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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 20
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Haec methodus etiam serviet si non ad summandas series omnino, saltem
ut summandae reducantur ad alias summandas simpliciores Ut s
E sit summanda series cujus terminus X aequy. fiet: y. Xta aequ Z
xtatax
Xta. X + a + dx
ex y. X+a +  aequ =. _ y. X+ a + dY = y. X+ a aequ y dx
xta
aequ
X dx
X+a. X +a+ dx
se Generaliter ergo dispiciendum an series quaelibet altio reduci
possit ad prexime inferiores. Ita enim aliae quadraburae
reduci possent ad Quadraturam Circuli et Hyperbolae.
L
sunt ter Est Terminus seriei progres sionis Harmonicae, item
reducatur ad priorem nam
item B
xta
xta
X+a  F a aequ 1. Ergo X aequ 1 - a
xta
X,
X+a
x ta
X reducetur ad priorem. addendo a xa + aa, (quae jam dantur quia datu 2Xa et aa
X + a
X +a
ex supposita pr summa progressionis harmonicae) fiet
xta
ergo L aequ x+a L
X+a
X
rrataa aequ x - exa
x+a
xta
X+2xataq Xta, X+a
Xta
Eodem modo habebitur
aequ 2+a
et X. Et ita porro. Ergo habentur
et compositae ex potentiis xta numeralorem ingredientibus
Sergamus jam ad secundum denominatoris gradum, e
h + m unde fiet:
X+n +x+m si hx + uhi xeaxib
1
X + LX + In V
.
X+I X+n
X + Ex + In
Oblata jam serie quaecunque, cujus numerator sit constans, nominator vero
formula secundi, gradus, quaratur divisor ut . comparetur
X + bx +c
X +bX FC cum X + 1X + In vel quod idem est quaerantur divisores vel
radices formulae X CbX +C consideratae instar aequationis, nempe X. si x+bxte
erit X+ bx + b aequ. b- c. seu X +  aego Yb - c. seu X + b =   -c aequ.
vel X+ b + st -C aequ. 0. ergo divisores ert  formulae: XX + bX + C
erunt: X + b + Yb -C et X + b - L -C. Ubi cpjo. fient X + b et X
Sumto jam uno divisores ut x+b inde formetur novus terminus hujusmodi:
qui ductus in alterum X + b  Y -c dabit: P X + pb - p b C
X+ L + (b-C
aequ. P
-c
Et fiet.
X + bx +C
1 + pX + pb + p Nb-c
aegu  + Y
XX + b X +C
EXtXtC X+B+ NF-C
Ergo conferatur D cum C. fiet paego 1+ B. et 1+ PB + PAb c aequ naml.
X + b + 
fiet: l aequ. b + sb = c et n aego = - 1b∞c. et p aequ h+ m. et
denique: 1+ Pb + plb -c aequ ( b) + (m Yc+ h 6) - h N-c
 d restabit 1 aequ = 2h st - c.  seu h aequ. 2
seu 1 aequ m autem assumi potest qualiscunque  ut 1.
seu
Ergo si sit:  fiet aequ. +
aequ
XX+bX +C
XX + bx +C
+ +
b- 4c
1-+ 51
X+ L - s.c 2 C. Xt hr C
X+ L- BC   Xb+  
ite t
 utu