# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0346
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0346?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 174v, page id 00068196:0346
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=346
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000346.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.82
# 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.

sit cuma 5G ciusque quadratiotC sic ut differentiae ipsarume
GG s sint proportinates ipsis BG, 
it alia curra HH cujus adinatae BHI sint prop
se
sint curvae GG, A, DD, HH, sitque ordinata BH proportionalis rectanguli
Assumatur alia curva CC, summntria mvae quadratux ipsius GG sic ut diffeentiae ordinataum BC
ex ordinata Bd in ordinatam B. Ga
sint proportionales adi ordinatis BG, et sumto ungulo recto. A BAE, sit AB sit abscissa commanis
jam
EF = Bd, et fiet semper AEF A _ ABHA quia ipsae EF seu DB ductae sunt in differeneris ipsam
C2
+
E seu BC proportionales ipsis BG, etBH sunt etiam propentionales ipsis DB ductis in B G
In calculo sit BG = X et BD = Z
(posito Z = l + m∞) et BH = X. Z. eL
0
 BC = _ L. XeF = v et BD = EF- Z = G l+ mX = y.  ergo ut tottatur  reperiatur
illatio inter X, V et y sine X, sint
u co
Ergo X. (+mX
co
1)
et
et
1: er = X = in
e v
1c
1:c0
=l.m. seu v = , (eril.
l: 2x se invicem pendent
d
i -
Unde habetur et Nethodus praeclara omnes
1
+ l d
alios valores binomios reducendi  ad polestates simplicium binomiorum
seu
H ti h
X limX dx = m er
dinidatur et pultiplicet. per Y siet. X. limx dx = C  D. M. C
to:
nonsmus
ponamus esse
sed hoc non licei:
ne
ha h: C+1 h. et1
Tor
+ l. V du
es
=h = 1 et
co
evanesceret enim v, videndum quid oostent, nempe non pte fieri
D
ponamus het et C+1 - hCCF
 et h= e+ 1. fiet erit (X limx reducta ad
e
me Fl.
Mart
 Et puisqu’on commence à changer les anciennes coustumes à l’egard des
Ainsi
uns, la raison veut qu’on en fasse autant à l’egard des autres, qui leur sont
egaux, et qui ont eu un traitement égal auparavant. Autrement c’est
temoigner du mepris pour ceuxcy. Et cela est d’autant plus juste
que les princes de Brousuic ont bien voulu changer l’ancien ceremonial
ou style à l’égard des Rors, dont ils doivent par consequent attendre
favorable que l celuy qu’on fait à leur egaux