W. Brown 363 
Sample of analyses of above two Geometry questions. 
1. (a) (i) Recognition of necessity of generality in the proof. 
(ii) Memory of general truth that three angles of a triangle equal 
two right-angles, and application to this case. 
(iii) Principle of " proof by superposition " : memory, sufficient under- 
standing, and application of it to case under consideration. 
(b) (iv) Power of recognising general relations in a particular case. 
(v) Readiness to note and make use of the more special relations 
obtaining in the particular case. 
4. (a) (i) Rational or merely visual memory of construction. 
(ii) Connecting equality of lines with equality of triangles, of which 
the lines are sides. 
(iii) Memory of result of a particular theorem (on right-angled triangles). 
(b)- (iv) Power of keeping essential and general relation of above theorem in 
mind, and of looking at the present case through the medium of it. 
(v) Memory of theorem on angle in a semi-circle. 
(vi) Power of seeing that the relation is a general one (i.e. power of 
noting from just what facts or relations the conclusion follows, and of 
realising that the sequence is not influenced by other facts). 
