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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 42r, page id 00068241:0083
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sit
e
(1)
26 Augusti 1b8gR adix aequationis extracta
Xaequy aequ bX + Cx + x + fX et
per seriem infini
dy aequ b dx + 2CXdx + 3Cx4 +q erc per 1.
tam
Methodus salis
r sine calculor pro Besta
sit aequ l + nV = ny + p+ q etc. Hc mojus cubendicpotepli at serienm
dx aeqo mdy+ 2nydys +3Py474447 dus etc
=I
infinilarum, aut aequalio nesque ex ipsis per
arbitraria, multiplicatis compositam
X aequ l’+ um y _lny + Elpy +9y. Oc +2lry +215y
s+my +Emnus +mpy
+n yt
+2mqu’+ 2mry
+2n p7 + 2n9
+3l my +3lny +3Ipy + 3l9y + 312
+lnus +stn
+ p 70
V +3l
+3
+3lm 5 oblmnus tblmpy + Clmqus +otmrys
+3In y +6Inpy +olngus
m’y
etc
+31 p y
Aliter sine interventuo differentiatum
Y aego a + bx + Cx + _x + f + F
X aequ B+ 1y + 2y+3y + 4 y + Sy +6y etc
e ccd
X aequ O + (2)0ly+ (2)0.2y X2) 03. G3 +()04 y + (30 5y 4s0by ek B. quomodo 
+ 1.1 +(2) 1.2 1() 1. 3 +6)1.4 +()1. 5. Cognoscemus an radix s se
+22 +)23 4(32.4.
43.3.
X aequ 0 + (3)0 y+ 38. 2V 63y4y 1605y b6 y6
+(3) O. 1 1)0. 12 +(6)a.13
(30. 22
+1. 1. 1 (3) 1. 1. 2
aqu. Hoy +202H 0oy A obs
46)072 +(26O 12 + (3. 6) 613.
+6)322 + (6)023
icuoie
valor ipsius X sit impossibilus
et quomodo diversas a–
debet etiam ea esse termino.
s
um natura deficientrum
tes.
utitur Tangente curoe, forte
+6)035 + (.6)034
facilius ostendie
eo redit, ut primum tem. Fuotere
et quol modis aequatio duta
quantitates (4)O13+ (34)912 + (234)0123  poss revocati
Din infinitum decres cat
Facila aurem apparet termini cujusque ipsius y polentiae oefficientes, auipe ita inX
psius X
ut  exponentium summa aequalis sit exponenti gradisexgrat. Oi Ent
lie
seu 0112. sue exponentum summa est 4 im  et at nuo semper eadem
u
pem summa ipsam literarum sit etiam aequalis sidem, ita 2 seu ottfa
militer gradui il exponenti gradus ipsius Y. ita 0112 seu 0+ 1+1 +2 facit 4
s s0 it et
et oet 3 seu 040+1+3 facit 4. et. Numeri autem praefixi habentur
ex omnibus modis possibilibus producendi, ita O11Z. varie produci potest, ex
primo ex orin 2 ium es. rursus produci potest ex orcu + vel ex omi vel ex nmo sebr tera
seuoexge
in 0, ursys3 Tertio (012mF p et sumi possunt ex Tabula 
alibi condita
X
aequ
C
a+ b+c + d
 10
so
a WX
anattbaetia
dices a se invicem distin
quemus Nota y debet
esse minor Unitate, et
O, 1, 2 ete. ut termini
sim in infinitum decrescen
caccedens Metho
dus per difcentiales,
amus an
jam
impossibilita