MATHEMATICS 19 



been a more convenient one, since 12 can be divided 

 by 2, 3, 4, and 6, while ten can only be divided by 2 

 and 5. 



To express numbers duodecimally, i.e., when twelve is 

 taken as the radix, we require two more symbols to 

 express 10 and n respectively by single figures. If we 

 represent 10 by the symbol , and n by o, then, of 

 course, groups of twelve will need to be represented by 

 two figures, and groups of twelve times twelve by three 

 figures groups of twelve always taking the place of the 

 groups of ten in the ten radix system. They may be 

 expressed as follows. 



Numbers expressed in the Numbers expressed in the 

 radix of 10. radix of 12. 



9 9 



10 



11 e 



12 i 



13 II 



18 16 



19 17 



20 18 



21 19 



22 i 



23 ie 



24 20 



25 21 



60 c 



