# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0383
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0383?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 192r, page id 00068199:0383
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=383
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000383.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
# Lines: 86 recognised, mean confidence 0.75
# 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.

et d(X)
sit y = X, erit ly = XlX et dy:y = dx, 1+ lX et  = dx, 1 (X, X
1 = X F ly = X lX et dy: y = dx, XR  + IX (1+ (X) X = dx, X, L + IX + qulx
sen e et d (XV) = dx, X, X, L + lx + qu. lx
V = XXXX ly = X  IX et dy: y =  dx, XX=, L + L. X Ix (L + lx + qu lX)
y = X erit ly = X lX et dy: y = dx, s X. L + lx et d X = dx, X,  1 t X) - d, L (1+ lx)
Y = X arit dy = dx. X (=) = dx (1)
n a (gla)
y - X erit ls = X IX et dy.y = dk, X ( + lX (X + F l∞)) sit a p = lx, X 1X, CL 1 t)
y= X erit l9= X Ix et dy. = de, X C = + lax ( + lx (e N x))) et tandempret
et
) = dx, X  GN, (L + LX X C= + Ix B (( + _ LX1))
d (ert
a
d = dx, X13, XZ (L + lx XF Z C + IX X (Z +Ax C 4+ Lx7)7)
q
sed se 3 ( L + lx gend  Ax XC 33 (L  IXX
Et generaliter d xed=dx.
logX X
t1
X
1X
109X. X]1 = legk X, XHI
+
x. X X = X X, ejus lg. est 
dn
d
ec
  (X +ls ) lg. X
squi log X) est X logx = XX log X sed
In  interest ne inter (X~) et inter 
et log X est X logx, quae duo plurimum hifferunt. Itaque et in calculo
sunt distinguenda. Hm )= x Et proinde non po opus habet super
hystertrans cenddenti vet proinde cum scribimus X intelligimus X, ita
,X X = - X segX + logX = ( + 1) log X I Ergo X X = X t C
1
ut l(X) sit X IX
log. XX x = X logX + logx. Ergo n X =  XF +
log X XX = XX + X, logX. Ergo X X = XX + X
lag XC XF Xd = et f +9  log X. Ergo X XF Xd = X et S+g
1og. XL =
d Ex D
(C. 3 logX  XLC) p fC- 1)  ens
(e) te1. 
LXLe3 =  _ dx Ae 
uta
e
Ae-1) + e. 1)
Le. 2e3.  bulxlx Il. 2) f. 53, fe 1) ete
1 + lX. ge 2) + HxIXX X
1
ungeo tit etc X
8 dx = dx V d xn = dx, X, 1+ lX d X = dx, X, X + + la +. HC lXIX
dx = LX, X, X,  + L. X IX + trla + lxl lx + L X _ lxk + = ZXX IX.
a
(43 03 + X lx + L Xed X lxlX +1 X) X  + 1 X x XlX
i
et gecalitur + Eo =  XFe3 e r) 14   l + XC rttC st (Xlx + C  3. C. at 
Pe 27
Se. 27 se. 3d (C 2) 1
d et = dx X X
X
e
 u es  + +(. 23 (C3+   M etc. X X. IX
sie non sit numerus integer rationalis. Et videndum an nihilominus ad vergatur. Si
ubi ultimum istud omitti oportet se u
scilicet tam x sit infra unitatem, quam lx Et hoc casu exemplum prodit quo
differentialis quantitas alterjus est generis ad integrali
in infinitum procedendo potent differentia ipsius dis aequari
aet
Quid sed si sumamus 1 grax t ie
seriei infinitae cuivis. nde et sic invenientur a bc, et Et ita etiam ipsa equantitas 
poterit aequari seciei infinitae cuivis. et ita quod mirabile est po potest dari quantitas
unius membri aequalis summae quantitatum quarumcunque, seu potest, haberis
eZa2bFC l+ m+ n eidque in definitis quae possuultrans ferri-
At hanc s sit 19dy= hoe -XB quod habetur serie infinita
habebitur y seu segmentum circuli per unum terminum exponentialiter sine fine replicatam
pa
ad defruita
ly  XZ = 7 logX et d X: X L  dX Z + d qe l0g X. ubi d X potest explicari
per quantitatem ordinariam dx ad- X), et x esta quaesitas porra ope seriei potest quaeri Z
et Z est  Quad si ergo hinc interi du et dy
qualua in qualo altits  acui  de e t X habebilur
quia est quanttas bene ut _y ham  y est ad
qualiu in qua solum alteru dy. Cujus cum detur varter habebitur aequatoin quas
e ablo veudm