QUADRATURE of the CONIC SECTIONS, &c. 341 



Example III. The length of an arch of 90 , calculated 

 from the fourth feries, (Art. 28.). 



cof a zz o cof 7 a — 0.980 785 280. . , . 



cof-jtf — 0.707 106 781 186 5 cof T V^ — 0.995 184 7 



cof^=: 0.923 879 532 51. . cof T ' T rf 3 0.998 80 



1 12 — cof a + 1 2 cof 7 a , rt 



— Z* -^-i c — r » = - l6 3 °53 9 02 0I ° 8 



3-io 3 + coftf — 4cofi^ j jo > 



■q-q- = - 001 2I 5 2 77 777 8 



8.8.9.10 J " /// 



Amount of pofitive terms, .164 269 179 788 6 



1 13 — cof 7 a — 12 cof 7 a 



J^S 3 +cof7tf-f- 4 cof 7 * = - 000 OI 3 26r 796 5 



T 13 Cof 7 tf 12 Cof 7 tf 



F? ~ :£ — l 77 ; r 1 — 'O 00 °°0 T08 7Q4 2 



3.16+ 3 -}- cof 7 a -f- 4 cof -j « ~ * /y^* 



1 13 — cof 7 a — i2cof T V^ 



/- - il — ; f7 ; r ■ = • 00 ° °°° °°3 074 4- 



3.163 3 + COf 7 * + 4 C °f T» « ' * 



I 13 — cof -V a — 12 cof t 't a 



2f 6 , r ■ i r , = «ooo 000 000 047 8 



3. 16 6 3 + cof T V a -f- 4 cof T ' T a *' 



Each of the remaining terms, being near-] 



ly 7 ' ? th of the term before it, their fum > .ood 000 000 000 8 

 will be nearly y T of the laft term, or J 



Amount of negative terms, .000 013 463 713 7 



Difference between the pofitive? _i_ __ — ■ 



and negative terms, or 3 JJ — * l6 4 255 716 074 9 



1 



- = .405 284 734 5 6 9 3 



- = .636619772 3676 



a 



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

 Uu 2 Example 



