% This paper has been transcribed in Plain TeX by
% David R. Wilkins
% School of Mathematics, Trinity College, Dublin 2, Ireland
% (dwilkins@maths.tcd.ie)
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% Trinity College, 2000.

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\centerline{\Largebf A GENERALIZATION OF PASCAL'S THEOREM}

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\centerline{\Largebf By}

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\centerline{\Largebf William Rowan Hamilton}

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\centerline{\largerm (Proceedings of the Royal Irish Academy,
   5 (1853), p.\ 100--101.)}

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\centerline{\largerm Edited by David R. Wilkins}

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\centerline{\largerm 2000}

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\centerline{\largeit A Generalization of Pascal's Theorem.}

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\centerline{{\largeit By\/}
{\largerm Sir} {\largesc William R. Hamilton.}}

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\centerline{Communicated March~16, 1851.}

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\centerline{[{\it Proceedings of the Royal Irish Academy},
vol.~5 (1853), p.\ 100--101.]}

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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:
$$\Sigma (\pm ABCDEF \mathbin{.} GHIK) = 0$$
$$\eqalign{
  ABCDEF &= \hbox{{\it aconic} function of a hexagon};\cr
  GHIK   &= \hbox{volume of a pyramid}.\cr}$$

Sir Wm.~R. Hamilton proposes to give a more full explanation of
the nature of this equation of {\it 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.

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