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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 20
# Folio 7r, page id 00068017:0015
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Demonstratio quod columnae serierum
exhibentium potestates ab Arithmeticis aut
numeros ex his cenflatos, sint periodica
Omnis series numeroriem rationalium
qui sint arithmelicorum potestules
ejuodem grudus, (exempli gratia series
omnium Xe, posito de esse progressionis
erithmeticae numeros) continuatis
quantum opus differentiationibus dut
differentiam condtuntem. Ultimu
differentia naturalium est 1. quadrato
tim ab ipsis, 2; cuborum, 6; quadra
toquadratorum 24; surde colidorum
10 etc. id ect 1; 1.27 1. 2. 3, 1.2. 3. 4; 1. 2. 3. 4.5.
simile aliquid fit, si Arithmetia non sint
Naturates, sed alio quicunque, verbi gratia
impares ordine positi, 1, 3, 5,7, eeo
Idem est, si series exprimi possit per
formulam analyticum integram ex po
tectatibus conflatum, v. g. X3+6ZH, X+ 1
dem est, etsi formula habeat nume
ros in denominatore; modo termini sint
Numeri integri. Nam multiplicata per
n
bc