A TREATISE ON ARITHMETIC. 179 



one to the treatment of each of the four subjects of calcu- 

 lation by the next of the seven operations, aggregation 

 or addition ; the four next are occupied, of course, by de- 

 traction or subtraction; the four next by multiplication; 

 and the next four by division, as applied to integers, 

 surds, fractions, and denominations. The four next 

 chapters treat of the extraction of roots; and the next 

 four of progression. The seven elementary operations of 

 arithmetic are thus discussed in thirty chapters. The 

 thirty-first chapter treats of the application of the seven 

 operations to calculations in which there are combined 

 both integers and fractions; the succeeding chapters treat 

 in the same way successively of the seven operations as 

 applied to combinations of integers and surds, integers 

 and denominations, fractions^and denominations, fractions 

 and surds, surds and denominations. The thirty-seventh 

 chapter treats of the seven operations as applied to pro- 

 portion, and of the logical difference between multiplica- 

 tion and division on the one side, and aggregation and 

 detraction on the other. The thirty-eighth chapter dis- 

 cusses astronomical operations ; the next, multiplication by 

 memory; the next is a clever dissertation on the kalends, 

 nones, ides, cycles, golden numbers, epact, dominical 

 letter, places of the sun and moon and moveable feasts, 

 with rules for easy mental calculation of most questions 

 arising out of details of the almanac. The forty-first 



N2 



