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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 65r, page id 00067993:0129
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3 Marti 1679
infinitae series, earumque
pomnasi et usus et modus verque inven
in
sil
ut eam inveniendi
timsa nqualis leges peliodicas docimalium
Omnis sinfinita) series vec esse
tae aequsqe. sd
ei aequalis demonstrari possit
t ad finit
Est autem aequalis
vel fomulae finitae rationali integrae, vel finitae rationali
fractae vel finisae circationali integu vel affecta vel denique
finitae transcendendi.
At s si aequalis est finitae inec rationali in tegrae, tunc
a ∞ b+ b∞c+ c +d+ dBC+eB etc.
infinita series erit:
quae aequatur ipsi a. Hoc in nuneris saepe sit, tametsi
- 5 + 1 - 1
ista destructio non appareat, ut - +
um E 3 t
+ + 12
uno verbo sunt differentiae seer cujusdam seriei cujuscunque
de  pria aut siml primo et allimo, si finita
series aequalis est
In series sit aequalis te formulae rationali fractae
ta im
S.
Se
necesse est ut ducta in aliam formullam, producat quantitate
finitram ita sit:
b c+ d + e+ f+g 4s
+ t
a + l X + CX + d X3 + e ducenda in L+ mX eto
Avel saltm l ut productum sit quantitus finula.   Et huc redit
tialis, methodus Merciloris per divisiones.
reducibilis pobest idem etiam in plibus formulis plurium literaum impitalium fieri
ad quan E a +bX +Cy + dxy + ex + fy erc. per l+ mxtny erc
finitari Eexplicando ita arbitiarias, ut productum redugattur ad pauca
sequtir ifactenus quam idem locum habet et in summa
ut   Xyt Xy +XIYy.
serierum fimitarum invenienda,
Pubi nota ut obiter dicam formulam,
est aequ. X- 7
X-V L hanc fractionem non apparere
isoscheticam, sed esse tamen, nam idem est X- y quod X+ Y
x + y
c’esserantem sescheticam judicatur patet ex i cum tamen formulu
primo aspectu non appareat sosahetica nisi reducatur ad
quam
ration nite gros, aut nisi sic scrbatur
X + y5
+X + y
Nunc videamus quomodo series haberi possint aequales
quantitatibus itrationalibus. Id  vero fiet sumendo
quantitatem, eifi infinitam eamque multiplicandot, in se ipsum
quantum satis est, quoties opus est productumque destine
bititar non nihis
uA ad spuncos terminos finitos diffica
constructu, quia literae ad altiores gradus
terinos attolluntur sed nihilorinus res semper aliquibus
hoc casu redditur
modis procedit.
Generalius adhum Eadem opera et habeta
sertes differen-e
titatem