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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 287v, page id 00068196:0570
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2
 duiap sit na + xy: yytya=F
 fiet xa + yy = yyt + y at.
faciamus g ga = E. t et xa + 5 y  ZV Abs   La 
vo
ex aq. T est y - -  a + Z. 0 + aa Ergo xa - L xa + x Y.. = Z. V
mex a. 4 est a = 7b - yy, : y fit 0 = _ydZ.V dZ + d x du -(9yy ag - Z. v  yjay
A)
et Z. V =O et Z0 = 9 et f.. = 8et ex aeque 7. et g. fiez
et
H
fiet y = ha + Y et ex 59. 9 fit y d0 dZ Fy d9 do - ec py dy - ay
X et ex  aeg. 5 pt A = 9 -xy
=c
facimus Yy+y a= O et Xa +Xy = D sie ut tam C, qquam D dentur ex Z.B.
e1 t d0 = 5oZ + do do et (3 = a D aZ + s9 av
EEx ag. 4 fit a= 0-gy: y cujus differentialis yde -Ovydys - Oaque 4 yy a9 20
et pro dC) ponendo vatorem ex b. fit 7 d0 dZu + 4 y a dv - yy dys - Odus 0
psus ex aeg. 5. fit a D- xyB,: X ergo cujus differentiali erit
cet 0 = xdB - XKdy = Xy dX = D ex F xy dx Et ex 7. et  2. fer
(9
O= X dD dZ + x  dv - Xx dy - D dx, ex 8 et 11 fit OX - yyx = Dy - xgy
(13
F ex aeq. 9. fit dy = yd0: 47+0
1
B
=. dy: dX
Z= X. y. a
(2)
_ Z. V = +
V  X. y. a
(4) 
 ra v. a
differentiulis ipsis 3 sit  R e dy = de
fix 3 et Z. fiet y = _X B X. Z. ∞
differentialis ipsius 3, dab
AE E liberata ab a dabit y =  F. Z. dy. dx. dZ et differentialis ipsius 4 liberata
8
a52
ab a dabit. y = X. v. dy. dx. d. Ex Ret 
Aequando ipsius
valores 5 et 6. fl habebitur X =  Rel. 6) Z. v. dq. dy dx et
Similiter aequando ipsius Y valores 5 et  fit X= (Xel. 7) Z. v. dv. dy. dx
Aequando duosvalores ipsius X, nempe ex 8 et 9.  x et  pro dy: X
ponendo Z: V (ex Ag. 1. et 2) habebitt et ponatur dv: d3= Y. tunc
ex ag,  8 et g. fiet aequatuo, nova AZ: dx = Bel. 8) Z. v. Y, ubi efficcendum
et, ut hel. D Zv.Y foret =0 et haberetur desideratum
si xa+ ny jyaga = t. tantum poni
si esset __yae Xar Kg y Kalt 7t a: 4 1B: (1)
set si etset Xta in t Cra +B  y ta a = + = ty: dx
amendo Xt aL Z et bF y+ 48B feret ZY: a2+ av = t (1)
(2)
si esset Xta in yta iP x + 2Xy + yy + 4Xa + 4y a + 4aa = + = dy: dx
 ponendo X+a =Z et y+ a =  fieret Zve: Z + 2ZV + v0 = t
 jam dx = dZ
e
et dy = dv. fiet, t = dv: d2., Ergo aeg. 5. est quosita
tolli potest a et a, et quorendo differentialem ipsius aeq. 4
sed hoc non procedit quando quamer
non sinmil  tolli potest  et a.
si aeg. 3. fuisset XX+ aX = ZZ. feret X = VZ +  aa - 2 a
(11
loce
(10)
et feret
et  e  a = ZE - XX, : X , et Emque
est
sed patet nihil him posse disci novum
(1) +ty u sit  yt a = v+ Z
quid ergo si sic: Xa +Xy: gy+ya
fict X VLXZ,: sit, Xa+ 9a = yX +ya = t  dy: dX. et
scribatur.  ytaZ nt Z+, 0 +pC et X+ a = 9Z+ rV+ se
differentialis est, o = _ 2X Z dX = (3XX dx = ZZd x (+ XX dx. seu dx L3) 2x Zd2: Mr 12
dx =  d 1Z7  aa c
11∞ X 2
2
n
 a
e  1
 
t (1I
d
c+
e
is