"The demand is unreasonable to throw aside Euclid in favour of any compendium however meagre and however unsound; and this is really the demand which is made: it will be time enough to consider about the discontinuance of Euclid when a better book is deliberately offered." It may be added that the superiority to Euclid must be established by indisputable evidence; not by the author's own estimation, the natural but partial testimony of parental fondness; not by the hasty prediction of some anonymous and irresponsible reviewer; not by the authority of eminent men, unless the eminence is founded on mathematical attainments; not even by the verdict of teachers who are not conspicuous for the success of their pupils. The decision must rest with students, teachers, and examiners, of considerable reputation in the range of the mathematical sciences.
It must be allowed that there is diversity of opinion among the opponents of Euclid, for while the majority seem to claim freedom in the use of any text-books they please, others rather advocate the construction and general adoption of a new text-book. The former class on the whole seem to want something easier and more popular than Euclid; among the latter class there are a few whose notion seems to be that the text-book should be more rigorous and more extensive than Euclid. There are various considerations which seem to me to indicate that if a change be made it will not be in the direction of greater rigour; the origin of the movement, the character of the text-books which have hitherto been issued, and the pressure of more modern and more attractive studies, combine to warn us that if the traditional authority which belongs to Euclid be abandoned geometry will be compelled to occupy a position in general education much inferior to that which it now holds.
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There is one very obvious mode of advancing the cause of the anti-Euclidean party, which I believe will do far more for them than the most confident assertions and predictions of the merits of the course which they advocate: let them train youths on their
