# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068059:0004
# Permalink to this reading: https://leibnizlegible.com/page/00068059:0004?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 14
# Folio 2v, page id 00068059:0004
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068059&page=4
# Source image: https://digitale-sammlungen.gwlb.de/content/00068059/jpgs/default/00000004.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 74 lines, status machine
# Lines: 74 recognised, mean confidence 0.85
# 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.

ex ponentiatium
cum e
dum scilicet
cum c
ol Xel solae X et y
vel sola a sunt in exponente; iba utroque modo differen
tiationis,
s
sit
calculus est in proclivi.
a
constate
esse
y. fit   X loga = loy y. seu sc
+
X log. a = (dy: y seu g dx = dy: y Ergo dy = loga dx a.
s
10(1
Sit. Ergo aequatio C = verf  Aequatio ad
curvam formatricem, et sit c constans; cd detur ex a et c
itemque v. sed eefdetur ex. X et y et c. Itaque
differentcando ag. 1 secundum a  posito log c = 1, fiet
deo C = e dv seu ex 1 et 2, follendo C fiet
d
(2
it
de ve +f,  e d et quia in Coa et V, non
latet nisi a, et C, datur hinc valor ipsius a.
terum
differentrando aqv. 1 secundum X et Y, fiet: O= vde + df
e quibus duabus aequationibus 3 et 4 explicando
utcunque co et v per a et c itemque C et F per X et y
ponendo C constantem, et X, y, a, variabiles; habebitur
aequatio in qua solum supererunt X, y c dx, dy.
QV5
proinde erit resolubilis per est quationem 1. exponentialem
Calimus omissa a ponamus  ed utcunque bari per v,
et esse a cd end  V
posito nl ess ny
tlogarsthisium ipsige, esse unitale
n et Hesse pumeri constantes, etC esse unitatem
ee
et fiet
Aut 
 d∞. Et ex aeq. 3. fiet: n . vetf=C
e deo = nvn
Est autem V=- dfide. ex aeq. 4. quem volorem substituendo in aeg. 7
fiet. _ 4
   p
ts AA-1 (9)
afidet - df: de fide +f. dfide. = C: A
quae aequatio differentialis solvi potest per aequ. 1
. posito loge c. esse
ad ribita aequ.
fiel n - 1 = 0 et fieret -df: de + f = C
si faciamus n= 
quae aequadio
seu -df + fde = ede  quae aequatio solui differentialis
1)
o quae prima specie non reducitur ad quadraturas, ulique rac
modo est resolubilis et aliae imnuumermbiles hac methodo resolvi
possunt. Hic igitur
tanocaus
verum runure
egregium obtimuimus
quia hac arte adribita non est necese
Exponentialibus descentere ad diffederard difercntiales, ante
via exarium obtinuimus scientiae incrementum
ali
an
im
hocmodo?C
ede- 35
df. de = f. e