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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folio 2v, page id 00068033:0004
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hoc
et substituto calore ipsius n in aequatione paecedenti
nihel aliud prodibit quam
B
-
gl
aequ. a
(possibilis tamen)
Quod si jam fingi posset aequatio arbit raria talis, ut ope
prorsus. 
(.) nempe
ejus tollendo aliquam literarum cytius, gule vel X vel f,
D. sponte sua evanescat d solitum esset problema.
pc rem ad miros analyticae terminos reductan
sed quia hactenus id perdifficile,
exempli gratia fingatur: C
Est g
X - a
ja
=91I aqu d, cl sitc  s sagu d)s
et 
g et X Secum cum postem volumus y. seu rationem
ejus ad 9. redeundum nobis esset ad c adeoque ad d
Redeundum ergo ad summam seriei:
1 -  + b - + + L - f erc cujus tuobus et positis, numeris naturalibus X
cujus seriei membrum.
3. et 5, s etc. positis (X. est
seu co
sic
12
quiliber est
etc quorum daptiaa sunt.
et C
30 nempe Erigonales, e saltum, quorum terminus
1 posito X esse naturales 1. 2. 3. 4.
ubi posito uno termino a, et termino proxinae sequente pposito b inveni calculo
2XX - X
praecedentis schedae b aequ raa +2 tar ac + 8a
1- 4a +3aa
sit jam series quaelibet, et sita ab. c. d. e. et sit ejus summatrx, a. s.g. h.l. et
e
a
a. b. c. d. C
 ubi posito f aequ atb. et eaequa 1b+e etc,
et quaeratur relatio inter tres quoslibet
ut f. g. h.
b e- f aequ. c. h - g aequ. d.
cd e
et d aequ. 2cC +2 +c fcc + BC aequ. h - g. inqua aequatione pro C substituatur valor g. f
habetur ergo valor ipsis h, ex duobus prioribus f et g. et quidem pure
1 = 4C + 3Cc.
 n 0 1
et fiet: seu rationaliter sed quomodo distulguemus 0. p. 4. ab h. g. C
eq
his quidem i erit 
sed niluo hincu quia positis h-g aqu h. g. f aequalibus
jam
quaeramus duas series, quarum summa eadem
l n AB aequ. a. A BC aequ X. . AC rqo tX
CDaequ aa aequ a - X + XXB X + x et.
a +X
Cuncta evanescunt
a a
EBCDE aequ ax = XX + X - X+ + X etc aequal.
af 4a 543
EFDE aego aa - ax  quia hic x qu a. fiet posito a aequ. 1.
set  aequ  + - 2 +  - + e
sit BC aequ Z. fier: X aequ  et fier 2BGHE aequq -  +  - 1 etc
4, 1C
et nuisus uit habeatur HGCDH sit AG aequ aGC sit z fier  aa aequ cd. aego au - Z + aZZetc
ergo HGCdH aequ. aaque a + at 2- ad zit
266
4b
r
b3U
. Ergo Z aequ 3
seu 2 aq. h. lip erit nGDX aqu  29 + in 4s eic Ergo addendo
verissimum
XX