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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 21r, page id 00068198:0041
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aec methodus investigande Series infinitae praeferenda aliis, quia
est plane determinata, nec nisi unicam exhibet expressionem
cum por extractiones radicum ex cunis vel aequationibus seriper
pluribus modis procedeae liceat:. Ad perficiendam hanc methoduus
ruut generalia condenda petremata, nempe quomod propestiantur: yds
y. V. y. etc. ilem g y quod facile est ex generali proguissione potestatum
Deinde quomodo progrediantur y du. Y dus. pty yt etc. nam
Sy. Yy erc idem ady. vet vel dus. hic considerari non est necesse. ita res
satis contruditur in arctum, quoad omnis p curvas aralyticas vel transcedtentes, quarum
X’+ y H N 2X X +2y dus 1 0. dx p -7. seu  posito Ex 1 1. fier.
dus  - . sit yBet b. + CX + d X + Cx 01 erit dus s ac X + 3 dX + a eX et
VH.
su fiet b + cx. y du p- X. siot: at bx+cX+ dx + Cx) n - X
t
Nuta b. d. f etc. hic fiunt 
+racc
propietas tangentium datur, ex datis osdinatis et abscissis, etsi ordinaturum vel abscissarum
b +2cX +3dx + 4 CX
+4a ex 44b1 X + 4ceX + 4deX + 4 CX) continuari facite
+hadx B3bdX +3ed 1d +3de
nEx tc +rcd tae
+bX +bC +bd + be
2ac -1 dgo 14aC7
A2a
+2c
c
21
X
2
H 4 a 144a
retatia non detur quaetarm hic serie infinita habetur eaque simplici num ut aliquando Neulono et Gregorio infinitie s infinita. semper enim rem ad simplicem hic redire
necesse est, ut scilicet termini vefficientes non crescant in infinilum, sed intra certum
8a
Ba
potest nam
sic p progresi
amn
in linea descendtuta
pa sunt 1. 2. 3. +.5
literae autem etiam facile haben
tur, nam descendendum (si
continuari ponatur ab a
ascendendum alu a ad a b.
nempe ac ba ec d 
unc fir
3
2
4ac +3bd +2c+ bd, nec
pus calculum continnasti.
cammtrum terminorum semper maneant. Hinc etiam condemus theoremata ut appareat ex infinita sine Hinc facile etiam invinitur regula continuandi
an sit curva analulica
rminata
simis generclis sic condi potest, expressio pro qualibet curva anclytica, que vere est
calentum aequationum.
et unica, cum alia methodo haberi eossint varia