# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068195:0022
# Permalink to this reading: https://leibnizlegible.com/page/00068195:0022?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 11v, page id 00068195:0022
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=22
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000022.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
# Lines: 29 recognised, mean confidence 0.87
# 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.

si simplicissime fnisset comn = umn + 12 =0
et
romp +21 = 0 et 30 np +31 =0 ex 2 et 3fiet p = - 21 : 20m
et  p = a8e - 31: 3on ergo 21. 30n = 31. 20m, seu fiet
H= M, EP 20. 31,: 530. 21, quo valore substituto in 164. 1. fier
10 m . 20. 31: 30. 21 + HIM 20. 31, : 20. 21 = 12
mup = a mng. b  m p9 = e npq = d fiet:
1 = b3: mn = C: mp = d np. Erbo  Et p jam p
hinc B. n = C. p et Hinc C: m = d3: n
Aursus.  p = b: m = d3: p seu p = d’m: b = a :mn ergo
fit n = ab: d’m = d’M: C fit denique abe: d = M
seu M = abc: d si quaesilsemus m +n = pendi esset X = abc: d + abd: C
aa  b   m + n = a m+n = b fiet m + n + 2Mn = 1
quod si fuisset
fietq 2mon = b - a et M= n = b - a,: 2n = b = m ergo fit
b - a = 2b M - 2 m. seu m = b M = 2 a - + b
n’+ n + p = a m + n + p= b mantp= c. ex 2a
fit in + imn = c seu 2mn = ce - bb misus
n 4. 3nn C + 3 mup seu  mmp = - a + cc - bb: 2C
x nidu quatuor rerum ternimes 4, biniones sex, ut
mn _mp _mq  ap Lnq , pq
mnam= aa Comisso ap Exopposilis is si
nu np nn+ np = bb
mp
N. hil hic novi repertum riem quod
quatu tres biniones trdarent lubicam baram, tsquatuor termones
dent quadruloquadraticam param. quiaque quaterniones; verum dent
surdesolidam purom jam noram
1