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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 33r, page id 00068194:0065
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=65
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0 1 9 25 49 8t 21
14 30 55
4 9 16 25 36 49
5
7 9 11 13
2 2 2 2 2
1 46
1 V 35 84 1b5 286
1 9 25 49 81 1n 1b9
S 1624 32 40 48
a 4 4 4
e
a
0
27 125 343 729 1331 2197
lequ.
sumtis x progressionis Aritimeticae quorum differentia sit e
X+ +IXte s mXte +n atemer
u
X= aqu X + e + Z,e, A+C + Z, Z1, C, AFC +
vel etiam
 dica a es
eeX . M _ B.
ecte + et
 le,  m e
1
711, (Xax aequ. e, Z 4 1,Z+ 1, e, X + m, 221, Z C, E + n, 261, 22, C) 5  eC
1
a
posito dx aequ C. et E aequ X + du seu pte.
regulam progressidnis in infinu
eoq 1 C. n a   tum sic tandem invenirgus ex tabulu
t
132
on
,2,3
parinae praecedentis
a
= M
1724, 5
L - n aequ. -
1,2,39 31, 2,3 1,2
in - n.. Et ita porro
et ponatur et terminus mmus seriei numerorum, progressionis Arithmeticae
 sm
quivis
terminus eusdem progrissionis promimevens sea panime major nanimo
a nihilo ineiaimes qes seast
C. et X ponatur.
Quaeritur jam summa Potestatum ab omnibus huius seriei numeris, cuiq
exponens ita ut omnium istarum potestatum idem sit exponens datus
nempe  qui sic designetur: Z- 1. aequatio generalis haec prodibit:
200
sutm uniun ( di aequatis. 
summa omnium  xE aequ. X + Z. e, X +M, ZZ, e X + M, 3 L. 121, C, X+
Unde patet hanc regulam inverireto aquationem semper esse finitam, modo sit numerus
integer. Si vero Z sit numerus fractus vel a irrationalis, tunc summa series quae summam
exprimere deberet, ibit in infinitum. Quae nihilo minus appropinquationi utilis erit. Sed viceber
magna inde oritur scientiae locupletatio. Nam ita habentur tormini aliquot finiti his infinitis aequales.
Si vecu non incipiat series a nihilo, ubique detrahenda sunt aliqua, quae ex
metuulo supra posita investigare, non difficile est. Sed nolui ascribete,
lic materiam inveniant ingenis exercendi videau sse
84 simil est pautma
omnium: F. 9. 2 f.4
et omnium 4. 16, 25. 35
utrique seriei communis
terminus 25. Exhis multa possent duci
8c
3