Elements of Algebra

EULER. xvii every page of the edition, which he had been accustomed to use. These are instances of a kind of memory, more frequently to be found where the capacity is inferior to the ordinary standard, than accompanying original, scientific genius. But in Euler, they seem to have been not so much the result of natural constitution, as of his most wonderful attention; a faculty, which, if we consider the testimony of Newton * sufficient evidence, is the great constituent of inventive power. It is that complete retirement of the mind within itself, during which the senses are locked up; that intense meditation, on which no extraneous idea can intrude; that firm, straight-forward progress of thought, deviating into no irregular sally, which can alone place mathematical objects in a light sufficiently strong to illuminate them fully, and preserve the perceptions of “the mind’s eye” in the same order that it moves along. Two of Euler’s pupils (we are told by M. Fuss, a pupil himself) had calculated a converging series as far as the seventeenth term; but found, on comparing the written results, that they differed one unit at the fiftieth figure: they communicated this difference to their master, who went over the whole calculation by head, and his decision was found to be the true one.—For the purpose of exercising his little grandson in the extraction of roots, he has been known to form to * This opinion of Sir Isaac Newton is recorded by Dr. Pemberton. b