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My purpose in bringing out the present volume is to fulfil the promise made in the Preface of the WEEKLY PROBLEM PAPERS, and to place before students the various methods which are serviceable in solving problems in Elementary Mathematics, many of which methods are not to be found in the ordinary text-books. My object being therefore both to increase a student's stock of mathematical knowledge, and to teach him to put it to a practical use, I have in many cases given two different solutions of a problem when I thought it would be to the advantage of the reader to do so.
In almost every case I have given a preference to the methods of Elementary Geometry, as I think there is a tendency at the present time to allow them to be to some extent supplanted by those of Modern Geometry, which, although more fascinating, are scarcely as valuable a training to a student previous to his entering the regions of higher mathematics.
With regard to the arrangement adopted in the following pages, a little explanation is necessary. Some years ago I began to form Problem Papers for the use of my pupils, without any