_Graves’ Life of W. R. Hamilton (New York, 1882-1889), Vol. 13, p. 446._ =1417.= The discovery [of Ceres] was made by G. Piazzi of Palermo; and it was the more interesting as its announcement occurred simultaneously with a publication by Hegel in which he severely criticized astronomers for not paying more attention to philosophy, a science, said he, which would at once have shown them that there could not possibly be more than seven planets, and a study of which would therefore have prevented an absurd waste of time in looking for what in the nature of things could never be found.--BALL, W. W. R. _History of Mathematics (London, 1901), p. 458._ =1418.= But who shall parcel out His intellect by geometric rules, Split like a province into round and square? --WORDSWORTH. _The Prelude, Bk. 2._ =1419.= And Proposition, gentle maid, Who soothly ask’d stern Demonstration’s aid, .... --COLERIDGE, S. T. _A Mathematical Problem._ =1420.= Mathematics connect themselves on the one side with common life and physical science; on the other side with philosophy in regard to our notions of space and time, and in the questions which have arisen as to the universality and necessity of the truths of mathematics and the foundation of our knowledge of them.--CAYLEY, ARTHUR. _British Association Address (1888); Collected Mathematical Papers, Vol. 11, p. 430._ =1421.= Mathematical teaching ... trains the mind to capacities, which ... are of the closest kin to those of the greatest metaphysician and philosopher. There is some color of truth for the opposite doctrine in the case of elementary algebra. The resolution of a common equation can be reduced to almost as mechanical a process as the working of a sum in arithmetic. The reduction of the question to an equation, however, is no mechanical operation, but one which, according to the degree of its difficulty, requires nearly every possible grade of ingenuity: not to speak of the new, and in the present state of the science insoluble, equations, which start up at every fresh step attempted in the application of mathematics to other branches of knowledge.--MILL, J. S. _An Examination of Sir William Hamilton’s Philosophy (London, 1878), p. 615._