THE FOURTH DIMENSION 119 



= x> therefore, God exists ; reply ! " Diderot, to 



n 



whom algebra was Hebrew, was embarrassed and discon- 

 certed, while peals of laughter rose on all sides. He asked 

 permission to return to France at once, which was granted. 

 Even such a mind as that of Buckle, who was generally 

 acknowledged to be a keen-sighted thinker, could not form 

 any idea of a geometrical line that is, of a line without 

 breadth or thickness, a conception which has been grasped 

 clearly and accurately by thousands of school-boys. He 

 therefore asserts, positively, that there are no lines without 

 breadth, and comes to the following extraordinary conclu- 

 sions : 



" Since, however, the breadth of the faintest line is so 

 slight as to be incapable of measurement, except by an 

 instrument under the microscope, it follows that the as- 

 sumption that there can be lines without breadth is so 

 nearly true that our senses, when unassisted by art, can 

 not detect the error. Formerly, and until the invention of 

 the micrometer, in the seventeenth century, it was im- 

 possible to detect it at all. Hence, the conclusions of the 

 geometrician approximate so closely to truth that we are 

 justified in accepting them as true. The flaw is too minute 

 to be perceived. But that there is a flaw appears to me 

 certain. It appears certain that, whenever something is 

 kept back in the premises, something must be wanting 

 in the conclusion. In all such cases, the field of inquiry 

 has not been entirely covered; and part of the preliminary 

 facts being suppressed, it must, I think, be admitted that 

 complete truth be unattainable, and that no problem in 

 geometry has been exhaustively solved." 1 



The fallacy which underlies Mr. Buckle's contention is 

 thus clearly exposed by the author of "The Natural His- 

 tory of Hell." 



1 * History of Civilization in England." American edition, VoL 

 II, page 342. 



