3. Note on Professor Bain's Theory of Euclid I. 4

Extract

In a paper communicated to this Society last session, I pointed out that the proof of Euc. I. 5, given by Mr Mill, is unsound; endeavouring, at the same time, to show that this is no mere accident, but that it is impossible to give a mathematically correct analysis of the processes of Synthetic Geometry on any theory that holds figures to be merely illustrative, and does not admit that intuition in the Kantian sense—i.e., actual looking at a single engraved or imaginary figure—may be a necessary and sufficient step in a demonstration perfectly general.