SCIENCE ABSOLUTE OP SPACE. 67 



circle on the sphere, all these conditions are 

 again satisfied. 



4 * The reasoning employed must therefore 

 be fallacious, and the error lies in the words 

 printed in italics; for these words contain an 

 assumption which has not been proved. 



"O. HENRICI." 



Perronet Thompson, of Queen's College, 

 Cambridge, in a book of which the third edi- 

 tion is dated 1830, says: 



'''Professor Playfair, in the Notes to his 

 'Elements of Geometry' [1813], has proposed 

 another demonstration, founded on a remark- 

 able non causa pro causa. 



"It purports to collect the fact [Eu. I., 32, 

 Cor., 2] that (on the sides being successively 

 prolonged to the same hand) the exterior 

 angles of a rectilinear triangle are together 

 equal to four right angles, from the circum- 

 stance that a straight line carried round the 

 perimeter of a triangle by being applied to all 

 the sides in succession, is brought into its old 

 situation again; the argument being, that be- 

 cause this line has made the sort of somerset 

 it would do by being turned through four 

 right angles about a fixed point, the exterior 



