CIRCA SUPERFICIES CURVAS. 
233 
38 
curvarum exprimendi, sequimur. Magni tamen momenti est, hanc quoque ela 
borare. Retinendo signa art. 4, insuper statuemus 
ddx 
a. 
dda; 
dà# 
dp 2 
dp. d q 
= a, 
~dcf 
= a 
ddy 
t, 
ddy 
- d\ 
ddr/ 
— d 
dp 2 
dp . d q 
d q 2 
ddz _ 
T- 
ddz 
= T» 
ddz 
= i 
dp 2 
dp .dq 
d q 2 
Praeterea brevitatis caussa faciemus 
h c' - 
ca 
ah' ■ 
-ch' = A 
-ac = B 
-ha: = C 
Primo observamus, haberi Adx-\-Bdy-{- Cdz — 0, sive dz = 
quatenus itaque z spectatur tamquam functio ipsarum x, y, fit 
— £dx — ~dy- 
dz 
dx 1 
ds 
— U 
d y 
A 
C 
B 
c 
Porro deducimus, ex d x = a dp -f- a!d q, dy — h dp -j- h'd q, 
Cdp = h'dx — àdy 
Cdq — —bdx-\~ady 
Hinc obtinemus differentialia completa ipsarum t, u 
c3di = (^a 
G : ‘du = (-Bj^— CA) [Vix—ddy) + — B~) (bix — ady) 
lam si in his formulis substituimus 
ai ?) 
,d C\ 
d A 
d p 
d A 
d q 
d B 
dp 
d B 
d? y 
^ = h' a-\~ad'—b a' — ad 
~ = h'a-\-ad"—h a"—ad' 
= cd -j- b y' — c d' — b'y 
— cd '-j- b y"— cd"— h'y 
= ciy-\-ccL—ay—ca 
f f i Jt it f r 
= ay ca —ay —ca