By William R. Hamilton

Hamilton published a paper entitled

which appeared in installments in the first four volumes of the Cambridge and Dublin Mathematical Journal for the years 1846-1849.On Symbolical Geometry.

This paper is available in the following formats:

In this paper, Hamilton develops an algebra of directed lines in space, avoiding completely the use of Cartesian coordinates or trigonometry. The `geometrical quotients' introduced in this paper correspond to the quaternions. Hamilton applies the principles of his `symbolical geometry' to obtain coordinate-free proofs of certain geometrical theorems relating to cones and surfaces of the second degree.

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D.R. Wilkins(

School of Mathematics

Trinity College, Dublin