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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 25v, page id 00068196:0050
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XX + 2Xy + yy + h (x+y) = 4b
XX + 2xy + yy + 2h (X+ y) + hh = ab + hh
X + y  h = +(ab + hh)
id hujus imitationem videamus an liceat aliquid comminisci pro differentiis
 e (vAeZ + 2 dxd Z + dv deZ) +, dh a (v dZ + dod Z) + d vZ -
PYZ + dh d(vZh
d(BZh) = d h d 1Z) + 2 dh aevZ + d vZ d h = 6 di= d vZ d h
 id unum incommodum subesse video, quod in hoc exprimendi modo non evanescit
0Z. An ergo mutabumus, ut dX sit X et d’X sit dx et d’X sit I
fiet dx = d’ux = vx, et dvx = dd + dvdz, et erit
Et fieret fieri posset sed nihil ita lucrimur
oportet ergo h assumi tate, ut sit d vZ d’h, quantitas summabilis,
(3∞7 = dvaque + 2d vd Z + dvdz
et videndum an reliquam _h dvZ + 2 dh dsoZ) = gdque conferri possit
cum aequatione data. jam ita enim foret vzh =  (dx Sdx Cd. vZ d h)
videndum primum quibus a casibus ipsa eZ ddh summabilis,  id primum
+r
Exxx tgydx aadus =0 in qus sir ts rexe . X dx) -pax  ap
fieret si 1 ax dat
sit VZ= _G fit 8H, =
iatg
M
fxy = ex y ax +hX  dy 75 X y dy  x y dx
e
-
xx _  3 = c q Zdv: dZ, X = a dv: dz dy = _ d7d z dv + 2Z d dx - Z dv da z
f sit 5 =0. erit h = - aaque et et m, et et h- 1 = n
s
d2dZ et dy = dx = a a dz ddv - a dvddze: dd 2 a 2dZ,
ondnde, dodo
dy: dx = dzdz dy + Zdz ddv Z d v ddZ,: a dz ddv - a dv ddz=  aadidZ dhaZue
y: a = v. Z et X: a = sdz. Z fiot dus :dx = Zdv - vdz,:  Zdq = vv. 77 + qusde
v y: a = dodz do: dz
X: a = v: Z
d (dvidZ): d (r. Z) = dvdo: dZ dZ + vv: Z.
seu das = _ = ve + qu saz sit qu saE =   sit
az
sit du=
12
 seu dedz: du = deo et firt 2d vd Z ddque - d2dz dd v = 0
22
tio
(a2 -   seu 22 d2 + d8 + 2 s d2 = ddz
et ve + e + 9)7
deo
deo
et dh + hde =s dah
dd  ddeD h) = h ad + 2d s d e +  ddh
sit th adg + 2 dhde = dx dg
posila x constante
ego fiet ph = farg + sax sestah
lrb)