Page:A History of Mathematics (1893).djvu/195

him Euclid's Elements, which he, without assistance, mastered easily. His regular studies being languages, the boy employed only his hours of amusement on the study of geometry, yet he had so ready and lively a penetration that, at the age of sixteen, he wrote a treatise upon conics, which passed for such a surprising effort of genius, that it was said nothing equal to it in strength had been produced since the time of Archimedes. Descartes refused to believe that it was written by one so young as Pascal. This treatise was never published, and is now lost. Leibniz saw it in Paris and reported on a portion of its contents. The precocious youth made vast progress in all the sciences, but the constant application at so tender an age greatly impaired his health. Yet he continued working, and at nineteen invented his famous machine for performing arithmetical operations mechanically. This continued strain from overwork resulted in a permanent indisposition, and he would sometimes say that from the time he was eighteen, he never passed a day free from pain. At the age of twenty-four he resolved to lay aside the study of the human sciences and to consecrate his talents to religion. His Provincial Letters against the Jesuits are celebrated. But at times he returned to the favourite study of his youth. Being kept awake one night by a toothache, some thoughts undesignedly came into his head concerning the roulette or cycloid; one idea followed another; and he thus discovered properties of this curve even to demonstration. A correspondence between him and Fermat on certain problems was the beginning of the theory of probability. Pascal's illness increased, and he died at Paris at the early age of thirty-nine years.^[30] By him the answer to the objection to Cavalieri's Method of Indivisibles was put in the clearest form. Like Roberval, he explained "the sum of right lines" to mean "the sum of infinitely small rectangles." Pascal greatly advanced