This textbook presents the foundation for a second high-school year mathematics course. It aims to teach "how to study" as well as the "content" of a second unit of secondary mathematics through the nature and form of the material, explicit exhibits, formulated tests of both sound and unsound reasoning, through study-helps, directions for working, and systematic chapter summaries. A unique feature of the book is the attractive presentation of a considerable body of associated solid geometry. This is an economy and is in accord with modern educational precepts.