PREFACE THIS book is essentially practical. It is intended for young men and others who want to obtain such a knowledge of mathematics as shall be of service to them in their business as mechanics or engineers, and to obtain it by study at home, without the advantages—and without the expense of outside assistance. The book covers a pretty wide field, and no young man can master it without finding himself greatly benefited that is to say, greatly strengthened and armored for the battle of life. And yet there is nothing in the book which may not be mastered by a little diligent study pursued at home, day by day, say for a year. In some of the topics a few principles, taken from the higher mathematics, have been assumed without proofs. The proofs of them would be too difficult for useful insertion here. But these assumed principles are so presented that their reasonableness can be very well inferred, although the proofs for them be not mathematically established. Each part in the book is complete in itself, and therefore may be taken up without a knowledge of the other parts. But it will be better if all the parts be mastered before the book is laid aside. Especially is the part entitled "Elementary Algebra" recommended. A knowledge of the solution of simple equations, for example, is one of those things which no one needing to make calculations can possibly afford to do without. The "First Course in Geometry" is also especially recommended. It is a course in pure reasoning based upon a method of study that has been pursued with immense. advantage to mankind for over two thousand years. Also, the results established in the course will be of great help in throwing light on processes made use of in other parts of the book. But especially is the course commended to students for the insight that it will give them as to the rigorous way in which all reasoning in mathematics is pursued when the study is taken up under suitable conditions. |