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 PASCAL 145 ing upon geometrical figures, until lie had gone through a series of definitions, axioms, and de- monstrations as far as the 32d proposition of Euclid. On discovering this, his father gave him mathematical instruction. Blaise was soon admitted to the meetings of scientific societies, where he astounded the most learned ; and at the age of 16 he composed a " Treatise on Conic Sections." In 1639 he accompanied his father to Eouen, where the latter had been ap- pointed superintendent of finance for the prov- ince of Normandy; and there he invented a calculating machine, which was improved by L'fipine and Boitissendeau, but it never came into practical use. He published an account of it in 1645, and in 1650 offered it to Queen Christina of Sweden. During his stay in Kouen he also invented the vinaigrette (wheel- barrow chair), the haquet (a kind of dray), and, according to some, the hydraulic press. His health was seriously impaired by his labors, and his subsequent life was a succession of suf- ferings. In 1648 his brother-in-law M. P6rier, in accordance with instructions given by Pas- cal in a letter of the previous year, executed on the Puy-de-D6me, near Clermont, and at Rouen, and Pascal himself at the tower of St. Jacques-la-Boucherie in Paris, a series of bar- ometrical experiments, which went far to con- firm the discoveries of Galileo, Torricelli, and Descartes respecting the weight and elasticity of air. Pascal was led by these experiments to use the barometer for levelling, and for ascertaining the pressure of fluids upon the sides of the vessels containing them, and estab- lishing the laws of their equilibrium. His Ex- periences touchant le vide were published in 1647, and were assailed by Father Noel, a Jes- uit, who presented himself as the champion of the old system, and whom Pascal answered in two letters. About this period he had a stroke of paralysis by which he lost for a while the use of his legs ; at the same time he studied in- tensely devotional works. In 1654 he with- drew from society, and entered upon a course of self-denial and austerity, which character- ized the remaining years of his life. Amid his previous gayeties, however, in which he had engaged on the advice of his physician, he had written some of his philosophical works, such as his treatises De la pesanteur de la masse de Vair, and De V equilibre des liqueurs, which was first published in 1663. In 1654 he com- pleted an "arithmetical triangle," by which he illustrated mathematically certain laws con- nected with bets and games of chance ; it was an approach toward the binominal theorem of Newton. After his death three treatises of his were published (1665) in which he had laid down the principles of the calculus of probabilities. The F'ort Royalists were now the upholders of the doctrines of Jansenius, and Pascal frequently visited their house, and soon interested himself in their quarrel with the Jesuits. When, at the end of 1655, An- toine Arnauld was expelled from the Sorbonne on account of his letter in defence of Jansen- ism, Pascal published the first of the series of Lettres de Louis de Montalte a un provincial de sea amis et aux RR. PP. les Jesuites sur la morale et la politique de ces peres, which be- came so celebrated under the abbreviated title of " The Provincial Letters." The first of these letters, which appeared Jan. 23, 1656, was eagerly read and circulated ; it was followed at intervals by 17 others within a period of 14 months. The replies of the Jesuits, the con- demnation of the letters by the holy see in 1657, and the sentence of the council of state and the parliament of Aix that they should be burned by the hand of the executioner, could not check their popularity ; and 20 years later, as appears from Mme, de Sevigne"'s correspon- dence, the Petites lettres, as they were now styled, had lost nothing of their original attrac- tions. They may be said to have been the origin of that hostile feeling which, a century later, brought about the expulsion of the so- ciety of Jesus from France. They were trans- lated into several languages ; and one of the Port Royalists, Nicole, produced a Latin version un- der the name of Wendrock. Pascal's health con- tinued to fail, and his sufferings scarcely left him any respite; he nevertheless returned to his wonted pursuits, and studied the properties of curves, and especially those of the cycloid or roulette. He completed the researches of Galileo, Torricelli, Descartes, and Fermat on this particular point, and in 1659 published his Traite general de la roulette. He had also en- gaged in the composition of a new demonstra- tion of Christianity, but was able only to write occasionally detached thoughts, which were published in 1670, under the title of Penseessur la religion. Modern critics, especially Victor Cousin and Sainte-Beuve, availing themselves of previously neglected sources of information and original manuscripts, have succeeded in giving an outline of Pascal's design. The last four years of his life were an almost unbroken series of bodily suffering and charitable em- ployments; his alms absorbed more than his income. His remains were buried in the church of St. Etienne du Mont, where his tomb is still to be seen. There are two editions of Pascal's complete works, including his scientific trea- tises, namely, that of Bossut (5 vols. 8vo, 1779), and that of Lefvre (5 vols. 8vo, 1819). The Lettres provinciales, collected for the first time in 1657, were published in 1684 at Cologne under the supervision of Nicole, with Latin, Spanish, and Italian translations. The Pensees were reprinted from the original edition of 1670, first in 1672 (2 vols. 12mo), and with a life of Pascal by his sister, Mme. Perier, in 1684; by Desmolets, with some additions, in 1729 ; and by Condorcet in 1776. These were the foundation of every subsequent edition un- til 1842, when Victor Cousin, in a paper read before the French academy, pointed out the alterations and omissions in every one of them, referring at the same time to the autograph