Elements of Algebra

xviii EULER. himself the table of the six first powers of all numbers, from 1 to 100, and to have preserved it actually in his memory. The dexterity which he had acquired in analysis and calculation, is remarkably exemplified by the manner in which he manages formulæ of the greatest length and intricacy. He perceives, almost at a glance, the factors from which they may have been composed; the particular system of factors belonging to the question under present consideration; the various artifices by which that system may be simplified and reduced; and the relation of the several factors to the conditions of the hypothesis. His expertness in this particular probably resulted, in a great measure, from the ease with which he performed mathematical investigations by head. He had always accustomed himself to that exercise; and having practised it with assiduity, even before the loss of sight, which afterwards rendered it a matter of necessity, he is an instance to what an astonishing degree of perfection that talent may be cultivated, and how much it improves the intellectual powers. No other discipline is so effectual in strengthening the faculty of attention; it gives a facility of apprehension, an accuracy and steadiness to the conceptions; and, what is a still more valuable acquisition, it habituates the mind to arrangement in its reasonings and reflections. If the reader wants a further commentary on its advantages, let him proceed to the work of