THE COMPOSITION OF MIND 



chical process by the manifold compounding of 

 which is built up this highly complex series of 

 inferences ? 



From beginning to end, the fundamental pro- 

 cess is the cognition of the equality of sundry 

 relations. The thought which underlies and de- 

 termines the whole calculation is the cognition 

 that the relations between the sides and angles 

 of a great triangle, having for its apex the moon, 

 and for its base the chord of the arc of the 

 meridian of London measured to a point in the 

 southern hemisphere upon the same parallel 

 with Cape Town, are equal to the relations be- 

 tween the sides and angles of a similar small tri- 

 angle, having an inaccessible tower for its apex 

 and a measured line of five or six rods for its 

 base ; and that these relations, in turn, are equal 

 to the relations between the sides and angles of 

 a still smaller and similar triangle which may 

 be drawn on a sheet of paper, and of which the 

 sides and angles may, if necessary, be directly 

 measured. Now, this cognition implies the pre- 

 vious establishment, in the calculator's mind, of 

 sundry cognitions of the equalities and inequal- 

 ities of certain relations between the sides and 

 angles of triangles. To show briefly how such 

 cognitions have been established, let us cite the 

 simplest case — that in which the two angles at 

 the base of an isosceles triangle are recognized 

 as equal to each other. Euclid establishes this 



VOL. Ill 



145 



