# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0596
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0596?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 300v, page id 00068196:0596
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 301r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=596
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000596.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 121 lines, status machine
# Lines: 121 recognised, mean confidence 0.73
# 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.

Ut calculum absolvamus, inveniendus valor quantitaliam
e mmntun et q.  nm+mun
invenimus autem esse mmn = ecez3 = 2aceZ + a eZ- b1cZ + 2 abcZ- a b
p = eez - ae - c
q= cez - be- e
mnn = cecZ= 2bcez + b cZ - a eez + 2abeZ - ab
mm = ccZZ -2acZ + aa
un = eezZ = 2beZ + bb
m ser comperdium faciams r ee bec race s= ce - a ee - 2bce
i = bb - ab
ee-bcerace
+ = aC + 2abc = 2be
53 e aee ibce B - Vc + abe - Eac
v= aetc
co- bc+ e
 = ac = a
siet mmntun= ese L E+ L2F N, in esz.  sat Ec t ncere et t ce
r. 18
mmtmu - eee 2+ 92 + x.
+2
in cez- co dat e +ces Z AcerZ + ce Z
a
6 i
certo Z3 = sed Z -vid Z
am in 3 nihil destini eut, addaum in unum coefficientes Z pet
oer
(Ce bee Daccee
(e)- ace -bccee
pro
Eaccee =CC)  se fit lib Z in ce betac + hacet abec
eeco
=bcce9F ce
y
ctabee 2bcee n e abe) +Daacee  -cce t be 2acC) susi   b
s
 EcdC
co
GWeetiabce (race) (= be fabee) 4 Ebbcce = ce ( ae)  2 bc CB)
HAI
icau
M 
H
+cev
BceC abce ab ab
+ 2bC
Le
t
cabre
2bce
aace) Cabce)=  (3abce) +3abbce = bcd - 2abee + race
teee
1
C aboet be - bb b + ab)
eo
Carber abe - aae  ab e)
Ergo tandem fit
yc
-2uce Z3
seu Z nirabe =aac
acc
bce
acee.
dx = hdZue in-
+C P7t -ce siber 93
tCce. Iices
F2ac
bce
Se. Gsa + abce -2abce + 2bc8
JBC + abce = rabee + race
 e cujus ope solvebur. aequatio h + ax  bus ebu = cZx + eZ) posito  1. dx
sed si absit h vel c, vel e non procedit Modo calculus rectus est, cui non
fide nisi in numeris peregerim
Interum sumam exemplum h= czX + ezY. Z= dy .dx Ay = h. Z - ex ergo
dy = - haz: 72 - cdx et pro dy ponendo Z dx fit Z dx = - hdz: ZZ - cdx
seu fit dx = = h aZ: ZZ ~C atque ita habetur solutio ex constera Hyp.
(2)
Rurjus sit  Z= du. x et h + ax = eZy. Ergo fit  ejus differentialis
adx = eZay + eydque seu ad = eZZ ax + Py dque ex  1 et 4
et fit y = a dx: 4Z = eZZ dx: dZ quem valorem substatuendo in aeq.
jam supra  ex aeg. 2 fit, y =  h + ax,: eZ quos valores aquando
fit dx: h+ ax = dque: ez. a- e7
3
sit Zax = dy, et h + by= eZX ergo fit bdy L ez ax + ex AZ
Ergo bzax = eZ dx + exdque et fit dx b = e: C X = dZu: Z et habetur
AX + by = X CZX + CZy sil et   Z x L ay fit.
atx agus  c Z da t CXdque 1 eZ ag+ eydque seu adx + bzd x  CZ ax + Cx du t CZ ax teya
 X =, Z b et:  cZ a seu X = nV. m ( se sit e cZ a = m et ez - b = n
fiet dm- d = dn et ex aeg. 1. fit MX + py 20 ergo = - ny: m et 
et mnaet X = -nay ydZue f nydZ seu y mm + nZx : = Z + n aZ= = MX: n. Ergo
Aq
il
dx: mx =
sin 
Het nxanyl
seu X
im- 1: m ny+ nZ
 grobile
h- ny, im fitax = Cal notus gax M  h -nu d+
et pro dex port adr, E. fit pr de 
an
   u at as e e eat
tabe = bbc
et
d
in
23
havee
a -nf: m = - dufim
dnf: m = an m -amn : mn.
erso d- nm =-aumtannim solutio
-n. m
4. 2. 5
yl in ee (abe + 3aae -c
 Thabe +3bbC = C
Est eria in calculo
Haec oro non procedunt
nec licet simul tollere
rego generaliter Xel 
abcc
1sed
c