thing; therefore v 
[ 5 * ] 
- V a =- 
V 2 Px 2 
2 M L a* 
v- 
V z P. 
2 M L a' 
But, by the Contention, 
2 M L a 
P 
fore, v 2 = V 2 — 
V* -2 
* 9 or, v 2 
/^ 2 x 
or t/-j = 
F 2 ; there- 
R 2 —x 2 i 
~RT v ' " P 2 
and, when x becomes equal to /, and o to-y, v 2 = 
yi x and, by t he Property of the Circle, 
R 
y 2 — / 2 being equal to B F 2 , V 2 — V 2 x 
V — FY- £ , 
B F 2 
R 2 * ° r 
E- c D. i 
2 . We have above, "£ZJL ; and u 2 — V 
2a v 
R ‘ K ** s or, u —Vx)L!iL — — :Therefore, i == Tr x _ x 
* R or, r = — x R * 
2 
VX'/R* — x 2 ' ' 2a j R 2 — x 2 
Now let CF), jF/£. 5- be equal to at; and draw the 
Co-fine D E , the Radius C E , and the Perpendicular 
ed—x : Then will the Triangle DEC be fimilar 
to the nafcent Triangle deEb and confequently, 
*D E : de C E : e E — - DE ==.-^====z. 
T G E 
Therefore, T * = — -x^F, and t = T x — And 
2 <7 2a, 
when ^ becomes equal to C B , and t to z 1 , the Arch 
G F becomes equal to the Arch G F : Therefore t = 
r*f£ g.E. v.zo, 
Scholium 
