Every reader may now see in what way the higher branches of mathematics 

 are concerned in our present subject. They are the abbreviators of long and 

 tedious operations, and it would be perfectly possible, with sufficient time and 

 industry, to do without their use When both the ordinary and the mathe- 

 matical result are derived from the same hypothesis, the latter must be the more 

 correct : and in those numerous cases in which the difficulty lies in reducing the 

 original circumstances to a mathematical form, there is nothing to show that we 

 are less liable to error in deducing a common sense result from principles too 

 indefinite for calculation, than we should be in attempting to define more closely, 

 and to apply numerical reasoning. — De Morgan. 



