extracted from his father some hints as to the subject matter of geometry, went to work by himself, drawing circles and lines, or, as he called them in his ignorance of the received nomenclature, rounds and bars, and investigating and proving the properties of his various figures, till, without help of a book or oral instruction of any kind, he had advanced as far as the thirty-second proposition of the first book of Euclid. He had perceived that the three angles of a triangle are together equal to two right ones, and was searching for a satisfactory proof, when his father surprised him in his forbidden speculations. The figures drawn on the walls of his bed-chamber told the tale, and a few questions proved that his head had been employed as well as his fingers. He was at this time twelve years old. All attempts at restriction were now abandoned. A copy of Euclid’s Elements was put into his hands by his father himself, and Blaise became a confirmed geometrician. At sixteen he composed a treatise on the Conic Sections, which had sufficient merit to induce Descartes obstinately to attribute the authorship to the elder Pascal or Desargues.
Such was his progress in a study which was admitted only as the amusement of his idle hours. His labours under his father’s direction were given to the ancient classics.
Some years after this, the elder Pascal had occasion to employ his son in making calculations for him. To facilitate his labour, Blaise Pascal, then in his nineteenth year, invented his famous arithmetical machine, which is said to have fully answered its purpose. He sent this machine with a letter to Christina, the celebrated Queen of Sweden. The possibility of rendering such inventions generally useful has been stoutly disputed since the days of Pascal. This question will soon perhaps be set at rest, if it may not be considered as already answered, by the scientific labours of an accomplished mathematician of our own time and country.
It should be remarked that Pascal, whilst he regarded geometry as affording the highest exercise of the powers of the human mind, held in very low estimation the importance of its practical results. Hence his speculations were irregularly turned to various unconnected subjects, as his curiosity might happen to be excited by them. The late creation of a sound system of experimental philosophy by Galileo had roused an irresistible spirit of inquiry, which was every day exhibiting new marvels; but time was wanted to develope the valuable fruits of its discoveries, which have since connected the most abstruse speculations of the philosopher with the affairs of common life.
There is no doubt that his studious hours produced much that has been lost to the world; but many proofs remain of his persevering activity in the course which he had chosen. Amongst them may be mentioned his Arithmetical Triangle, with the treatises arising out of it, and his investigations of certain problems relating to the curve called by mathematicians the Cycloid, to which he turned his mind, towards the close of his life, to divert his thoughts in a season of severe suffering. For the solution of these problems, according to the fashion of the times, he publicly offered a prize, for which La Loubère and our own countryman Wallis contended. It was adjudged that neither had fulfilled the proposed conditions; and Pascal published his own solutions, which raised the admiration of the scientific world. The Arithmetical Triangle owed its existence to questions proposed to him by a friend respecting the calculation of probabilities in games of chance. Under this name is denoted a peculiar arrangement of numbers in certain proportions, from which the answers to various questions of chances, the involution of binomials, and other algebraical problems, may be readily obtained. This invention led him to inquire further into the theory of chances; and he may be considered as one of the founders of that branch of analysis, which has grown into such importance in the hands of La Place.
His fame as a man of science does not rest solely on his labours in geometry. As an experimentalist he has earned no vulgar celebrity. He was a young man when the interesting discoveries in pneumatics were working a grand revolution in natural philosophy. The experiments of Torricelli had proved, what his great master Galileo had conjectured, the weight and pressure of the air, and had given a rude shock to the old doctrine of the schools that “Nature abhors a vacuum;” but many still clung fondly to the old way, and when pressed with the fact that fluids rise in an exhausted tube to a certain height, and will rise no higher, though with a vacuum above them, still asserted that the fluids rose because Nature abhors a vacuum, but qualified their assertion with an admission that she had some moderation in her abhorrence. Having satisfied himself by his own experiments of the truth of Torricelli’s theory, Pascal with his usual sagacity devised the means of satisfying all who were capable of being convinced. He reasoned that if, according to the new theory, founded on the experiments made with mercury, the weight and general pressure of the air forced up the mercury in the tube, the height of the mercury would be in proportion to the height of the column of incumbent air; in other words, that the mercury would be lower at the top of a mountain than at the bottom of it: on the other hand, that if the old answer were the right one, no difference would appear from the change of situation. Accordingly, he directed the experiment to be made on the Puy de Dôme, a lofty mountain in Auvergne, and the height of the barometer at the top and bottom of the mountain being taken at the same moment, a difference of more than three inches was observed. This set the question at rest for ever. The particular notice which we have taken of this celebrated experiment, made in his twenty-fifth year, may be justified by the importance attached to it by no mean authority. Sir W. Herschell observes, in his Discourse on the Study of Natural Philosophy, page 230, that “it tended perhaps more powerfully than any thing which had previously been done in science to confirm in the minds of men that disposition to experimental verification which had scarcely yet taken full and secure root.”
Whatever may be the value of the fruits of Pascal’s genius, it should be remembered that they were all produced within the space of a life which did not number forty years, and that he was so miserably the victim of disease that from the time of boyhood he never passed a day without pain.
His health had probably been impaired by his earlier exertions; but the intense mental labour expended on the arithmetical machine appears to have completely undermined his constitution, and to have laid the foundation of those acute bodily sufferings which cruelly afflicted him during the remainder of his life. His friends, with the hope of checking the evil, sought to withdraw him from his studies, and tempted him into various modes of relaxation. But the remedy was applied too late. The death of his father in 1651, and the retirement of his unmarried sister from the world to join the devout recluses of Port Royal-des-Champs, released him from all restraint. He sadly abused this liberty, until the frightful aggravation of his complaints obliged him to abandon altogether his scientific pursuits, and reluctantly to follow the advice of his physicians, to mix more freely in general society. He obtained some relief from medicine and change of habits; but, in 1654, an accident both made his recovery hopeless, and destroyed the relish which he had begun to feel for social life. He was in his carriage on the Pont de Neuilly, at a part of the bridge which was unprotected by a parapet, when two of the horses became unruly, and plunged into the Seine. The traces broke, and Pascal was thus saved from instant death. He considered that he had received a providential warning of the uncertainty of life, and retired finally from the world, to make more earnest preparation for eternity. This accident gave the last shock to his already shattered nerves, and to a certain extent disordered his imagination. The image of his late danger was continually before him, and at times he fancied himself on the brink of a precipice. The evil probably was increased by the rigid seclusion to which from this time he condemned himself, and by the austerities which he inflicted on his exhausted frame. His powerful intellect survived the wreck of his constitution, and he gave ample proof to the last that its vigour was unimpaired.
In his religious opinions he agreed with the Jansenists, and, without being formally enrolled in their society, was on terms of intimate friendship with those pious and learned members of the sect, who had established themselves in the wilds of Port Royal. His advocacy of their cause at a critical time was so important to his fame and to literature, that a few words may be allowed on the circumstances which occasioned it.
The Jansenists, though they earnestly deprecated the name of heretics, and were most fiercely opposed to the Huguenots and other Protestants, did in fact nearly approach in many points the reformed churches, and departed widely from
