William Rown Hamilton, Lectures on quaternions (1853)

Publisher Summary William Rowan Hamilton's book, Lectures on Quaternions , was the first such piece devoted to quaternions, which appeared ten years after their discovery by Hamilton. Later, many of his useful concepts were separated from their quaternion context and were reformulated as a part of vector analysis. In his early work Hamilton assumed, not unnaturally, that the task was a kind of finding the appropriate system of triples of numbers, and it was only after many unsuccessful efforts that the possibility of a quadruple of numbers presented itself. In spite of this introduction of an algebraic approach, the presentation remains geometrically oriented. The controversy between the vector and quaternion camps is unusual in the history of mathematics in its intensity and international scope, comparable to the dispute between the followers of Isaac Newton and G.W. Leibniz over the origins and best form of the calculus. In addition to many publications from both sides, quaternionists founded an International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics, which published bulletins between 1900 and 1913..