IV 



NOTE ON PROFESSOR BAIN S THEORY OF 

 EUCLID I. 4 1 



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. I 

 now venture to draw the attention of the Society to the 

 confirmation which I conceive that this argument derives 

 from the way in which Euc. I. 4 is treated by Professor 

 Bain in his recent Logic a book which, on the whole, 

 is based on Mr. Mill s principles, and which is mainly 

 original in an attempt, which I cannot regard as felicitous, 

 to bring these principles into closer contact with the 

 special sciences, especially with Physics and Mathematics. 

 It will be remembered that Mr. Mill, undertaking to 

 demonstrate Euc. I. 5 from first principles, has to supply, 

 in the course of his proof, a demonstration of Euc. I. 4, 

 and it is in the attempt to give to this process the form of 



1 Communicated by Professor Tait to the Royal Society of Edin 

 burgh on June 6, 1870, and published in its Proceedings, vol. vii. 

 pp. 176-179. 



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