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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 43, page id 175906937X:0067
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=67
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000067.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 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.

aleimi.
nc.
e1dI.
qutioum
quemli.
A
ponendi
Prodatis
Alphabeti
Eut pet-
MBUM Id-
Oine.
lependent,
DdiS expit.
Mti uu
quae ratio
DItaS d In.
tae, divet.
ex lequem
idem adu
+
201.
AIA TEESEOS TINLVERSALIS.
Ethabeacur b - Z e00, Fiet, addendo uerobique Z, b 30Z. FF (I Ha-
DCatUE
=a9∞ O, eTII
Fier Z3 ∞ a a4, eec.
∞ ag: UC _ (1Z3 - a a G _GHCEUF O,
Non secus lihabeatur Z+ - - a 23 -- b b27 ∞ dt = c3Z, adden-
douerique parti f a 73 F bb 
n
L a
Ex quibus constat, quantitates signo = adfectas ad di utrique
parti, li eximantur ab una parte, e in alteram partem transte-
rantur sub signo.
De Deductione per Subtractionem.
FindesitueritZ = 3 ∞ 12; quia si ab aequalibus aequalia vel
idem auteras, illa quae relinquuneur (unt ae qualias tit ue, sub-
erahendo utrinque L 3, habeatur Z ∞9.
Fodem nodo (ihabeaturZZ F aZ 0 bb, Suberacto utringue
Y aZ, HCLZ Z ∞ = aZ F bb.
Similiter Z3- f 2C3∞ aZZ F bbZ L C3 reducetUE ad Z3 DAZZ
1bbZ - c3, Suberahendo utrinque + 263.
Unde colligitur quantitates igno -L adfectas ab utraque parte
Suberahi, eximendo ipsas ex una parte de transterendo in alteram
partem sub signo -: atque adeo quicquid rel additione rel sub-
cractione transtertur, adtici ligno contrario.
DeReductione per Mulciplicationem.
DOrro si ad reducendu prOPONATUE = ∞ 5: quoniamm X qua-
lia per aequalia vel idem mulciplicata, producunt aequalia;
Eiet mulciplicando utrinque per 3, Z ∞ 25. Sic de si habeatur
ag
2 ∞= inrenietur, mulciplicando utrinque per Z, ZZ ∞ aq, eC.
Fodem modo si fuerit.
a: quoniam, delendo denomina-
FOrCM Z b prioris partis 22
E. ipla pars mulciplicatur per 2-- b:
hinc oportet etiam alteram partem a multiplicare PCFZ = b, UE
habCaEUL AqUatIOItCFZZ _C aZ. = a b.
Similicer (I (it ~ ∞ 22 -- b2. +- bB
:quoniam, Tublato denomina-
tOrc