On Symbolical Geometry

By William R. Hamilton

Hamilton published a paper entitled

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

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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.


D.R. Wilkins
School of Mathematics
Trinity College, Dublin