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This is a strange question and I'm not sure where to put it; I'm currently writing an essay for a history of maths course, and I've chosen the topic of Hamilton's discovery of the quaternions. I assume that after he discovered them, he would have published a paper explaining his thought processes etc., but every paper I can find is on the applications of quaternions rather than their discovery.

I know he experimented with triplets before he realized that he needed a fourth dimension, and I'm looking for his papers that document this.

Any recommendations would be greatly appreciated!

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While most of this paper is not dedicated to the discovery itself, I sure found the description and context of the discovery very good. Altmann's book also has a great description of the discovery. – rschwieb Mar 21 '14 at 17:03

See Hamilton's Research on Quaternions.

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This story is told by van der Waerden (with the same references as in the link above) in A History of Algebra From al-Kwarizmi to Emmy Noether‌​, pp. 179-183. – Per Manne Mar 20 '14 at 14:02

You might want to examine the possibility that this was discovered earlier by the Spanish mathematician and banker Olinde Rodrigues in 1840.

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