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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 4
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dua
Hic jam probandum si qua columnae periodicae sint in unum
addendae oriri columnam periodicam, in columum additionum primu
et secunda, neque enim possunt esse nisidua. Nempe hac duco
Columnae perodica aut habe sunt periodirum aeque longarum
quoneasa aut reretitine ejus quae periodorum est brevicrum
reduplicatione, redm intelligunt t factae periodorum aque longari
us
suppdno enim pereodot ser
esse ae ertidines n uctum
in dyudicis semper metibi numeros progressionis duplae. Redacta jam
re ab re duas colmenus periodicas aeque longas pel additio
ostendemus per additine prodire uns columnas perodicas, prima
ubi cocurunt p et 1
secunda columnus additione getahabet  bi occurit. oxplex 1
al
a columgaesnt
in addendie alias sicm oiuncta sunt conplantes sacund ariae pro sequs
e
qe
t
finc patet si quotcunque columne perddicae sint inanum
Vet
p
addendae  prodire periodicam. Nam ex duabus periodicis fit periodica
a
pe demonstritum. Huicsi addatuo otro fit tura fit item priodica,
et ex hac em ita, et ita porroig
aate
ni
finc tam demonstratur Serici summatricis
Columnam quamdes esse periodicam. Nam quaevis
lest
conflatuo ex periadicis conflantibus primariis et secundariis
alumela
audero finitis itaque quaevis harum sererum est perodita
Hinc sequitur omnes serres ptotentiarum
s
9.E. d.
cuigamque gradus e ritem Triangulorium postamidatum,
et figumtum altiorum habere locummas periodicas; 
s
s
vereraliter omnes seriess numerorum quae analyti ce pa
a
formutam interrcum exadm possunt exentes i
perti conuadus exprimi possunt, se sest vel quarum
differentra seplicata aliquando evenescunt.
iin est in tarioncis, ubi exprassio analiticaest
erfractas formulas, et ex gometricis ubi est
lia gradus variantis, seu ubi calculus adhibetur ex pus
s
nentialis. Et notandum in Gcometricis difse entras
esse Geometricas. in gargonlis hafdnctas
1
t es differentiata tran vesa
sen
cotinet eaf in Aitthmesicis veli ham resplitatis
e et qua
aequale sud
geometrias esse
tarmonitus conbidere en i sa peumaria sene
exhamcili, a