THE GENESIS OF LOGARITHMS 159 



This table is readily formed by subtracting "from radius 

 with seven cyphers added ... its 10,000,000th part and from 

 the number thence arising its io,ooo,oooth part and so on." 1 

 A specimen of part of the First Table, showing its construction, 

 is given in the accompanying figure. 



First Table 



( 1 ) 1 0000000 ' 0000000 



1 ' 0000000 



(2) 9999999" 0000000 

 '9999999 



(3) 9999998*000000 1 

 "9999998 



(4) 9999997 '0000003 

 '9999997 



(5) 9999996*0000006 



and so on, up to the iooth term, which is 

 (100) 9999900*0004950 



The Second Table is a geometrical progression of fifty 

 terms, radius (with six cyphers added) forming the first term, 

 the numbers being in the continued proportion of the first 

 term to the last term in the First Table; that is, in the pro- 

 portion of 100,000 to 99,999. This table again may be formed 

 " with sufficient exactness by adding six cyphers to radius and 

 continually subtracting from radius its 100,000th part in the 

 manner shown." 2 



Second Table 



( 1 ) 1 0000000 "oooooo 

 1 00 '000000 



(2) 9999900*000000 



99*999000 



(3) 9999800*001000 



99*998000 



(4) 9999700*003000 



99*997000 



(5) 9999600*006000 



and so on, up to the 50th term, which is 

 (S°) 9995001 '222927 s 



The Third Table is much more extensive, consisting of 

 sixty-nine columns, each column containing twenty-one terms. 



1 Construction Prop. XVI. 2 Ibid. Prop. XVII. 



3 This number is erroneous {Vide Note B, Appendix). 



