%UJDkA'fURE of the CONIC SECTIONS, &c. 339 



Example I. The length of an arch of gc°, computed to 12 

 places of decimals, by means of the firft feries, (Art. 12.). 

 Here azz. 90 . 



tan 7 ' T a zz 0.0245486221089 



±: cot a zr o 



tan a 



tan ~ azz 1 



tan \ a = 0.4142135623731 



tan j a — 0.1989123673796 

 tan T V a = 0.0984914033571 

 tan T ' T a — 0.0491 268497694 



tan t4 t a •=. 0.012272462379. 



tan T j T a — 0.006136000157. 



tan T 4- T a — 0.003067971201. 

 tan T -V* a — 0.00153398194. . 

 tan -jo'tt a = 0.00076699054. . 



S < .0000001248357-1 

 S > .0000001 248356 j 



. ~ tan ~ a rr .500 000 000 000 o 



^ tan ^ = .103 553 390 593 3 



i tan i a — .024 864 045 922 5 



T * r tan T V a = .006 155 712 709 S 



T ' T tan ^ = .001535 214 055 3 



V4 tan <rV a = - 000 3 8 3 57 2 220 5 



T ^ T tan r 4- F # = .000 095 878 612 3 



jIs- tan T | r ^ z= .000 023 968 750 6 



ttt tan 7tt * = '°°o 005 992 131 3 



ToV? tan to'tt a = * 000 001 498 029 3 



•2-V4-8- tan TT '4 ¥ # = .000 000 374 507 1 



Hence S =: .000 000 124 835 7 



- -.6366197723677 

 Arch of 90 , or a = 1.570 796 326 795 . 



Vol. VI. P. II. 



Uu 



Example 



