310 REASONING. 



serve as representatives of all which resemble them ; 

 and in the present case the conditions which qualify a 

 real object to be the representative of its class, are 

 completely fulfilled by an object existing only in our 

 fancy. Without denying, therefore, the possibility of 

 satisfying ourselves that two straight lines cannot 

 inclose a space, by merely thinking of straight lines 

 without actually looking at them ; I contend, that we 

 do not believe this truth on the ground of the imagi- 

 nary intuition simply, but because we know that the 

 imaginary lines exactly resemble real ones, and that 

 we may conclude from them to real ones with quite as 

 much certainty as we could conclude from one real 

 line to another. The conclusion, therefore, is still an 

 induction from observation. And we should not be 

 authorized to substitute observation of the image in 

 our mind, for observation of the reality, if we had not 

 learnt by long continued experience that all the pro- 

 perties of the reality are faithfully represented in the 

 image ; just as we should be scientifically warranted 

 in describing the shape and colour of an animal which 

 we had never seen, from a photogenic picture made of 

 it with a daguerreotype ; but not until we had learnt 

 by ample experience, that observation of such a 

 picture is precisely equivalent to observation of the 

 original. 



These considerations also remo\ 7 e the objection 

 arising from the impossibility of ocularly following 

 the lines in their prolongation to infinity. For though, 

 in order actually to see that two given lines never 

 meet, it would be necessary to follow them to infinity; 

 yet without doing so we may know that if they ever 

 do meet, or indeed if, after diverging from one ano- 

 ther, they begin again to approach, this must take 

 place not at an infinite, but at a finite distance. Sup- 



