Length mid Space. 73 



of confounding those two objects. But it is not enough 

 to perceive this difference. We wish to communicate our 

 perceptions to others witii whom we have already conversed 

 on other subjects. We wish to tell some other persons 

 which object it is wc perceive, or which description of 

 objects. For this purpose wc apply the word straight to 

 the one, and the word round to the other. When still 

 greater precision of language was required, all lines which 

 are not straight were called curves, and the word roimd 

 appropriated to circular botlies, or circular lines. 



Mathematicians have been at vast pains to discover an 

 appropriate and logical definition of the word straight, 

 but hitherto with very little success. Whether a logical 

 definition of it may be obtained, 1 shall enquire afterwards. 

 What 1 mean to state at present is, that mankind in 

 general, learn the meaning of this term solely from exem- 

 plification* We teach children the distinction, by placing 

 a straight and a curve object before them, and telling 

 them that the one is named the one way, and the other the 

 other way. It is certain that they all learn the distinction 

 very (juickly in this way, and understand very clearly what 

 is meant by these two words. But if they were left to be 

 taught the distinction by logical definition, millions must 

 certainly remain for ever ignorant of it ; and it is extremely 

 doubtful, whether any could, ever by this means, become 

 ac(|uaintcd with it. 



14. — The science of geometry is founded on our know- 

 ledge of lineit. Before men can study geometry, they must 

 be agreed about the meaning of certain tirms xvhich lie nt 

 the foundation of that science, but which Ao not admit of 

 any logical definition. The following appear to be the 

 principal terms used in geometry, which fall luider this 



K 



