SCIENCE ABSOLUTE OP SPACE. 69 



true in theirs. It has been shown that, as a 

 general proposition, the connexion between a 

 line returning to its place and the exterior 

 angles having been equal to four right angles, 

 is a non sequitur ; that it is a thing that may 

 be or may not be; that the notion that it re- 

 turns to its place because the exterior angles 

 have been equal to four right angles, is a mis- 

 take. From which it is a legitimate conclu- 

 sion, that if it had pleased nature to make the 

 exterior angles of a triangle greater or less 

 than four right angles, this would not have 

 created the smallest impediment to the line's 

 returning to its old situation after being car- 

 ried round the sides; and consequently the 

 line's returning is no evidence of the angles 

 not being greater or less than four right 

 angles." 



Charles L. Dodgson, of Christ Church, Ox- 

 ford, in his " Curiosa Mathematica," Part I, 

 pp. 70-71, 3d Ed., 1890, says: 



"Yet another process has been invented 

 quite fascinating in its brevity and its ele- 

 gance which, though involving the same fal- 

 lacy as the Direction-Theory, proves Euc. I, 

 32, without even mentioning the dangerous 

 word 'Direction.' 



