282 NEW SERIES for the 
fhall have 
I 2 
| z += 
tan’ a 3 
B spices I ie | 
== — (7 tan’ 5 eats fant?= pat pen gars, ~ tan ety FP 
7 16 
| 4.) 
and “a may be confidered as a ‘Reond formula for the reétifi- 
eation of any arch of a circle; for the procefs by which an 
arch is found from the fquare of its reciprocal is fo fimple, 
that the latter being known, the former may alo be regarded 
as known. 
16. InstEAD of exprefling the fquare of the reciprocal of 
the arch in this manner, by the fquares of the tangents of its 
fub-multiples, we may exprefs it otherwife by the {quares of 
& 
their fecants. For fince tan’ <a = fect a—r1, and tan*la@ 
2 4 
— {ec 1 a— 1, and fo on, therefore the feries ° 
4 a a 
x I I 
— tan? sats . tan’ plasshi “ tan’ 5 a+ — tant + a4, &e. 
4+ 16 
is Sc Hs to 
I I I I Te aoe 
= fec? —a+ = fec” = 2+ — fec’ = 
4 2 4 4 4 8 
I AE 
a+ poe maa oot &c. 
I Oo I T 
a oc atm cat! ak 
But the latter part of this expreflion is evidently an infinite 
geometrical 
