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Disquisitiones generales circa superficies curvas / auctore Carolo Friderico Gauss
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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*:,