THE UTILITY OF SCIENCE 231 



"Monge was bora the son of a French pedlar 

 about 1750. The construction of a plan he made 

 of his native town brought the boy under the 

 notice of a colonel of Engineers, who got him 

 admitted to one of the military schools. His 

 humble birth precluded him from receiving a 

 commission in the Army, but he was taught 

 surveying and drawing; though he was told he 

 was not sufficiently well born to be allowed to 

 attempt problems which required mathematical 

 calculations. At last his opportunity came. He 

 observed that all the plans of fortifications were 

 constructed by long and tedious arithmetical 

 calculations from the original observed measure- 

 ments. Monge substituted for these a geomet- 

 rical process he had invented which produced 

 the plan so quickly that the officer in charge re- 

 fused to receive it, because professional etiquette 

 required that no less than a certain time should 

 be spent over making these drawings. When 

 once examined, its obvious superiority was recog- 

 nized. This geometrical process discovered by 

 Monge was nothing less than a new branch of 

 geometry known to students of engineering as 

 practical solid geometry a science in which, by 

 the now familiar method of plan and elevation, 

 a solid object can be represented adequately 

 by construction on a plane a method whose 

 practical, or, let me say, occupational, value 



