_Graves’ Life of Hamilton (New York, 1882-1889), Vol. 3, p. 634._ =1717.= The circumstances that algebra has its origin in arithmetic, however widely it may in the end differ from that science, led Sir Isaac Newton to designate it “Universal Arithmetic,” a designation which, vague as it is, indicates its character better than any other by which it has been attempted to express its functions--better certainly, to ordinary minds, than the designation which has been applied to it by Sir William Rowan Hamilton, one of the greatest mathematicians the world has seen since the days of Newton--“the Science of Pure Time;” or even than the title by which De Morgan would paraphrase Hamilton’s words--“the Calculus of Succession.”--CHRYSTAL, GEORGE. _Encyclopedia Britannica, 9th Edition; Article “Algebra.”_ =1718.= Time is said to have only _one dimension_, and space to have _three dimensions_.... The mathematical _quaternion_ partakes of _both_ these elements; in technical language it may be said to be “time plus space,” or “space plus time:” and in this sense it has, or at least involves a reference to, _four dimensions_.... And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be. --HAMILTON, W. R. _Graves’ Life of Hamilton (New York, 1882-1889), Vol. 3, p. 635._ =1719.= It is confidently predicted, by those best qualified to judge, that in the coming centuries Hamilton’s Quaternions will stand out as the great discovery of our nineteenth century. Yet how silently has the book taken its place upon the shelves of the mathematician’s library! Perhaps not fifty men on this side of the Atlantic have seen it, certainly not five have read it. --HILL, THOMAS. _North American Review, Vol. 85, p. 223._ =1720.= I think the time may come when double algebra will be the beginner’s tool; and quaternions will be where double algebra is now. The Lord only knows what will come above the quaternions. --DE MORGAN, A. _Graves’ Life of Hamilton (New York, 1882-1889), Vol. 3, p. 493._ =1721.= Quaternions came from Hamilton after his really good work had been done; and though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell.--THOMSON, WILLIAM. _Thompson, S. P.: Life of Lord Kelvin (London, 1910), p. 1138._ =1722.= The whole affair [quaternions] has in respect to mathematics a value not inferior to that of “Volapuk” in respect to language.--THOMSON, WILLIAM.