In the address which he had the honour of giving at the Annual Meeting of the Association the object of the writer was twofold: (1) to urge Secondary School teachers to study non-Euclidean Geometry for the purpose of improving their own scholarship; and (2) to sketch a method of approach to the subject which seems both interesting in itself and much easier than that usually adopted. In preparing this paper for the Gazptte he has thought it better to omit the former and to develop the latter a little more fully than time allowed at the meeting; the title has been modified accordingly.

My desire is to emphasize the importance and simplicity of the notion of “differentials” in introducing a student to the calculus. I find that pupils have but little difficulty in realizing the ideas connected with them, and that the notion of a differential coefficient as the ultimate value of the ratio of two connected differentials comes automatically.

To cut up an isosceles triangle so that the parts may be put together to form two triangles similar to the original triangle.

Let ABC be the triangle, having the angles at B and C equal, and let D be the middle point of the base. Draw a circle, passing through A, having its centre on AD, and cutting AB and AC in E and F. Join DE, cutting the circle in G.