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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 34r, page id 00068194:0067
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2 Novembi
1679
cujusque
Hic discimus modum inveniendi progressionem serici
generalis aequationis affectae, per differentiales ilem
seu lamentum de demonstranda quadralicae impossibilate
nempe
na constans ratio series exprimendi servanda est, pper
 differentiales. Ita facilius postea comparando videbimus
undata series per differentiales  facta comparari possit
i cum serie alia d infinita per differentiales, facta ex curva
o algetraica. videamus et de aequationibus:
SN + P X 4 qX B V sela fiet 3 X dx + p X dx 1 9 dx p dys
stiat X sit X + pX  H y. fier 2X dx + p ex B dys
E5. sit _ XH a + by+ Cy + y + fy rgy + sqy dc.
Prit du  0 +bdys + rcydy +3(3 u t af atus 4 593) de +6hy dy ponamus ayp 1
it ex B 0 + b + 2cy +3By + afy + 5gy +6sy0
Xdx B ba +ibby +ibcy +. 68,3 + bfy +bgy + bh Y
treay tecb +2ce nce tief t2cg
tea + 3e b +3eC, + 3ee +3Cf
Si H a + uby + nC y + 2aey + 2a5y tragy + rahus
+ V y + 2bcy +2be y + 2b5 4+ 2bgy
C y +2cey + 2cfY
+ e
C
quia evanescit
patet jam progressio
in infinitum
ba 1fbab. y + Ebuc G ribaC y + ebafy + _bagy bah yb
+bb +lbc 1+Ve +bF aplibg id
trc a +2czab t2crac
+bac gplce 1fbc5
2c2ac + 2C2af + bp2
12c b. 2C 2bc.
13e a +denab
30a 302ab. 3e eac
bb
+feab
2C2be.
2C, ce 1 4 c ile
3erac Be rac
3erae + 3e2af
3C2bc
+fhac
4f bb
59 ab
6hae
a9
302 be
3Ccc
14f2ae
4f2bc
sgrac
5g bl.
nutile hoic
6hrab
inferiore lon
ga supe
amonium
3e2be
esa
de ex
ab + 2ab y td abet 18 abe 1 + 1d abs
+ b3 + 4bc e+ 5 be
+ 3a 2 4ac + 5b 
membra
s
+ 10ace
temmnos prodo
5ag
demto a. de et quoad numeros illud constante
qui in cubo ab +
servari mirable ut termini membra primaderminu
2
omnia in lsisplicentur per 1 secundi pa
numerum termo
 simplum si una duae sint
ta tum literae, duplicatum, si tres; plures
enim non conveniunt et hic, et ita habetus
modus contituandi in infinitum ubi
una tantu litera ea solum multiplicata per unitatem
X d
7.
patet omnis