Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. This text presents a course in elementary mathematics adapted to the needs of students in the freshman year of an ordinary college or technical school course, and of students in the first year of a junior college. The material Of the text includes the essential and vital features of the work commonly covered in the past in separate courses in college algebra, trigonometry, and analytical geometry. The fundamental idea of the development is to emphasize the fact that mathematics cannot be artificially divided into compartments with separate labels, as we have been in the habit of doing, and to Show the essential unity and harmony and interplay between the two great fields into which mathematics may properly be divided; via, analysis and geometry.