# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068255:0087
# Permalink to this reading: https://leibnizlegible.com/page/00068255:0087?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 44r, page id 00068255:0087
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 45v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=87
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000087.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 76 lines, status machine
# Lines: 76 recognised, mean confidence 0.84
# 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.

(-1). = 1 vel = 1 prout R est par vel impar, in integris
2 vel 0
+ R 1 + (1) =  nt Et 1 - (= 1) = D vel 2.
A=
1- (-1)2 = 0 vel 1 prout n est par vel impar. id est.
1- (- 1) = 0 si n est 0 vel 2 vel 4 vel 6 etc
1= (- 1)2 = p si n est 1 vel 3 vel 5 vel 7 ete
quaeritur formula B, quae sit 0 cum n est 0, 1; 4, 5i 8.9; etc
 ((
A
a
++
(-
(1) )+
1 cum n est 2, 3;6,7; 1, 11; ete
1= A est oppositum ipsius A, id est si A est otur =A est 1. Et similiter Cest
coincidens
I BC
et si A est 1 tunct- A est C oppositum
B est oppositum ipsius A,  eparin extremis
oppositum
in mediis
ipsius B
Et similiter C est coincidens ipsius B in extremis. Et Dipsius C siniliteralusita porro
oppositum
in mediis
une dimidia
itaque dividendo casus in duas partes aequales, ut una medictas comprehendat
Raonta. itaqe in D
partes extremas, alterum dimidium partes medias, fiet
incasu extremorum B = A C= B DEC
ete
mediorum B = 1- A C = 1 - B DE 1-C ete
exemplicausa casus ipsius B sunt 0 e 1 1 00 L
0 0 0 0 1 1 1
 1- A = (A) (A)  = A seu = Hinc fiet
 1- 
= 1 - (1)nX
adeoque 2 - 14 (-1) 3 = 1 - (= 1)n+
adeoque tandem  (1) =-(, , et generaliter
2
sit sit 
et (1)  ( 1)2+
(17 (
sit x alterubrum horum, seu X - (1) n + (- 1)a
er
2
-0 et X
= 1
 =0 sed (13 = (-, )2n72
.1)2 + (.1) n2 X + ( gia - (. fut2
= (In (. )nL X
Ergo fit XX = (-1) n X = 0 seu XX = (-1)2 X
Unde si X est 0 omnia utrinque evanescunt, sin x sit ti fit X -( 1)n
et fit 0 = 0, imo et _0 = (D (1) X. sin X sit 1. fiet
e X = (- 1): seu n erit  par
sicese
genralitur B - 1 - () seu . sico. 
sis et B- ) sin n sit  impar erit B = 1 - (B) sed
B)
et generali dibent
differentiaum inter sues ut seu si habent
seu si duae, B habent d  (n) = n, pare erunt oppositae, sim minus coincidentem
a nota
generatr .
In sequente colunase in C est C = 1 = (4 (C). itaque generaliter dicere licet, fore
A = 1 - ((A) B = 1 - (CB) C = 1 - (4(C) D = 1 - (8(D) et caet
Adeoque si duae nota ejusdem columnae habeant numeros re indices n, in prima
columna differentes unitate, in secunda differentes bipario, intertia differeptes 
quaternario, in quarta differentes octonario eum etc. erunt opposita
sidem est se in pina cturna difcientia sit 2r HI, in secunda R 9T. +2, in 3tia 81 4. 4, est . s aud
CBF
1
00]0
1 10 14
1115