A GENERALIZATION OF PASCAL’S THEOREM

By William Rowan Hamilton

(Proceedings of the Royal Irish Academy, 5 (1853), p. 100–101.)

Edited by David R. Wilkins A Generalization of Pascal’s Theorem. By Sir William R. Hamilton.

Communicated March 16, 1851.

[Proceedings of the Royal Irish Academy, vol. 5 (1853), p. 100–101.]

Sir William R. Hamilton communicated to the Academy a generalization of Pascal’s theorem, to which he had been led by the method of quaternions.

Equation of Homodeuterism:

Σ(±ABCDEF . GHIK) = 0
ABCDEF = aconic function of a hexagon;
GHIK = volume of a pyramid.

Sir Wm. R. Hamilton proposes to give a more full explanation of the nature of this equation of homodeuterism, and of what he calls the aconic function of a hexagon, at a future meeting of the Academy. The equation itself was exhibited by him to some scientific friends so long ago as the August and September of 1849; and also at the Meeting of the British Association, at Edinburgh, in 1850.