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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 152, page id 175905688X:0174
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=174
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000174.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.81
# 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.

FR AN CFSCF d SCHOOFEN
non cogiret. Inrentis ergo tor liquationibus, quor suppolitre
luerune incosntae linex; quoniam in utraque bina reperiuntur
quantitares incognitae; hinc talis reductio tieri debet, uE exuna
parte tantum habeatur xx, ut lequitur. Duocirca cum primum
a3 F aX x F ayy aequetur 4a d Y, diridatUE HETaGUC PATS PCF2a3
et HE aequatio inter aa L ~ N L yy ec 2dy; e a a, yy in alteram
parcem cranctacis, inter X x e 2 d y - 7y - a a. Deinde cumm = a a6
L 2aCX = CCC aQUETUT 2 ab Y, reltituto ralore quantitatis a(-
sumpex ce, iploque ducto in -c, prodibitX quatIO a aC = CN X
cyy∞ = aby. In qua Sitac porro terminorum transpolicio, ut
exx unam teneac AEquationis partem (ub signo. F _ reliqui par-
tem alteram, atque utraque pars per cdiridatur, proveniet Aquan
tiOx ∞ ∞ aa - 7 7 - = a by, TCUI N N ∞ a a = yy -=fy, (Tcriben-
donempe 2 fpro ==: quandoquidem liberum est quolibetno.
mine datas quantitates insionire).
Reducta erso ueraque A:quatione inventa ad eandem quanti-
tatem xx, ada quanda lunt reliquae quantitates inter se, ut inre-
niiatur inde quanticas incognita y. Juare cum 2 d y -- yy - AA
aequetuTaa -yy = fy, addicis utrinque yy de a a, erit 2 d y D 2 aB
2fy, Teu, dy ∞ aa -fy: _ tranlato 2 f y ad alteram partem,
Factaque urrobique dirisione perd. Lf, Rety ∞ 
d InVenta au-
tem quantitater, non est difficile alceram quantitarem incognitam
x inrenire. Si enim in PrXeCCdeNEI X QuatIONE X N ~ Ay -yy-aa3
PrC
dec
TUImE
NX
dd
Fur
balle
ipsi RA
riEL
scriba
FI
Paralle
seriproe
Catus ext