The topics in this book are arranged for primary courses in calculus in which the formal division into differential calculus and integral calculus is deemed necessary. The book is mainly made up of matter from my Infinitesimal Calculus, Changes, however, have been made in the treatment of several topics, and some additional matter has been introduced, in particular that relating to indeterminate forms, solid geometry, and motion. The articles on motion have been written in the belief that familiarity with the notions of velocity and acceleration, as treated by the calculus, is a great advantage to students who have to take mechanics. Part of the preface of my Infinitesimal Calculus applies equally well to this book. Its purpose is to provide an introductory course for those who are entering upon the study of calculus either to prepare themselves for elementary work in applied science or to gratify and develop their interest in mathematics. Little more has been discussed than what may be regarded as the essentials of a primary course. An attempt is made to describe and emphasise the fundamental principles of the subject in such a way that, as much as may reasonably be expected, they may be clearly understood, firmly grasped, and intelligently applied by young students. There has also been kept in view the development in them of the ability to read mathematics and to prosecute its study by themselves. With regard to simplicity and clearness in the exposition of the subject, it may be said that the aim has been to write a book that will be found helpful by those who begin the study of calculus without the guidance and aid of a teacher. For these students more especially, throughout the work suggestions and remarks are made concerning the order in which the various topics may be studied, the relative importance of the various topics in a first study of calculus, the articles that must be thoroughly mastered, and the articles that may advantageously be

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