Explore the geometry and operation of quaternions with one of the field’s foundational texts. This classic work presents the ideas of vectors and quaternions in a structured, progression-based approach, guiding readers from basic signs and operations to the richer theory of quotients, products, and powers. The text is organized into three books, each building a guiding conception and illustrating it with carefully chosen examples. It also places the topic in a historical and practical context, including notes on exposition and teaching how to study the material effectively. Clear development of vectors, quotients of vectors, and quaternion concepts Rules for addition, subtraction, multiplication, and the geometry of quaternions Introduction to advanced topics such as exponential and logarithmic forms, and algebraic equations in quaternions Editorial notes, cross‑references, and an expanded index in later editions Ideal for readers of mathematics and physics who seek a rigorous, historically important treatment of quaternions and their applications.