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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 216, page id 1815201908:0273
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=273
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.88
# 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.

TR
s
Demonstratio.
Inea A F 2d A F duplicatam habex rarioneHi
LA B ad AD, cum Eam AC, AB, AF, quam
AC, AD, AF concinue sinc proporcionales, ha-
beancque communem primam A, unde cum ra-
eio rectanguli F AB ad F AD compolica sic ex
raTIONC AF ad AF, _ AB ad AD, PAFCE
E A B rectangulum ALCcaSulum F AD rriplicatam habere rarionem ejusquam
hrabet AB ad AB. Duodsudemonstrandum.
PRODOSTTTOXCILI
Fomento cuiuis B C criangulum inscribatur AB C, ductisque con-
CsCus HC, CL, Pohuncur ex B verticerrianguli dux BD, BF,
contingentibus rquidictantes.
Dicorectangulum D AB, ad F. C B, eriplicaram concinere rarionem
eius, quam habet AB ad BC.
Demonstratio.
Vm RC Ac concingens, eric angulo
G AB id cst ABD (ob A C+. BD P2-
FallelaS) aqualis angulus a AC B: e quia
FC quoque circulum concingie, angulo
FCB id CA RBC (Ob B B, FC Paralle.
la5) aequalis cst angulus B A C: criangula
isicur ABD, BP. C Similia lunc criangulo
ad secundam: rario aurem rectan  AB ad F C B, rectangulum, composita est
exratIONE AD ad F C, d AB dd CB, criplicacaisicur racio est rectanguli D A B
ad P C B rectangulum. Ouoderat demonstrandum.
CKet ootIO XCI,V
irculi ABC diamerex Sece  D d F, punctis, aqualirer à cen-
Mclo semoris; ex quibus bia ad duo quaedam perimerri puncta B, P
rectae dcua B, DF, LB, F F.
Duo quadrara DB, B E. sitmul Cumpra quadraris DF, F F. esse xqualia
Demonstratio.
Vngancur AB, BC, AL, FC, Ct V
de F demiccantur perpendiculares
BG, FFT ad diameerum AC, qua ca-
danc primo incer D ex L, erunc igicur
anguli ADF, C F. F rectis maiores; vn.
de quadcatum c F C excedic quadra-
cum FF, guadraco C F una cum re-
ctangulo C F HI bis sumpro, et quadra-
rum
AB
IdC vE AC ad AB, SIC AB ad AD: _C VE A C ad CB, itA CB ad C F
duxe ivicur continue proporcionalium series communem habene primam AC; unde
26. terris.
27. de
Eropureton
AD ad F C, cerria ad cerriam b duplicatam habet racionem AB ad BC sccundx
12. Secun
 p