62 SCIENCE ABSOLUTE OF SPACE. 



"the length of the straight line is called the 

 distance between two points." If the length 

 of the one straight line between two points is 

 the distance between those points, how can the 

 straight line itself be the shortest distance? 

 If there is only one distance, it is the longest 

 as much as the shortest distance, and if it is 

 the length of this shorto-longest distance 

 which is the distance then it is not the 

 straight line itself which is the longo-shortest 

 distance. But Wentworth also says: "Of all 

 lines joining two points the shortest is the 

 straight line." 



This general comparison involves the meas- 

 urement of curves, which involves the theory 

 of limits, to say nothing of ratio. The very 

 ascription of length to a curve involves the 

 idea of a limit. And then to introduce this 

 general axiom, as does Wentworth, only to 

 prove a very special case of itself, that two 

 sides of a triangle are together greater than 

 the third, is surely bad logic, bad pedagogy, 

 bad mathematics. 



This latter theorem, according to the first 

 of Pascal's rules for demonstrations, should 

 not be proved at all, since every dog knows it. 

 But to this objection, as old as the sophists, 

 Simson long ago answered for the science of 



