Subjects for Mathematical Essays (Classic Reprint)

Excerpt from Subjects for Mathematical Essays<br><br>The object of what are here called "mathematical essays" is to co-ordinate a pupil's knowledge on certain subjects which are not specially dealt with in text-books. The essays, of which outlines are given in the first part of this book, are of the following types:<br><br>(i) A group of theorems on one subject, the theorems in ordinary text-books being often scattered in one or several volumes (e.g., Essays 19, 26, 70, 91);<br><br>(ii) A series of questions leading up to the solution of an important problem (e.g., Essays 79, 87, 90, 93);<br><br>(iii) A collection of different methods of proving the same theorem (e.g., Essays 28, 61, 75, 78);<br><br>(iv) A series of applications of the same theorem (e.g., Essays 37, 48, 75);<br><br>(v) A classification of tests of the same geometrical condition (e.g. Essays 3, 4, 40, 41).<br><br>The subjects given in the first part (Essays 1-100) are, as a rule, of an elementary character. In several of these, a question, which throws light on different subjects, is repeated, Those given in the second part (Essays 101-200) are taken from papers set for entrance scholarships in the Trinity and Pembroke groups of Cambridge colleges from 1905 and 1907 respectively.<br><br>I should be grateful for notices of any errors that may be found in the text or answers, and for any suggestions from teachers for the improvement of the book.<br><br>About the Publisher<br><br>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com<br><br>This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.