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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 164r, page id 00068201:0327
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alculus tollendarum plurium literatum simplicium
quarum si posterioes supponunt solas r ex aequa
tionibus ubi priores sunt liberae a posse sioribu tis
omnis literahic in legehou net
sunt rau nesatio bae sect  a , cro -1 a2
pro seriebus infinitis
20 21si 30 31 32 40 41 42 43 58 5
e
21+27a = 0 seu a = - 20:21  1b 3 9 30 6 a 9 10 10 7 89 10 Resid. Undenar
esi
8
B30+ 31 a + 32b20 seu b = - 30 - 31a, : 32 = - 30, 21 + 20, 315, : 21. 32
40 +41a + 42b +43C = 0 seu C = - 40 - 414 - 42b: 43 =. 9140 4 30. 42 +31 4rlx 31b u9 
= -21 32. 40 + 21. 30. 42 = 20. 31 42 + 20. 32. 41, : 21. 32.43
= - 31-3
40+ 41a + 42 b + 43c =0 seu c = - 40 - 41a - 42b, : 43 = 42 - 21. 40 + 20.41 - 21. 42 b, : 21. 43 =
50 +51 a + 52b +53C + 54d
= - 21. 32. 40 + 21. 30. 42 - 20. 31. 42 + 20. 32. 41,: 21. 32. 43
50 +51 + 52b + 53C +54 d = 0 seu d = - 50 - 514 - 52b - 53C. 54 = - 2159 + 20. 51 - 21. 52b - 21, 52C,: 21. 59
C
= - 21. 32.50 + 20. 32, 51 + 29, 28. 52 - 20. 3]. 52 -, 21. 32.53C,: 21. 32. 54
3(9
= - 21. 32. 4750 + 20 72.43 61+21 30. 1352 - 20. 3, 93 52+ 1. 32 4053- 21. 39,72 53+ 20. 31. 42.53 - 20. 33, 91, 53,: 21. 32 93,. 4
6(2
(10
3(10d
0 (10
135
B(5)
0(1)
 3) 20 1 01iCo
Ita 32+ 5 1430-0
Cit.
ubi numeris 20, 30, 40
residui ascribuntur, non
veri sed tales, quibus
truantur omnia
30=-3
Resid. Habenar
Nacuri terrc m 1, 1t 1 se 2, et a siu + 4++ fd Ergo procedunt ger metrila prorossione
= - 21, 32.9350 + 20. 92.43. 51 + 21. 30. 43. 52 - 20. 31. 43. 52 + 21. 32. 40. 53 = 21. 30. 92. 53 + 2031. 42, 53-20. 52. 41. 53,: 21. 32. 43.54
C = - 21. 32. 40 + 21. 30. 42- 20. 31. 42 + 20. 32. 41,: 21. 3243
valores litrarum a, b, C, d, etc sunt terminorum 1, 2, 4, 8, Ct. respective
et nonis postertorib
e = - 21. 32.43 bo + 20. 72. 43. 61 + 21. 30. 4362 - 20. 31. 4362 + 21. 32. 40. 63 = 21. 30. 42. 63 + 2a. 31. 42. 63 - 2. 32. 41. 63 - 21. 3 43.640:
CEb 1hC. 43165
b = - 30 - 31a, : 32
d = - 21. 32. 50 + 20,. 32. 51 + 21. 30. 52 - 20. 31. 52 - 21. 32.53C,: 21. 32.54
Generaliter inta atdire pars litem valoris literae per certum numerum
non differt a parte
C = - 21. 40 + 25. 41 - 21. 42 b,: 21. 43
proxime praecedentium literarum ex pressi
valis respondente valoris literae praecedenti
C = - 21. 32. 60 + 20. 32. 61 + 21. 30.62 - 20. 31. 67- 21320 B3C- 2131ba9.   ceci noram psis tu altissinam ujus
d = -250 + (0. 51 = 21. 52b - 21. 53C,  21. 54
ate
N
(21.31 64
nior hetist
a = - 20:21
b = - 29. 30 + 20. 31,: 21. 32
2p. 32. 43. 54. 6
A 32 45 65
c= -40- +ta - 42b,. 43
Namori terminor.
libera valoris et
procedunt
ucionem litera
Himustaum entien habetur
e
inistnatu
tima
unoquoqr valore per se
Respectu Nitarum mosteriorum
in eodem valore, sunt 
ec xe
cundis ad
natis
uis
in 0, 1,
ternariorum dups
e
uut
2, 3,
est no
tu a Y
partim 2
tertiis E
ex I fiunt
1 nat
notarum hun
ransitu ex a tert
ressui quo summa
valoris supli summa
nesdem est
um
tabet 1, pri ims
eblid posirumes sd smbrum ve
  pe
mumem
ipmndior
qui
trtiis
lum o
1,2, 3
ita porro. Numerus
l1
Numeris
et ita
 lutris caed se
1.  in transu
natis et
3 et 2; ex
E et  ficnt 4
Hinc sy num tolum membrum aeapose
cujus numerus H
riorem rq
niatuis
tm
xo fimme
tis ex 0
et 2
quactos. Ex 3 nabus
bnalis
aut 4 et
Ex G natis ex 1et o. fui
4 et 2: ex
ust bi
 natiy ex
.Z
sait
esoissia
rodtimes habet inalet
guum ejus siguo oppositum, et hoc sufficit
numero pimos a
e
i spe formenda
C = - 21.60 - 20.61 - 21.62b - 21. 03C-11. 640: 21.64
-21. 324350 2 +2. 32. 43.50. 6C
H. 32. 
as sri ( 4. . (6 - 21.32. 40 2+ 4 31 4053  2. 2. 40.
1.30. 43.54
P1. 30 p.2130. 42. r. 30. 42. 52  1. 10 0
(20. 3241 Se0. 32. 43. 51 (= 26 22.
to. 31.
sidi 
P20 3241. 53 2+
20. 31. 42 f. 2a31. 4354 . 20. i51. 
20. 31. 42.
53. 8
Ed. 213 b 2132 4C 231 43S+d 272. 49. 54. 65C
quid nenbrm
habent +.
prafcum
numere post
d= - 50 - 51a - 52b - 53c,: 54
A
phas cabp
est
ntmore
Notae posteriores
aut insu
0(1, (3(B (10
perteratunt H234
Numeri sunt 1)2)3)45
in quovis membra
formanda duo mem. 1
equentis
retinentur du qua
omnes d
apta praeterque vornq
mero distinuatur
enim vel retinetur
emmuiatur et tunc tuogu
altanus abjicitur cujus
vinitate, tota. El signum autem nnc
tatur, vel non retinetur umeru ultimus membrifor-
2
3. 54. 60
.54
ultim
rmandimntro ut
nota frioc etimam prate entis excer
membriformandi sunt quid in Membr
les notae sunt
pantis, et tunc retinetur signum; notae ps ir
ior in novorum nomeronus sustilu
mtr
in qu
vinar