC, cam habererationem, quat
Luoderac demontrandum:
PR OPOSIFIO XLIF
d
bitaltam  D, L, F.
tria ad qualuo.
emonstrate.
Vadrata AB, B C limul sumpta, aequalia tunC quactalis
BD, 2AD bis sumpliS; _ AC, BC quadrata, aequalia
sunc quadlraris F C LFbis sumptis; quadrata verd AB, AC
aequancur quadracis AF, C F bis lumpeis; ipieur quadraca
Cemel sumpea, aequalia TunE quaatatis A F, C F, BD, AD, AF, CL
is, Sed AD, A F, C F quadraTa, suNE quarta parS quadraEOTUM A B,
Neriangulis rectagulis qu2-
dracum, quod sc à lacere
rectum angulum subcenden-
ces aequale est eisqua a laceri-
bus rectum angulum conti-
nenribus, describuneur qua-
draris.
Demonstratio.
IE AB C eriangulum rectangu-
cum AB, BC, AC. Duod crac demonstrandum.
Cintet su
BC, A C; igicur quadrara reliqua AF, CF BD, ires habent quartas, quadrato
P ROPOSITIO XLILI
AL, LL, CHI, _ FB linea (CCCE AD in C. OUa alS RC L L. C A MI
eteaequales dempio communi angulo E. C. B. Ct lG AC B. L. C. R reliqui.
lum, et lacerum quadraca line
LaeL
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