This book aims to present a course suitable for students in the first year of our colleges, universities, and technical schools. It presupposes on the part of the student only the usual mini mum entrance requirements in elementary algebra and plane geometry? The book has been written with the hope of contributing something toward the solution of the problem of increasing the value and significance of our freshman courses. The recent widespread discussion of this problem has led to the general acceptance on the part of many teachers of certain principles governing the selection and arrangement of mate rial and the point of view from which it is to be presented. Among such principles, which have guided us in the prepara tion of this text, are the following.