Show that the area of the infinitesimal triangle SQP of Figure 17.6 can be written as 1 2 (y dx - x dy).

17-8E
In the SQP triangle, the force F is proportional to QR and inversely proportional to the
square of the area of the infinitesimal triangle SQP. By standard techniques, that area is
given by
 
1
2
ydx xdy
. Because F is also inversely proportional to
2 2 2SP x y  , to get

 
 
2 2 2
2
Replace by
bd x x y
a b
x ydx xdy
 

…… (1)
To show that this expression is equivalent to the expression for r
a
in exercise 6, here
given that
0a  .
Now...