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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 79r, page id 00068207:0157
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Vir clarissime Amice
honoratissince
Vaeris mihi profunde admodum
in aenigua implicatissimum penetrasse
et pulchiam quandam coefficientium pro generali
additione duadica compositionem detexisse,
qual descio an geertiliter saltent metior
Quoniam tamen in in primis duabus
columnis commudae qua commodiores quaedam
expressiones se detexere columnis quaedam
sese compendia offerunt; videntur. vid
per otium poterimus, an non liceat (procedere
ad etiam ad columnas alteriores. dabo
modum quo ea compentia calculo literali prodiere
qui fortasse nonnihil pro caeteris inservire aliquando
poterit: (∞) = sit  sit  prima columna, D secunda, et su
P, nova nota addenda (C) - D,: p vocetur S
et (D) -D,: P vocetur 2. Hinc si fia
ponatur O = 1a + 12 ab + 13 abc + 14 abcd + 15 abede + erc
erit ~ = 11 + 12 a + 13 ab + 14 abc + 15 abcd + ere
jam ex nostris Theorematibus constat esse 1 = 52 +20
et fet se- 11 + 12 a + 13 ab + 14 abc + 15 abcd + etc) = ∞
20 =. + 211a +2. 12 ab + 2. 13 abc + 214 abcd + etc
Ergo sit 11 = 2 Et 12 - 2 et 13 = + 4 Et 14 = - 8 Et 15 = - 16
fiet
et ita porro. Atque adeo
O = a - 2 ab + 4 abc - 8 abed + 16 abcde + ete
22ab + 23 abc + 24 abcd + 25 abcde + etc. Erit
t O- neab n abe  drtaled + 15 abedet etc quia igitur
5
Eut2 Est jam
3 = 22 a + 23 ab +24 ab 125 abcd + etc Et quia
Et quia 4 = C - 20D, prodibit aequatio identificanda sequens
20
seens + 22a + 23 ab + 24 abe + 25 abed + 26 abede + exc )
+20D =-
-C =.
- 1
+ 2. 122 +2.123 +2.124 +2. 125
- 16
+8
+ ex
+ eted
2 Et 29 + 2. 123 = 4 Et 25 + 2. 129 = -8
+ 2 - 4
Et. 2. 124 = - 8 - 25 Et 2. 125 = + 16 -26
vet  quia duorum gonerum sunt incognitae assumtitiae
Unde 27 = 1 Et 23 +2. 12 =
identificatoriae, nempe 22, 23, 24 eHc; et 122, 123, 124 etc)
ideo nova adhuc aequatione est opies, nempe.
(1D) O3: p. (O D) -OD,: p = D - 20D
jam (5) (C D) - OD,: p = 122a + 123 ab +14 abC + 125 abcd + etc.
Ergo fie
(C5) - OD,: p =
20D = 
1n2a +123 ab + 124 abc + 125 abed + 126 abede t erc
2.122 +2123 +2.14 +2.125 +2. etc 3 =0
-otc
nq - 24 -25
 Unde prodibunt aequationes identificatoriae sequentes
22
122 =0 Et 123+2. 122 = 22 Et 124 +2. 123 = 23 Et 125+ 2. 124 - 24
et ita porro.  Et hanc aequationum, seriem conjungendo
Cumpriore siet 123 =  22 +23+2 se in his aegg. pro
2. 122, 2. 123, 2. 124 etc. substituendo valores ex prioribus
fiet 123= 22+23+2 124 = 23+24- 4 125 = 24+25 +8
2. 123 = 2. 2242. 23 +4 2. 124 = 2. 23+24 - 8 2 125 - 2. 24 +2. 25 + 10
2. 126= - 26+ 16
126 = 25 + 26 -16. et vel
2. 124 = -25 + 8
22  1 25-
2. 123 = - 24 +4
Ergo hos valores aequando fit 2
24 = - 2. 22  - 2. 23 25 = - 2. 23- 224 26 = -2. 24 -2. 25
potuis meodat porilade egactores aret in (at maear eae aadsue