The Elements of Analytical Geometry

Abstract

It is not often that the writer of a mathematical book is privileged to have such a varied experience as the author of this volume. Mr. Craig declares in the preface that he has been called upon to “deal with questions in fields as diverse as Celestial Mechanics, Sport, Geodesy, Hydrography, Meteorology, Ballistics, Census, Agriculture, Food Supply, Statistics, Pensions, Public Health, and Currency Theory”. In all these, he pays a tribute to the value of the mathematical habit of thought, in general, and to the practical utility of analysis applied to geometry, in particular. The course embodied in the book is the immediate outcome of lectures delivered at the Royal School of Engineering, Cairo, and these are based to a large extent on a long experience in the application of analytical geometry to the solution of practical problems. The straight line and circle form the subject matter of this first volume, and the treatment is not only full—trilinear and tangential co-ordinates and vector equations of the circle being included—but also, as might be anticipated, is characterised by numerous practical applications. Amongst these, such interesting topics as railway curves, circular nomograms, and sound-ranging are excellently dealt with. Whilst, however, the book certainly has a practical bias, the theoretical side is not only well covered, but also appears to be mathematically sound. The volume, which has also been translated into Arabic, should be very useful, especially to the engineering student who desires more than a superficial knowledge of analytical geometry.