Elements of Quaternions is a mathematical treatise written by A. S. Hardy and first published in 1891. The book provides a comprehensive introduction to quaternions, a type of mathematical object that extends the concept of complex numbers to four dimensions. The book is divided into two parts. The first part covers the basic theory of quaternions, including their definition, properties, and operations. The second part covers more advanced topics such as the geometry of quaternions, applications to mechanics and physics, and the use of quaternions in computer graphics and animation. The book is written in a clear and concise style, with numerous examples and exercises to help readers understand the material. It is considered a classic in the field of quaternion mathematics and is still widely used as a reference by mathematicians, physicists, and engineers today.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.