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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 438, page id 1815201908:0495
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=495
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000495.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.85
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

AR A BOL A
AC vero pataSolam AD C in C d prO.
ducta, CF. lirseam in HI. ducatuT ex B
ordinatim linca Bl IccanS ADC para
bolam in B, ce per D ex A linca ducatur
Dico AD ad AK, duplicatam habere
rationem eius quam habet AC, ad AH.
cuus quam habet AC ad kLL. Ctatdemonttranaum.
IECII PROPOSITIO CEXXVI.
DArabolas equales AB C, AD C communem habentes verricem con-
EinGANEIn A LInCX AC, A F, Secentque sese invicem parabOlX IN C; CK
quo ductis ordinatim lineis C E, C F, deseribatuF per A parabola A HIB
habens verricem in A, _E CONLInGENLEM AE, OCCUTTONS AUTEM AD C Pa-
rabolx in C. iunetisque punctis AC, A G, CrIfaEUE ex G diamerex GM
sccans AC lineam in M, puncto per quod ordinacim ducacur linca lR
secans parabolas in B, FI, D, lineam A C in L.
Dicorarionem IH ad IB criplicaram esse eius, cuius 1L. ad LM, ha-
bet duplicatam.
AIL OCCUTTeNSEC in R.
Demonseratio.
AD C pALAbOIX, quam AB, A C linex xqualessune, exic L B linea quoque xqualis
GF _c LB a qualis MI G. Rursum ratio T B ad F C, id est A T ad AF; id cst AD
ve
XB de C punctis, diametri BL, GM, ON: ac BL, e CM quidem
FaNC A F lincx in P _ MI. C: N verO recta A P in NV. Ouoniameam ABC
ad AK duplicaca es racionis IB 2d E C, id cst NTG ad F C; LCd VE MG
ad F C, siC AN ad A F (nam AL id est TB aequalis CA ReCtE AN, _E F C ips
ohnins. AF, 2 est aequalis) He en AG ad AFI; isicur racio AD ad AK, duplicaca cst
Demonstratio.
BArhums Vuemiacurincer ID ec TE media TVF quoniamigicur +D, LL, LM PLOPOO
estuce La  B, LE,CtanEcam YD, IN, CPE. TEIlinca, quam LD.
dabid. sTE. LM, YB concinux proporcionales: quarc racio YH 2d IB, quatcE ad quarram.
xipli
674. Buis
   e  s  At.   e  Au te   1 BI. Ae  . . Aes   s A  1 1.    . M u  B A.  .   1  1 t   u V. 1 p  1    r 1 p  1 ur u u s p p