Elements of Algebra

EULER. xiii towards which they are most frequently directed, and the invention becomes habitually most active and most acute in that channel of inquiry. The truth of these observations is strikingly illustrated by the character of Euler. His studies and discoveries lay not among the lines and figures of geometry, those characters, to use an expres- sion of Galileo in which the great book of the universe is written; nor does he appear to have had a turn for philosophising by experiment, and advancing to discovery through the rules of in- ductive investigation. The region, in which he delighted to speculate, was that of pure intellect. He surveyed the properties and affections of quantity under their most abstracted forms. With the same rapidity of perception, as a geometrician ascertains the relative position of portions of exten- sion, Euler ranges among those of abstract quan- tity, unfolding their most involved combinations, and tracing their most intricate proportions. That admirable system of mathematical logic and lan- guage, which at once teaches the rules of just inference, and furnishes an instrument for prose- cuting deductions, free from the defects which obscure and often falsify our reasonings on other subjects; the different species of quantity, whether formed in the understanding by its own abstrac- tions, or derived from modifications of the repre- sentative system of signs; the investigation of the various properties of these, their laws of genesis, the limits of comparison among the different