universe as an incarnate Euclid, shows the rational consummation of the experiment. Now, Pascal was obviously a heaven-born mathematician. By the age of twelve, we are told, he had thought out for himself the elementary propositions of Euclid; by nineteen he had invented and constructed a calculating machine, and obtained results which were important steps towards the differential calculus developed by Newton and Leibnitz. In his last years, when attacked by a bad toothache, he returned to the studies which had long been thrown aside, and in a few sleepless nights discovered certain geometrical theorems. His results were published, and the mathematicians of Europe challenged to find out the proof. After three months' labour, Wallis, the ablest English mathematician of the day, produced a proof—not, it was said, satisfactory. Patriotism induces me to add that Wallis had no toothache to stimulate him. At an early age, however, Pascal's health had broken down; from his eighteenth year until his death he never had a day free from pain. His first conversion, at the age of twenty-three, induced him to throw aside scientific activity as a worldly vanity. He became closely associated with the remarkable Port-Royal community, and appeared as their
