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# Title: Leibniz-Handschriften zur Philosophie LH 4, 2, 11
# Folio 4v, page id 00068571:0008
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068571&page=8
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a +b = a a +b - 2ab) ab
1 = ta iac 1+ abe
-2ab- 2abc
-4 abed
4aabe + q abed + 4 abide
lG abid - 9 abide
et
et
-8 abril. 5
ex
ab a + b +C = a + b - 2ab + C - 2ac - 2bc + 4 ab c12c + bc
2abc
Htim consequentia si . a = b = c = d- ex et sit numer  + ab
fiet et sit nunerus n, fiet a
n- 2 non - 1 + 4. h. n - 1. n. 2 . 8. nter n. n. 1. n. 2. n. 3, 16. n. n - 1. M. 2. M 3,
.2
2.
12. 34
D si esit par, et + si n sit im par 2. 3. 2 + 4. = 3- 6 + 4 - 1
si n sit 3, fit 3-
62
si atit a fit 4 - 2. 4. 3 + 4. 4. 3. 2.  5. 4. 3. 2. 1 -4 12 + 16- 32
1. 2. 3
1. 2. 3.4 20 - 44 =2
1. 4 - 2. b + 4. 4 - B. 1 = 4 = 12 + 16 - 8 = 0
itaque alternis summa dato o vel
1 n. n - 1 = 2. n. n- 1. n- 2 + 4. R. n - 1. n- 2. M-3 = E
1. 2. 3. 4
n. 2 - 1 - n - 2. n- 3. 24
3. 2. 3. 4.5
et ita quousque licet, summa alternis dat 0, 0, 1,1. prout
2.3
s D duplicetur et red quod prodit subtrahitur ibn
crescunt n ner unitates
podit n Erg O = n - 2D nema 2 videndum
quomo hinc talis alternat sequatur
pro summis a+b+ C, esc. Calenlemus summas ex conbina honibus, eb 6.5. 4
aprimum ex binionibus ab + ac + bc = ab -b 2. n nab
1.2.3
si ab +ac + bc tek sut A+B+C + ea fit t AB = ADC ABC ABCd quia 6 rerum
ab +ac + ad + bc + bd + Cd
ab tac tad tae
Betbd+be
edtae
de
quia 3rem
biniones 3
ABCd = 210 aC quia 10 rerum
quaterniores 2V
10, 9. 8. 7
1. 2. 3. 4
70.
rermines 20
Inde regula glaeratis facile construi popro Binionibus summandis
ita perri potest ad
Inde alia pro summandis ternionibus si ab C+ abd + aCd +b cd = A + B+ C+ d
Haec utilia ad generales Calculos
pro quadratis cubis, aliisque potentiis calculardis syadue
Et, la porro.
abc abd ab2 ab f
Nam quadratum est summa omnium laterum, et summa omni
In cubis adhibentur biniones e terniones nam in quad dyadicis
una cum dupla summa oium biniorum
ubi nullae potentis ab redit ad ab e) ab = 2 ab, nam
p = a sit un = a + 2ab p = a + 2. 3 ab +, 6 abc = a +6ab +babe
ab et ab coincidunt et sunt ab
n4 = a + 24. ab + 1. 6ab + 3. 12 abc + 1. 14 abcd = a +14 ab + 3babet 24 abcd
quid si hic potius ad hibeaum vatores t combinationum per potentirs
2ab = v  a a = An -2ab N 2ab = nn - a et fit a = te a - nn L a =  a - n
a+b = n fit a+b = 2a- n sed B non est uius noto Ergo hic calculus no predit
ab cd et
ald ace acf
ade ads
aes
beo decbes
bde bdf
be
Ede Edf
ce
des