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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 65, page id 1815201908:0122
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=122
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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 0.76
# 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.

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G F OM P TRIC A
Demonstratio.
DROduCatuE C D in F, vE DF linca aquetur BD composix: B A vero produ-
CaEUE IN GE VEGA, B C aeGuCNEUT. CNOmam C A, B C linex MML a GuatES, CTMI
DC, DB, D C continuxe proporetoales. Rurtum cum E R Xequelt LCCLa BC,  28. Huins.
AF ip( F B licxequalis, Crit C C in F bifariam quoguc aiiIa: CH AMLCM D L a qua-
lisipl BD per constructionemierso EB, B C, b P F, hoc est AP, P C, e compolc2 b15. Fuius.
Ex A F ex BC C D bis lumpris, sunc CominuX propOrtiOnaleS, GuIOA CTAE PTHHEM.
2. Ouoniam R B, F C, E F sunE ContinUX, ex F C liHCX XGUIAEUE F G. de BF lI.
ea ex construc. sic in D bitariam dta, crune D C, DB, C DC continuX: qualC d a.
X V
BbC. CDEeS erunE SConcnux proporS. quod erac demonstrandum. 11, 89. Huius.
R0P051f10
prima ad secundam, ita cerria ad quartam, CriE ve prima CUIM
aned a cectaus, la Bisites Gualttot de plititum cum cerria; vet di
rima cum secundzad lecundam, ica omnes quatuor ad lecundam cum
JuaITa.
Demonstratio
ISto AB ad B C, DE DE ad FF, dico eNse A C ad AB, VEASSrCGATUM Cx AC X
LD F adAGOrCSATUM ex AB, D F. Cum enim sic AB ad BC, vE DF ad PF, eric
inuerrendo e compotiendo AC A AB, S DF ad DL: GuapoP CCCAII
veraque ancecedens AC, DFc ad veramque conlequenrem AB, D L, VEra aN. cr2. Duinct.
recedens AC. ad AB vnam consequemem. quod erat proxosirum.
Corolarium.
Lio Cx Quacdor proporrionalibus hat vna equalis omnibus quatuor, verbi oratid
C: e hacalcera S aequalis primae, ac cerria, d rande recta Y exto a Guas
Primae e se cundae:denique siponacur V aqualis primxe, eric R adS, ve T adV: limili-
cer  omnibus quatuor hat aequalis C, et secundae cum quarra, aequalis H, d pla
cum lecundaxqualis +, de lecurca dfclanis e C Lad R. resA2C 2
PappO