SCIENCE ABSOLUTE OP SPACE. 71 



AE, viz., BE, revolves into the position BF, 

 another little bit of it, viz., AG, revolves, 

 through an equal angle, into the position AH; 

 and that, while CF revolves into the position 

 of lying along CD, AH revolves and here 

 comes the fallacy. 



"You must not say * revolves, through an 

 equal angle, into the position of lying along 

 AD, ' for this would be to make AH fulfill two 

 conditions at once. 



' ' If you say that the one condition involves 

 the other, you are virtually asserting that the 

 lines CF, AH are equally inclined to CD and 

 this in consequence of AH having been so 

 drawn that these same lines are equally in- 

 clined to AE. 



"That is, you are asserting, 'A pair of lines 

 which are equally inclined to a certain trans- 

 versal, are so to any transversal. ' [Deducible 

 fromEuc. I, 27, 28, 29.]" 





