POPULAR MATHEMATICS. SECTION I. GENERAL REMARKS, AND DEFINITIONS. THE Common opinions of mankind upon a subject are frequently at very remarkable variance with the nature of that subject; and this variation is not perhaps more striking in any one case than in that of Mathematics. Those who have never studied any portion of mathematical science, however acute they may naturally be, and however well informed upon other, and in themselves more difficult subjects, generally, if not invariably, turn away from every mathematical expression, as if it were an adder in their path; and even they who, to use the homely but most appropriate expression, have "gone through" that which is called mathematics at the common schools, shake their heads at the subject, with a silent expression of, "These matters are beyond our depth." The conduct of such parties puts one very much in mind of that of the porter in a northern University. This porter was a very "whale" of books, and one of the professors, whose particular attention he claimed, found the supplying of his appetite from the University library no easy task. At length he tried him with "Euclid's Elements B 2 EUCLID AND PTOLEMY. of Geometry," to see how far sheer appetite would be able to digest that. The porter came not for an exchange till after two weeks had elapsed; and at last he came, somewhat crestfallen, saying, "Docter, I hae read a' the wirds, an' leukit at a' the pikters, but it's the maist puzzleanimous beuk I hae seen, an' I dinna onderstand ae wird o't; sae ye'll jeust hae the gudeness to gie me a beuk that has nae As nor Bs in't." It is probable that some part of this general dread of mathematics may have been occasioned by the reply of Euclid to Ptolemy Philadelphus, the Egyptian monarch. The king wished to know if there was not an easier method of learning geometry than that which was practised in the schools; and the mathematician bluntly, but somewhat ambiguously replied, "There is no royal road to geometry." Now, all that was meant by these words was, that geometry must be studied by man as man, and not as monarch; that it must be conquered by the mental exertions of the individual alone, and not by any subjects which he can command, or any armies that he can muster; so that, if we take it in its true meaning, the saying of Euclid is an express declaration, by one of whose judgment no one can doubt, that any man might be a geometer if he would bring his own mind to bear upon the subject; and that in this science, the civil and political distinctions of mankind go for nothing, for it is as open and as plain to the humblest peasant as to the proudest king. Sixty-three generations of men, at the average allowance of one-third of a century for each, have been born and have died since this reply was given by the Alexandrian geometer; and during this long period, men of all ranks, from the monarch to the peasant, have studied and promoted geometry, and the other branches of mathematical science; but this reply has been brought forward as a sort of bar in the way, not of kingly |