Page:Carroll - Euclid and His Modern Rivals.djvu/266

228 issued throughout England in a single year, including those proposed at the Universities and the Colleges, and those set at the Military Examinations, the Civil Service Examinations, and the so-called Local Examinations. I say then, without fear of contradiction, that the original problems and examples contained in these papers will for interest, variety, and ingenuity surpass any similar set that could be found in any country of the world. Then any person practically conversant with teaching and examining can judge whether the teaching is likely to be the worst where the examining is the most excellent.

The sentence quoted from MM. Demogeot and Montucci, in order to have any value, ought to have proceeded from writers more nearly on a level with the distinguished mathematical teachers in England. So far as any foundation can be assigned for this statement, it will probably apply not to mathematics especially but to all our studies, and amount to this, that our incessant examinations lead to an over cultivation of the memory. Then as to the practical bearing of the remark on our present subject it is obvious that the charge, if true, is quite independent of the text-book used for instruction, and might remain equally valid if Euclid were exchanged for any modern author.

The French gentlemen further on contrast what they call Euclid's verbiage with the elegant conciseness of the French methods. It is surely more than an answer to these writers to oppose the high opinion of the merits of Euclid expressed by mathematicians of European fame like Duhamel and Hoüel. See the First Report of the Association for the Improvement of Geometrical Teaching, p. 10.

When we compare the lustre of the mathematical reputation of these latter names with the obscurity of the two former, it seems that there is a great want of accuracy in the statement made in a recent circular: 'The opinion of French mathematicians on this question, is plainly expressed in the Report of MM. Demogeot and Montucci…'