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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 7
# Folio 2v, page id 00068079:0004
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Videamus an et alid ratione possimus Theoremata comminisciim seriebus
Numericis ut d X terminus seniei sit X 
dcdx= et differentia seriei Ax
dx = X + AXAx + dx = X ergo
a=  X = 2 X dx + dx Ergo X = 2 SXdx + sdx. similiter
X3 = 3 (X dx + 3 (X x + sax et X = 4 (Xx + 6)X  + 4 (xdx + sax 2
et ita porro.  dxZe = x dZu + ZdXtt Errga XZ = f XdZue + sZ ax
dXZ = X  Z1dq +Z L X +d in Ztaq = X Z seu _ XdZ + Zd x + dxdzue
Ergo XZ = (XdZ + sZaX + saxdzue 
=  - 1
= X + dx - x = x ex
X X+do
Xx dX
x tadx
LtAX = a. 1 - a. Ergo
vel eliam P d. a dc +a t = co
a
ac an. B. sa ex
Sed nunc tandem incipit ratoo primam ratiorem, qua potentias de ((n) X
explicuimus, applicandi etiam applicando ad ((n) nimia scilicet facilitas rem reddidit
obscuram quia scilicet infinitis modis res fieri potest. Exempli gratia sit
Y = 1+ 2 + 3+ 4 +5 ec. scribamus y = 1 Y + 2X + 37 + 4 gc. hcaet subintet si ponatur y = (0) X + (1) X + (2) X + B) X + (4) X + (5) X + (6) X  modo
ligere possimus X = 1. unde eo casu X ubique evanescit. Interim secundum hanc expressione
possumus investigare y ex Theoremate supra dicto. sed possimus etiam alias adhibere
potectias v.g. y = 1 X + 2 X + 3 X + X 8 c. posito enim X = 1 res
eodem redit. Atque ita ps eligere possum modum cujus ope commodius habentur
summae particulares, seu colliguntur in unum termini, qui finguli sint ad fummandum aptiores
sit n  Hinc cum arculus sit _  - 3 + L - L Nc potest intllgi 1H. 1X + 1 X - =X 
quonm diffecita est = y fiet du = C  - 2 X + 2 Z = 4 X
dy A- L X + 2 n - 2X = 1 -X + x - k e et y + ix - 2 x  3 x etc. de
= dy 1 L X  X en
quomodo autem eligi possit oplima
ratio  supionendi, ex calculo. superiore poterit duci. Hinc etim
multa nova Theoremata duci possunt, oriuntur enim multi diversi modi
ac praeclarisima
summandiu qui omnes redeunt ad unum.
sunt  magni momenti, utileque crittam ad circuti s expressionem
a me inventam applicari tam pro a = +- f + fesc
quam pro a circ  - - + 1-=NC
comlat quod si supra ostensum est