Originally published in 1936, this textbook was primarily designed for students of applied mathematics to provide a solid foundation for studies on the practical side of the subject. The book, whilst carefully keeping the groundwork of pure mathematics, covering key elementary aspects of the subject, such as quadratic equations, in the main explores the 'generally understood technical allusions, illustrations, and graded applications'. The book provides multiple useful and challenging exercises and is shaped and established around the syllabus at the time of publication. Chapters are broad in scope, detailed and clearly written; chapter titles include, 'Curved graphs', 'Trigonometry ratios and exercises' and 'Loci'. Aiming to achieve a 'logical sequence of leading theorems, clear deductions and concise, practical applications', this textbook will be of great value to students of engineering mathematics as well as to anyone with an interest in physics, materials science and the history of education.