FROM NUMBER TO QUATERNION. 69 



although Warren published in the Phil. Trans, two papers as a 

 sequel to his treatise, and a short account of Mourey's work was 

 given in the "Lec,ons d'Algebre" of Lefebure de Fourcy, a 

 then, well known French standard book. It was not till Gauss 

 treated the same question again twenty -five years after Argand, 

 that these ideas began to be known — principally in Germany — 

 and for a long time Gauss was considered as having discovered 

 them. However, justice was done to Argand, first by Oauchy 

 (Exercices d' Analyse et de Physique mathematique, Vol. iv., p. 

 157), then by Hamilton (Preface to his Lectures on Quaternions) 

 and Hankel (Gauss Werke, t. II., p. 174 — Anzeige zur "Theoria 

 residuorum biquadraticorum. Commentatio secunda "). 



But as late as 1874, although Argand was generally considered 

 as the inventor of calculus of complex quantities, his work was 

 not yet more extensively known owing to the great scarcity of 

 the copies of his pamphlet. Under those circumstances, Honel, 

 my learned professor of mathematics, thought it would be useful 

 to give a second edition of that work. Through Chasle's kindness 

 he was able to get the only available copy of Argand's pamphlet — 

 that offered to Gergonne — and he published it with a very 

 remarkable, although short historical notice, adding as appendix 

 the two papers of Argand given in Gergonne's Annales. As a 

 bibliographical curiosity, the first page of the second edition is 

 the autographic reproduction of the first page of that copy of 

 Argand's pamphlet dedicated to Gergonne. 



In this historical notice I have purposely almost left aside the 

 great personality of Hamilton, simply because the history of his 

 invention of quaternions (16th October 1843*) and of his first 

 paper on it (read before the Royal Irish Academy, of which he 

 was the president, the 13th November 1843) is so well known 

 that nothing can be added on the subject. f 



* He discovered that very day the fundamental equations, basis of all 

 calculations in quaternions : i 2 -j 2 = fc 2 — ij k= — 1 



ij - — ji = k jk = — kj-i ki- — ik-j 



t See for instance, " Life of Sir W. B.. Hamilton by R. P. Graves, m.a.," 

 Vol. ii., pages 434 and following. 



