C is] 
befides thefe, the fuperficies- is given likewife, it will 
— z 
then be — i y j\ + ^ 
w X X 
hy'^ — o. 
e y X 
-\-yy 
Thus, in like manner, by alhiming m = — and 
e X 
y ^ X 
« = 4, we have 77 ^ ---= r=. + ^ + 
V XX j >> y 
Fv+ 
“h jy jp 
= + = O) for the general equa- 
fy + w- . :-7 ' . : 
V XX-\- y y 
tion of the curve of the fwifteft defcent : which, 
when efj gy and hy arei all of them taken equal to 
y 
nothing, will become ~ 77~'. ■ = + d ; which is the 
X X — y y 
cafe, confidered by fo many Others,, anfwering to the 
cycloid. When the length of the arch defcribed in 
the whole defcent (as well a& the values of x and y) 
is given, the equation will then be "T= 
X X 
+ yy 
+ d + 
e X 
V XX-]- yy 
: =: a, o r e 
— y * 1 * X X^ = d‘ 
X xx-{- y y. And thus may the relation of x and y 
be determined, in other cifes, and that under any 
number of reftridionSr 
Hi, 
