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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 384v, page id 00068196:0764
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Quod si vero hac Methado conjungendo scilicet ipsat
y de ddus d3, eM. et su ssy By est n nempe hocum
potentiis cul, s combinatianibus in unum codditis uut post multiplica–
tionem per formulas ex X, in unum additis, uit prodeat novi, sed
forte recidatur, in differentiatem in 1iodatum, vel ex ea
jamntum decivabitem quod semper Cognosci potest) contego
procedendum jam erit ad ipsam seriem  per considere
in qua consideratur X ut constans et n naturalis
si placet, ut varians. Et consideratu dignum et est
posse hic fingi novam seriem infinitam, aquasi transformando
n in X et X in n. qua s utando y quasi
esset _ co = 20n + 2ln + 22N, etc. ubi, in 20, 21, 22
Contineretur p, (ut in valore ipsim y continebatur ibi n.
Et bunc etiam licebit videre an non per deo, aldeo, et (anco
Cansdnco, etc. horumque polentias e quadraturas efici possit
Et pulcherrime consideratums est quod eti etiam
i ipsie dd in uvalore dy, vel ddye vel yy et aut
quavis combinatione aut composito, talis possit instrtui transformatio
Et rossus in ipsis deo, ddeo, et fieri poterit talis transforma-
recidatur in serres prispe
combinatione
ay, aut , quanquam eo reducere cum it comparere liceat
tiodi redeundo ad y.
ut appareat un tandem aliquid prodire possit, saltem per
uod dabit opinor aequationes finitas rangentiales replicatas
jam quaevis seres ex tot seriebus infinitis quas
formata, e
per se corsiderare int conjungerelicet, separatim consi-
derata et reducta ad n vel ad X, tanquam in ipsa
dariantem; licebit examinart. remapeado eam ad simpliciores
et raliocinari de ejus summetione
si fui H. prias enim tantum summas et diffe-
Hoc fiet re esus quemabet
der esset temminum qui
dntias Geometrica consideravimus.
terminum ex primendo per unam legem en per unum terminum
monsione quod ostendi fieri posse in
 semper rescunt altem per summas arithmebicas
bjanithnotume fingi possunt ex pressae per rationes relationes finitas
Pe Ad summarum autem Arithmeticarum  inventionem
conferent plurimum differentiae institutae authmeticae, cum datis summandis
compatanda, quanquam revera i jam eo non sit opust methodum meam
presolutionis rationaxium in partes Utile  quoque erit fingere
summes quasdam arithmetica) simpliciores, et ad ea reducer caeteras.
Et considerandum est idemi si termini alicujus summa vel differentia
reometrica cujus cunuse gradus, nempe summa summarum, vel differentia differen
tiarum sit terminum, quo progressio sit arithmice summabilis; ipsam
utes f _. Eip. Gr
proposit terminum arithinetice summlibilem esse.