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certainly pertained to the modern method ; but it seemed to him that all 

 Mr. Brent's demonstrations were assumptions, and he did not see what 

 intellectual advantage could be gained from such demonstrations. An 

 acute reasoner might find flaws in Euclid's definitions, but the results 

 were marvellous, and the fact that all our geometry had grown out of 

 Euclid's plane geometry, was one reason why we shoiald revere him. 



Mr. Hawthorne wished to explain that so far from thinking that a 

 divorce should take place between the modern method and " Euclid," 

 they should be united, and that the modern methods, up to a certain 

 point, were the very best preparation for " Euclid." 



Mr. Brent also explained that he did not advocate the abandonment 

 of "Euclid," but the use of the modern methods for elementary teaching. 



Mr. Bathgate thought it a mistake to teach children abstract 

 mathematics first. Practical matheraatics should precede instruction in 

 abstract principles. 



Mr. J. S. Webb said those gentlemen who had spoken against the 

 modern method had argued as though it entirely depended on what you 

 could see with the eye, and what had been called sensuous notions had 

 been alleged in proof of its deficiencies. But Mr. Brent had accom- 

 panied each proposition by new definitions from which flowed the resvilts 

 shown. The great fault in the old mode of teaching mathematics was, 

 that the pupils were kept so long in the elements, that they became 

 disgusted, and were deterred from entering on the higher branches. 



The Chairman said although it was true there were no royal roads to 

 learning, the moderns knew many shorter roads than the ancients did, 

 and if modern geometry would shorten a boy's education in mathematics 

 it would be a vast improvement. 



Mr. Cargill said that although a sufficient knowledge of mathematics 

 for practical use might be given by that sort of jDrocess which allowed 

 demonstrations to be made with a piece of chalk on a board, yet the 

 object in studying "Euclid" was not to give a practical knowledge of 

 mathematics so much as a healthful exercise to the mind, correct methods 

 of thought, and to lay the foundations in the mind of logical reasoning 

 of the purest kind. For this purpose, the old system of strictly following 

 argument was much to be preferred. As to the difficulty of teaching 

 boys mathematics, in his days there was no such difficulty ; and a boy's 

 power of comprehending mathematics seemed to depend upon natural 

 ability. 



2. " On the Moon and the Weather," by J. S. Webb. After 

 pointing out that observations made by the Earl of Rosse confirm 



