2UADRATURE of ihe CONIC SECTIONS, &. 339 
Exampte I. The length of an arch of 90°, computed to 12 
places of decimals, by means of the firft feries, (Art. 12.). 
Here a= 90°. 
I 
——_ = cota—=o tan > 
tana ta 
tanta=TI tan iy 
tan 4 4 = 0.414213562373r tanzts 
tan 3 a= 0.1989123673796 tan =+> 
a= 
a 
a= 
a= 0.024.5486221089 
= 0.012272462379. 
= 0.0061 36000157. 
= 0.003067971201. 
tan 7's 4@= 0.0984914033571 = tan -75z @ = 0,001533981094.. 
tan 3; 4= 0.0491268497694. tan >'75 4 = 0.00076699054.. 
ae 
—_——==_e==== 
3 tan a= .500 000000 c00 0 
4 tan | 4 = .103 553 390 593 3 
“y tan ¢ 4 = .024 864 045 9225 
‘jf -tan sa 
.006 155 712 7098 
zz tan zy 4 = 001 §35 214 056 3 
S < 0000001248357 
S > .cocococor iy 
q 4 = .000 383 572 2205 
= .000 095 878 612 3 
= -000 023 968 7506 
= -000 005 992 131 3 
= -000 001 498 029 3 
= +900 000 374 507 1 
Hence S = .000 000 124 8365 vf 
ee 
a — 036 619 772 367 7 
Arch of 90°, OF 4= 1.570 796 326 795. 
Vou. VI. P. Il. Uu 
EXAMPLE 
