Mathematics Self-Taught e-bog

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. If it were possible to produce an introduction to the science of mathematics which should give a broad, comprehensive View and insight into this marvellous creation of the human mind, such a treatise could not fail to produce the most inspiriting effect upon the emotions of the student. But the innumerable variations and conditions which aecom pany all the details of this branch of knowledge make such a general view a practical impossibility. It is necessary to assume a certain amount of preliminary knowledge on the part of the beginner, in order to make even the simplest introduction intel ligible. Without a knowledge of the system of numeration no one can learn addition; without these, multiplication cannot be understood; while all are necessary for the study of division. So it goes on throughout the whole range of mathematics; the principles overlap and lead into each other. From the simplest propositions we advance step by step upwards, and the higher branches are accessible to all who have climbed the lower steps. No principle can be properly understood if one has not fully mastered everything which has preceded it and upon which each fact hangs like a link in the chain of which it forms a part. In fact the word Mathematics belongs not to one, but to several branches of knowledge, (arithmetic, Geometry, Mechanics, Optics, Astron omy, etc., etc.) each of which is daily extending its scope, and each of which is practically without limits. A true conception of the meaning of the term Mathematics, both in the pure and the applied branches of the science, can only be obtained by continuous and earnest study, but we canassure the student that every hour spent in the study possesses both a theoretical and practical value. Before entering upon the immediate subject, the following explanations will serve to give a notion of the first principles upon which all the others are founded.