Mr. milner on the 
514 
fent the fine and cofine of the angle ctp to the radius 
unity. It is eafy to prove in his way that lxlmxmt 
+lxlmxmr is equal to 2 Lx nix nx lat-tat, and the 
fluent of l A d multiplied into the fluxion of the circular 
arc lx is eafily found in the following manner, without 
having recourfe to tables of fluents, or the methods of 
continuation. 
From a known analogy the fluxion of the arc la: is to 
the fluxion of its verfed fine as the radius 1 x of the fame 
circle to la: the right fine, la: multiplied into the fluxion 
of the verfed fine is the fluxion of the area of the femi- 
circle l /, and calling ix,y, the fluent of lx~ multiplied 
into the fluxion of the arc la* is evidently equal to 
T-, where a ftill reprefents the area of a circle whofe ra- 
dius is unity: Ay is equal to the femi-circumference ik 
and AjrxTAd is equal to the fluent of tat multiplied into 
the fame fluxion, and calling ta, v, and fubftituting for 
1 i its equal py , the fum of all the l x lm x mt + &c. in the 
annulus 1 i is equal to m np a xy 4 - This laft quan- 
tity multiplied into the fluxion of v, and the fluent taken 
by the common method when v is equal to tp or unity 
nearly, comes out - and twice this quantity gives the 
15 
fum of all the l x lm x mt, without the whole lphere p ap, 
and therefore the fpace deferibed by a particle of the equa- 
tor 
