This textbook is designed primarily to follow the third book of the author's series of textbooks of secondary mathematics. Therefore, it presupposes the essentials of high-school algebra, plane and solid geometry, and trigonometry. It aims to combine the work which is commonly covered in separate courses in college algebra and in analytical geometry. The course is therefore suitable for the first year of the junior college and may be taught either in the fourth year of high school or in the first year of college.