QUADRATURE of the CONIC SECTIONS, &c. 343 



Example V. Napier's logarithm of 10, calculated by the 

 third feries for logarithms. (See Art. 64.). 



x = 10, X — 5.05 X /y " = 1. 0417078207. . . 

 X' =1.739252713093. X IV = 1.01037315... . . 

 X" = 1.17031036761. . X y = 1.0025899 



^ ( 6' ( trJ l) --°35B I77I o 7r4 8 



1 X+I2X'— 13 



Z", v , vT-; = .OOI 121 003 A2I 4 



3.16' X + 4X+3 ««■ .* 



1 X+12X* — 13 

 &iP X + 4X- + 3 = • 00002 4°4i 122 9 



1 X"+i2X"— 13 

 3 Ti6^ y + 4X*+3 = • 000000 4°9 2394 



I X"-f-I2X IV — 12 , 



TaI y^j.,y.v.. = -°°° 00 ° oo6 535 7 



3.163 X^ + 4 X IV + 3 



I X IV +I2X V -I2 

 Z? Yiv I , W 1 = - 000 °°° ° 00 I02 7 



3.10^ X lv + 4X v +3 ' 



.' T of laft term = fum of the re- 1 , 



y . . . J- .000 000 000 001 6 



maining terms nearly, J 



From fum of pofitive terms, = .036 963 261 138 5 



• Subtrad — - — = .001 388 888 888 o 

 8.9.10 * 



There remains ,4 jq = .0355743722496 



-_! — = .188 611 697 on 2 

 log 4 10 yt ° 



=-1— =.434294481903 . 

 log 10 



Example 



