70 SCIENCE ABSOLUTE OP SPACE. 



1 ' We are told to take 

 any triangle ABC; to 

 produce CA to D; to 

 make part of CD, viz., 

 AD, revolve, about A, 

 into the position ABE; 

 then to make part of this 

 line, viz., BE, revolve, 

 about B, into the position BCF; and lastly to 

 make part of this line, viz., CF, revolve, about 

 C, till it lies along CD, of which it originally 

 formed a part. We are then assured that it 

 must have revolved through four right angles: 

 from which it easily follows that the interior 

 angles of the triangle are together equal to 

 two right angles. 



' ' The disproof of this fallacy is almost as 

 brief and elegant as the fallacy itself. We 

 first quote the general principle that we can 

 not reasonably be told to make a line fulfill 

 two conditions, either of which is enough by 

 itself to fix its position: e. g., given three 

 points X, Y, Z, we can not reasonably be told 

 to draw a line from X which shall pass 

 through Y and Z: we can make it pass 

 through Y, but it must then take its chance 

 of passing through Z; and vice versa. 



"Now let us suppose that, while one part of 





