# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068041:0042
# Permalink to this reading: https://leibnizlegible.com/page/00068041:0042?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 23
# Folio 21v, page id 00068041:0042
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 22r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068041&page=42
# Source image: https://digitale-sammlungen.gwlb.de/content/00068041/jpgs/default/00000042.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 132 lines, status machine
# Lines: 132 recognised, mean confidence 0.74
# 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 proponatur
V 1+ 7d
Many
fiet 1+X aequ 1+ = y. et y aequ n X et dus aeq. m ax. erxo fiet: (a aa
ergil Be jam s est odimine incipiat a o imtnu
im angus p y sulstimatur alia sita ut vile terin nncipia a o minus
x
nus 2nscex
Si proponatur s d scribatur yaequ 1+X. et du aeq. dx. fiet s AX, qui est log. 1+ X
sclrtu  pono autem X incipere à 0
+X
Si sit f9ay. se pro Y scubatur P aequa pe m+ nym
many
m+ ny
meny
ma ny
erg sudlita t LB(q hic tt lits fite um scubatur pt d. unde addendo
minus
_) fit pm + pnu +4 et faciendo pm +quq0. seu quu pm
im
n
umtunus mtny. Ergo (ydy
fit m+ny - m, seu
m + ny
Sisit S dy. Scribum  WV. aequ. ex 3 + impus qu +F
nd mtpus
∞43 aeq nggy +ngy +IZ aeq.
scribattmanus
in + ny
gnagu (posito t  r Daq 4. M q aq - mg.) aeq. 7y (posito gaequ. +)
manus
manuL
 mtnus aeq. 2 y - m s y dy
 aq nye-  Ergo su dus
osito g
m+ ny qua L
n manus
Si sit y dy et scribatur 9y + 4 rq ngy 4 mg +45aqu
aeq
ilmens
m+ny
Ergo generaliter
N’ay
aeq e
manus
minus
CM
manu
s
Et epplicando  aeque L y - m ye it m
ed
1
 dy
in+ ny
temario majorem C.2N.
menys l en.
many
mtny
2 m
nyd
Corfito. Yor. 19)
im+nys
vay.
menus
posito e esse integrum, quo casu series est finita, et locum habet terminus per +
ad rectus, qui significat  cum e est par,  et -cum est impar
rempe Cy ay
du
manys aeq ny  dmtnus
y dy
3
- m y + intys - n C dus
enid is
manus lan
31
13
2n
syeague L yt- mB +
m+ny 7 20
n ntny
y- ites 
hornus ie ntq minus
ay
n+ meny
n2d
ay  aq  y -
Se aq.  (nam . t 7 q
L
 e
aequ lia
ay+byu
equ.
acbytor
es
e
ergo alluscgus
hagy) acy atue
bia
ae ay
en.
eqecqur
teq
n menus
17
aebsteus altaueju
abyreusa
aq. P + 9 aeq.
atye by
et fei at rayrgus q nq. +d la
L1. lua aq
=Z. H
y et.
y
4 ay daty
an-yy
Brau  ma q+a + mus is
a f +9y2
a +y
1Y
Ly
(quod quiem proritu potrat
e
Venio ad seundum gradum seu ys in denominitore 
dy
XP
aubys par
amus pagab
sat mar
lx + py + 9a + 4y  qua- p.
a x.. 149
 et 1p  pa rg.1.
seu pol a