This textbook aims to develop the main thoughts in elementary mathematics in such a way as to show the relation of its various subjects and thereby trace their relation to each other. The book also attempts to present the principles of physics in a simple and orderly fashion so that the reader may get clear and accurate ideas concerning mechanics, heat, sound, light and electricity which, taken together, constitute a complete presentation of the elements of the subject. The subject is not treated mathematically in order to make it as interesting as possible.