The Mathematical Gazette, Volume 3Bell and Hyman, 1907 - Mathematics |
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12 Gloucester Terrace Algebra analysis analytical angle applications Arithmetic BELL & SONS boys C. S. JACKSON Calculus Cambridge chapter circle conic convergent corresponding cosine course cubic curve D.Sc definition differential equations E. T. WHITTAKER elementary mathematics elements Euclid examination examples F. S. MACAULAY finite formula fraction functions G. B. HALSTED G. H. HARDY Gauthier-Villars Geometry GEORGE BELL give given Göschen graphical Greek H. W. LLOYD-TANNER HAROLD HILTON idea infinite integral interesting introduced limit LINCOLN'S INN London Marling Endowed School Math Mathematical Association Mathematical Gazette Mechanics Messenger of Mathematics methods obtained papers PENDLEBURY perpendicular plane PORTUGAL STREET positive practical principle problems Prof Professor projection proof prove Quaternions question R. F. DAVIS solution straight line student surfaces tangents teachers teaching Teubner text-books theorem theory tion treatise triangle Trigonometry volume W. J. GREENSTREET
Popular passages
Page 16 - A. A very large room for calculating Greatest Common Measure. To this a small one might be attached for Least Common Multiple: this, however, might be dispensed with. B. A piece of open ground for keeping Roots and practising their extraction: it would be advisable to keep Square Roots by themselves, as their corners are apt to damage others. C. A room for reducing Fractions to their Lowest Terms. This should be provided with a cellar for keeping the Lowest Terms when found, which might also be available...
Page 17 - continually producing the Lines," may require centuries or more : but such a period, though long in the life of an individual, is as nothing in the life of the University.
Page 20 - Egypt' that, unsought and unsolicited, like a ray of light, silently stole into my mind the idea (simple, but previously unperceived) of the equivalence of the Sturmian residues to the denominator series formed by the reverse convergents. The idea was just what was wanting, — the key-note to the due and perfect evolution of the theory. Postscript. Immediately after leaving the foregoing matter in the hands of the printer, a most simple and complete proof has occurred to me of the theorem left undemonstrated...
Page 170 - This definition, almost unanimously abandoned, represents one of the most remarkable examples of the persistence with which an absurdity can propagate itself throughout the centuries. " In the first place, the idea expressed is incomprehensible to beginners, since it presupposes the notion of the length of a curve; and further, it is a vicious circle, since the length of a curve can only be understood as the limit of a sum of rectilinear lengths; moreover, it is not a definition at all, since, on...
Page 72 - ... of imaginaries in geometry, and from 1870 he was in possession of the directing ideas of his whole career. I had at this epoch the pleasure of seeing him often, of entertaining him at Paris, where he had come with his friend F. Klein. A course by M. Sylow followed by Lie had revealed to him all the importance of the theory of substitutions; the two friends studied this theory in the great treatise of C. Jordan; they were fully conscio'us of the important role it was called on to play in so many...
Page 172 - The foundation of all proof by Euclid's method consists in establishing the congruence of lines, angles, plane figures, solids, &c. To make the congruence evident, the geometrical figures are supposed to be applied to one another, of course without changing their form and dimensions.
Page 6 - That, with the object of diminishing the multiplicity of examinations affecting secondary schools, and of providing a test of adequate general education which may be widely accepted, a general system of school certificates is desirable. The well-known term ' Leaving Certificate ' has been purposely avoided because it is to some extent misleading and is not unfrequently misunderstood. (2) That it is not desirable that examinations for such certificates should be conducted by means of papers set for...
Page 52 - This has already been comprehended in many countries, and notably in Italy, where the great geometer Cremona did not disdain to write for the schools an elementary treatise on projective geometry. IX In the preceding articles, we have essayed to follow and bring out clearly the most remote consequences of the methods of Monge and Poncelet. In creating tangential coordinates and homogeneous coordinates, Pluecker seemed to have exhausted...
Page 53 - ... discovery, of which we shall speak further on, has already connected the geometry of spheres with that of straight lines and permits the introduction of the notion of coordinates of a sphere. The theory of systems of circles is already commenced; it will be developed without doubt when one wishes to study the representation, which we owe to Laguerre, of an imaginary point in space by an oriented circle. But before expounding the development of these new ideas which have vivified the infinitesimal...
Page 92 - The metric system and the use of decimals in approximative calculation, with contracted methods, will be specially insisted upon. Neither the extraction of the cube root, nor the use and theory of recurring decimals is required. [Neatness and accuracy of working are expected ; and the methods of solution employed must be clearly indicated. There...