SCIENCE ABSOLUTE OP SPACE. 63 



geometry, that the number of assumptions 

 ought not to be increased without necessity ; 

 or as Dedekind has it: &quot; Was beweisbar ist, 

 soil in der Wissenschaft nicht ohne Beweis 

 geglaubt werden&quot; 



Professor W. B. Smith (Ph. D., Goettingen), 

 has written: &quot; Nothing could be more unfor 

 tunate than the attempt to lay the notion of 

 Direction at the bottom of Geometry.&quot; 



Was it not this notion which led so good a 

 mathematician as John Casey to give as a 

 demonstration of a triangle s angle-sum the 

 procedure called &quot; a practical demonstration &quot; 

 on page 87 of Richardson s Euclid, and there 

 described as laying a straight edge along 

 one of the sides of the figure, and then turn 

 ing it round so as to coincide with each side in 

 turn.&quot; 



This assumes that a segment of a straight 

 line, a sect, may be translated without rota 

 tion, which assumption readily comes to view 

 when you try the procedure in two-dimensional 

 spherics. Though this fallacy was exposed by 

 so eminent a geometer as Olaus Henrici in so 

 public a place as the pages of Nature, yet it 

 has just been solemnly reproduced by Pro 

 fessor G. C. Edwards, of the University of 

 California, in his Elements of Geometry: Mac- 



