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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 9
# Folio 1v, page id 00068006:0002
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series ex suis differenties cujus cunque gradus
continuabis summationibus conflatur.
Hinc jam pergo ad Numerorum expressionem
per proportiones Geometricas sive dyadicam
cum
sive decadicam aut atiam quamoungue. Et quia
omnes series Arithmeticorum, sed manifecte impri-
mis dyadice expressa, habeant columnas periodicae
sequetur omnes series potectatum vel rumerorum
figuratorum vel aliorum supra dictorum habere
columnas periodicas, ubi ostensum fuerit, omnem
periem summatricem periodicae esse persodicum.
Nam ita et summatrix summatrias periodica
erit, imo ex hoc sequitur, quod praesupposuor
mus, Arithmeticam seriem eose periodicam, cumqe
sit summatrix seriei constantium, quae utique
operiodica est..
seriei
Ut ostendatur summatricem perrodicae esse perio
dicam quod sit lemmat, consider emus initio separa
tim quamlibet clumnam Summandae serici, tan-
quam ipsa saec columna sola ess et summandai dico:
Si series summanda periodita unius esset columnae
asnes
Seriem summatrcem Sabituram esse columnas poria
dicas, e.g. Seriei summaneae constantis ex co-
sumna A, serier summatrix constet ex columnis
QMN etc, dico quia A est periodica, etiam Lnp
eto erse periodicas. Nempe ubi evenit ut periodo
(simplici vel replicatie) columnae A, respondeat o
in columnis summatricibus, omnia in usdem co
sumnis redeunt ut ante. Ji pro oolumnis Lae M
fit in loco C, ubi simplex oolumnae A periodus
finitur. At pro columnis QM N, it fit in lcD,
ubi finitur duplicata columna A periodus, qua
etiam ipsa per se integram periodum constituit.
Previder autem potest, quota replicatione penodi
columnae A incidat o in summatucem.
Nam constat, quol penodus simplex summanda
A Sabeat unitates, v.g. hoc loce 4 Jam semel
4 dat 100 dyadice adeogue 0 in prima et se
ounda columna summatrioe. Sed columna duarum