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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 125r, page id 00068198:0249
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2ad XX. CRY+m y + asen =0. differesitiando fit
d + ma am +  am =0sit  = 0 dy = L adn - ydm, i st 2
e
gy+ mu + Lmm =. L m m = an. seu y f N= nm - an) ==m
adn- mdy;: dytdu em
Seu
ydgus +Bd ydm = Bd.  = mydy seu fiet
M
2
dy = ( ad +L mr  aman +: mmdm  L....) - dat Y..  111..)
vel multiplicando per
eu de
2
+anam = um duc
mm - um +
1
andm- andu adi (nm - an)
an
nm
c
Repetatur
fit (2d)
yy + my + an = (1)0 Unde differentiando: dy + mdy t yam tano
ae
icu dy (3) = - ydm = a dn,:, 29 +m. Rursus 1) ex 1 est
s yua my+ L mm
e
Hicu quem valorem substituendo in aeg. 3 fiet: (5t0) du- 4= mdnadn- am s...
a
:2 S... (=m + m) seu dy (6to dy= L mam = a dn - dm
9-
a
2 V.c.
seu (7mo) 2du + dm = B i mam - adn
-adm +: man am v.
2.. (a M + M
(qua
ii mma an)
sit (400) mm -an = aZ piet 2dy tedm adque tar
(9n0) = dy + dm = a dZ: 2V aZ
Ex quo apparet
genrali methodo, hinc non facile aliquid duci,
Lmam . = adu s.:nm- an
a
x = a +b x= q 13 ab
Unde facie apparet rem redire ad differentiationem formulae irationalis
de  l
c
x=lm + ma ax = FImm +3fgm Ias fsim
3- +f3IM Slm = q3 mn Imn + scolmin
duaX = + 3fggr. . . +3gM..
an X = aet ... + atg..
ak =
aD= = (2abe. +2a ce
(+2aacdB .. +20a bd l...
+t
ta
4
q mn YH
at. XL
ad
omn
gaO = aX + aahx +aR
ac= bsm +C Itan + Dla
eeraabblm +2ade sn
iti possunt  m, n e haben peo indeterminatis ex
acemn
auodin bcnH.
 aC
seliquae pro tem constrnlibur
a
 (binae in qua vis indeter
minata,) et praeterea 5 constante (5,9 b, 1,9
t
C. d) m videntor t cissare
Torte et