honours at the University … will gain much through economy of time and the advantage of modern lights."
The final result is this; according to the promises of the geometrical reformers, one of their pupils might sacrifice five marks out of a thousand, while for all the remaining 995 his chance would be superior to that of a Euclid-trained student. It may be added that in future the Cambridge Mathematical Examinations are to be rather longer than they have been up to the date of my writing; so that the advantage of the anti-Euclidean school will be increased. Moreover we must remember that in the Smith's Prizes Examination the elementary geometry of Euclid scarcely appears, so that the modern reformers would not have here any obstacle to the triumphant vindication of their superiority as teachers of the higher mathematics. The marvellous thing is that in these days of competition for educacational prizes those who believe themselves to possess such a vast superiority of methods do not keep the secret to themselves, instead of offering it to all, and pressing it on the reluctant and incredulous. Surely instead of mere assertion of the benefits to be secured by the modern treatment, it will be far more dignified and far more conclusive to demonstrate the proposition by brilliant success in the Cambridge Mathematical Tripos. Suppose we were to read in the ordinary channels of information some such notice as this next January: "The first six wranglers are considered to owe much of their success to the fact that in their training the fossil geometry of Alexandria was thrown aside and recent specimens substituted;" then opposition would be vanquished, and teachers would wonder, praise, and imitate. But until the promises of success are followed by a performance as yet never witnessed we are reminded of the case of a bald hairdresser who presses on his customers his infallible specific for producing redundant locks.
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To those who object to Euclid as an inadequate course of plane geometry it may then be replied briefly that it is easy,
