‎HAMILTON, WILLIAM ROWAN.‎
‎On Quaternions" or on a new System of Imaginaries in Algebra. - [MAKING THE GENERAL THEORY OF RELATIVITY POSSIBLE]‎

‎London, Richard and John Taylor, 1844. Contemp. hcalf. Gilt lettering to spine ""Philosophical Magazine"" - Vol. XXV. In: ""The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. Conducted by David Brewster et al."". Vol. XXV. A stamp to titlepage and a few other pages. Entire volume offered (July-December 1844). VIII,552 pp., textillustr. Hamilton's paper: pp. 10-13, 141-145 and 241-246.‎

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‎First printing of this landmark paper in which Hamilton published his creation of a new algebra of quaternions (a noncommunicative algebra), a turning point in the development of mathematics and a discovery which made possible the creation of the general theory of relativity. His algebra was later to form the basis of quantum mechanics and for the proper understanding of the atom.""Gauss had treated imaginary numbers in combination with real ones as representing points on a plane and showed the methods by which such complex numbers could be manipulated. Hamilton tried to extend this to threee dimensions and found himself unable to work out a self-consistent method of multiplication, until it occurred to him that the cummutative law of multiplication need not necessarily hold. It is taken for granted that A times B is equal to B times A... and this is an example of what seems to be an eternal and inescapable truth. Hamilton, however, showed that he could built up a logical algebra for his quaternions only when B times A was not made to equal - A times B. This seems against common sense but, like Lobachevski, Hamilton showed that the truth is relative and depends on the axioms you choose to accept.""(Asimov).The creation of quaternions is one of the famous moments in the history of mathematics. ""The quaternions came to Hamilton in one of those flashes of understanding that occasionally occur after long deliberation on a problem. He was walking into Dublin on 16 October 1843 along the Royal Canal to preside at a meeting of the Royal Irish Academy, when the discovery came to him. As he described it, ""An electric circuit seemed to close.""18 He immediately scratched the formula for quaternion multiplication on the stone of a bridge over the canal. His reaction must have been in part a desire to commemorate a discovery of capital importance, but it was also a reflection of his working habits. Hamilton was an inveterate scribbler. His manuscripts are full of jottings made on walks and in carriages. He carried books, pencils, and paper everywhere he went. According to his son he would scribble on his fingernails and even on his hard-boiled egg at breakfast if there was no paper handy.""(DSB).Hamilton later developed his invention in his book from 1853 ""Lectures on Quaternions"" - see PMM: 334 and Grattan-Guiness ""Landmark Writings in Western Mathematics 1640-1940"", pp. 460 ff.In this volume other importent papers by Gassiot, Sylvester, Joule, Draper.‎