20 CAROLI FRIDERICI GAUSS
Primo obseruamus, haberi Adx -|- 2?dy -J” Cdz — 0 5 siue d z
A 3 B
— — -g dx — d y; quatenus itaque z spectatur tamquamfunctio ipsarum x, y, fit
d z A
d x ^ C
d z B
Porro deducimus, ex d.r zr aHp a'dq, d y — bdp -J- b'dq,
Cdp — l/dx — ccdyCdq — — 6dx a d y
Hinc obtinemus differentialia
completa ipsarum
t, u
f d C
dy/N
C 3 d* == i
\ A T P ~
• c ^
) (b'd x
— »’dy)
r d A
d O
V
+
dq A dq.
y (b d.r -
— ady)
y dc
d B\
C 3 d u zz {
B - -
V dp
■ c ^)
{b'dx —
- ad y)
y d B
„ dC\
+
( c a - q -
{bdx -
- ady
Iam si in his formulis substituimus
d A
dp -
c'l 3
+
b y —
- cff -
- b'y
dA
dq -
+
b y" -
- C0T -
- b'y
d B
d? “
a' y
+
ca -
— ay -
■— c a
di?
d7 ~
> >a y
+
tf
Cct -
n
— ay -
r /
— c a
•V*:,