# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068197:0169
# Permalink to this reading: https://leibnizlegible.com/page/00068197:0169?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 85r, page id 00068197:0169
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=169
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000169.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.80
# 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.

e Tangentes curvarum transcendentium per
exponentes indefinitos habentium
X+ de
dy aequ +a = a
Ergo 0 aequ dy aqu.
inquiratur valor
X∞dx
a
x
L
 yt dy
X+Ax
nta Xo
Xtx
seu +y
7 y+ dy
Xtdx
aqu 0
per seriem in infinitam secundum calculum loganthmorum.
Et ita puto lancentes quaesitas exhiberi posse
) + du xx p
tus (tc) Ergo fiec = xy + x y = X)
dx
xrax
L X, y X1 dy
J x Y ita
s
sed nihil hinc salis duci potest. Rocuorendum
ad exponentium in seres honsformaoem.
aec methodus etiam utile erit ad aequationes infinitas tiariis modis revocandas
ad aequationes finitas indelerminati exponentis dupliciter enim tangens haberi
poterit, fum si curva ipsa ad seriem infinitam reducatur quo facto et habebitur
aequatio secies differentialis infinita; tum si aequatiocdifferentialis ipsius currae
revocetur ad seriem infinitam, quo facto habebitur aequatio differentiaalis correcta
dem adhuc aliter tentandum; considerando ut series numerstm, et poster
postea ponendo differentins infinite parvas, vel saltem semper ad ea
accedendo, ut appareat in quae tunc desinatur.
Via hoc erit ad quadraturam
circul et Hyperbolae analytram ita enim labebitu
ex la natora quadatura HExperbolae per logarchmos
enim tangente quadratricis vel lonarichmicae habita.
dx aequ. log. X.
Et differentialis
 l0g
y C3)O
e aqu
d
2
si ergo sit equatio A et l0g
2)
aequ X dequ e logx. Exnatura cognithmolum
L; ergo per 2 et 3 erit y logX aequ
seu per 1 et 4 erit V sax
ipsius serit:  art
IV
X
N(5)
aequ
sax
d
X
+ y dx aequ. a XY. Ergo d X aequ.  du, X
C
g. XYax
a aequ’y.
l aqu