By William R. Hamilton

A paper by Hamilton entitled

appeared in the Transactions of the Royal Irish Academy, volume 21 (1848), pp. 199-296.Researches respecting Quaternions: First Series

This paper is available in the following formats:

In this paper, Hamilton discusses the algebraic foundations of
his theory of quaternions, exhibiting this theory as an
particular instance of a general theory of *sets*,
(i.e., ordered *n*-tuples in today's terminology).
There is extensive discussion of the associative law.
Applications of quaternions to spherical trigonometry are
discussed.

A letter from Hamilton to John T. Graves is appended to this paper. This letter is dated 24th October, 1843 (i.e., six days following Hamilton's discovery of the algebra of quaternions), and discusses quaternions and their relation to spherical trigonometry.

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School of Mathematics

Trinity College, Dublin