I should have to quote very largely indeed if I wished to draw attention to every hazardous statement which has been advanced; I must therefore severely restrain myself. Consider the following: 'Unquestionably the best teachers depart largely from his words, and even from his methods. That is, they use the work of Euclid, but they would teach better without it. And this is especially true of the application to problems. Everybody recollects, even if he have not the daily experience, how unavailable for problems a boy's knowledge of Euclid generally is.' The value of such a statement depends entirely on the range of the experience from which it has been derived. Suppose for instance that the writer had been for many years an examiner in a large University in which against each candidate's name the school was recorded from which he came; suppose that the writer had also been much engaged in the numerous examinations connected with the military institutions; suppose that he had also been for a quarter of a century in residence at one of the largest colleges at Cambridge, and actively employed in the tuition; suppose also that it had been his duty to classify the new students for lecture purposes by examining them in Euclid and other parts of elementary mathematics; and finally suppose that he was in constant communication with the teachers in many of the large schools: then his opinion would have enjoyed an authority which in the absence of these circumstances cannot be claimed for it.
If I may venture to refer to my own experience, which I fear commenced when the writer whom I have just quoted was in his cradle, I may say that I have taught geometry both Euclidean and non-Euclidean, that my own early studies and prepossessions were towards the latter, but that my testimony would now be entirely in favour of the former.
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I admit that to teach Euclid requires patience both from the tutor and the pupil; but I can affirm that I have known many teachers who have succeeded admirably, and have sent a large
