QUADRATURE of the CONIC SECTIONS, &c. 289 
Or, compute the feries of quantities ¢, 7’, ’, ¢’”, &c., one from 
another by means of the formulz 
I—cofa 
,_ VI+t—r1 Vrtis1 
ba, fe EY SS ce. 
1+ cofa’ Vat +a Vl tft 
Then will 
f r1+cofa 
. 4 1—cola te 
a Po A Posten Fete os E 
Un(Se+ hese te $¢T im tT 8), 
where T(m), T(m4x1), and S denote the fame as Before: 
I consipDER this fecond feries for the redtification of the 
circle (under either of its forms), as preferable to the other f{e- 
ries given at Article 12. for two reafons ; firft, becaufe of its 
greater rate of convergency, and, next, becaufe the quantities 
Ir a ee 
cofa, cof= 4, cof- 4, &c., alfo the quantities ¢, z’, 2”, &c. can 
2 4 
be deduced more eafily one from. another than the feries of 
I 
~a, &c. 
I I 
tangents tan 4, tan a 4, ir a, tan F 
1023. THatT, we may; inveftigate another’ feries, let us 
I I I 
eformiala, ————|== == _-_ tan = A: ¢ 
refume th m Gan sah S +A; the cubes 
of both fides of the equation being now taken, the refult. is 
eae a Oe 6 = 31 
‘tan? A 8tan3tA eee oA. Bene a} =tan 5A 
To 
