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Blaise Pascal

Blaise Pascal

Blaise Pascal was born in Clermont France on June 19, 1623 to Etienne Pascal. His mother died when he was only 3. He was the third of four children and the only boy. He was described as a man of: small stature, poor health, loud spoken, somewhat overbearing, precious, stubbornly persevering, a perfectionist, highly pugnacious yet seeking to be humble and meek.

Pascal’s father had somewhat unorthodox views on education, so he decided to teach his son himself. He forbade any mathematic teachings or material to be given to him and had any such texts removed from their house. Blaise became engulfed with curiosity due to this rule. He started to work with geometry on his own at the age of 12. He discovered that the sum of the three angles of a triangle is equivalent to two right angles. When his father discovered this he then allowed Blaise a copy of Euclid.

At the age of 14 Blaise began accompanying his father to Mersenne’s meetings. Mersenne was a member of a religious order of Minims. His cell held many meetings for the likes of Gassendi, Roberval, Carcavi, Auzout, Mydorge, Mylon, Desargues and others. By the time he was 15 Blaise admired the work of Desargues greatly. At 16 Pascal presented a single piece of paper at a Mersenne’s meeting in June 1639. It held many of his geometry theorems, including his mystic hexagon.

In December 1639 he and his family left Paris and moved to Rouen where his father Etienne was appointed tax collector for Upper Normandy. Soon after settling down in Rouen his Essay on Conic Sections was published in February of 1640. It was his first great work.

Pascal also invented the first digital calculator to aid his father in his tax collecting duties. For three years he worked 1642 – 1545. Dubbed the Pascaline, it resembled a mechanical calculator of the 1940’s. This almost assuredly makes Pascal second only to Shickard who manufactured the first in 1624.

Pascal faced problems with the design of the calculator due to the design of French currency at the time. There were 12 deniers in a sol, and 20 sols in a livre. Therefore there were 240 deniers in a livre. Hence Pascal had to deal with more technical problems to work with this odd way of dividing by 240. Yet the currency system remained the same in France until 1799, but Britain’s similar system lasted until 1971. Production of the Pascaline began in 1642. It was recorded by Adamson that:

“By 1652 fifty prototypes had been produced, but few machines were sold, and manufacturing of Pascal’s arithmetical calculator ceased in that year.”

In 1646 Etienne Pascal injured his leg and had to recuperate in his house. Two young brothers from a religious movement outside of Rouen came to help take care of him. Pascal was affected deeply and became very religious. It was at this time that Pascal began many experiments on atmospheric pressure. By 1647 he proved to himself that a vacuum existed. Descartes visited Pascal September the 23rd for 2 days in which they argued about the vacuum which Descartes did not believe existed. Descartes wrote a rather cruel letter to Huygens after visiting the young Pascal. he believed “?has too much vacuum in his head.”

In August of 1648 Pascal deduced that, because the atmospheric pressure decreases with height, there must be a vacuum that exists above the atmosphere. Descartes wrote to Carcavi in June 1647 about Pascal’s experiment stating: “It was I who two years ago advised him to do it, for although I have not performed it myself, I did not doubt of its success.” In October of 1647 Pascal wrote New Experiments Concerning Vacuums which would lead to disputes with various scientists who didn’t believe in vacuums.

Etienne Pascal died in September of 1651, which hurt Blaise badly. He wrote to one his sisters giving a deep Christian meaning to death in general and also to his father’s death particularly. These ideas were to later form the basis of his philosophical work called Pensees.

Then in May 1653 Pascal worked with mathematics and physics writing Treatise on the Equilibrium of Liquids which he explains his law of pressure called Pascal’s law of pressure. Adamson writes: “This treatise is a complete outline of a system of hydrostatics, the first in the history of science, it embodies his most distinctive and important contribution to physical theory.”

He also worked on conic sections and he also produced some important theorems in projective geometry. In The Generation of Conic Sections (which he mostly finished by March 1648, but he worked on again in 1653-54) he considered conics generated by central projection of a circle. Though never completed, this was meant to be the first part of a treatise on conics. Although the work was lost Leibniz and Tschirnhuas made notes from it. Using those very notes a fairly complete portrayal of the work is now possible.

Pascal was not the only one to study the Pascal triangle, but his work on the topic Treatise on the Arithmetical Triangle as the most important. With the work of Wallis, Pascal’s work on the binomial coefficients was to lead to the binomial theorem discovery by Newton for fractional and negative powers.

Along with the help of Fermat they achieved the foundation for the theory of probability. This collective effort obtained five letters and occurred in the summer of 1654. They considered the dice problem, and the problem of points, both of which were considered by Cardan, Pacioli, and Tartaglia. The dice problem raised the question of how many times one must roll a pair of dice before one expects double sixes while the problem of points asks how to divide the stakes if a game of dice is incomplete. They solved the problem of points for a two-player game, but unfortunately were not able to develop powerful enough mechanical algorithms to solve it for three or more players. Pascal was poor in health during their correspondence. In July of 1654 Pascal wrote to Fermat, here is an excerpt: “?though I am still bedridden, I must tell you that yesterday evening I was given your letter.”

In spite of his health problems Pascal worked fervently on scientific and mathematical questions until October 1654. It was then that he nearly lost his life in a horse carriage accident. The horses that were pulling the carriage bolted and when the carriage halted he was left hanging over a bridge of the River of Seine. Though he was rescued he suffered severe mental disorders from the incident. Soon afterward Blaise underwent another religious experience and on November 23rd of 1654 he pledged his life to Christianity.

It was then that Pascal made visits to the Jansenist monastery Port-Royal des Champs which was 30 km south west of Paris. He then began publishing anonymous works on religious topics, eighteen Provincial Letters during 1656 and 1657. These writings were written for the defense of his friend Antoine Arnauld who was an open opponent to the Jesuits and a fellow defender of Jansenism. At the time Arnauld was on trial before the faculty of theology in Paris for his controversial religious works. Pensees was Pascal’s most famous work, which was a collection of personal thoughts on human suffering and faith in God which he worked on from 1656 to 1658. Pensees contained “Pascal’s Wager” which claims to prove that belief in God is rational with the following argument: “If God does exist, one will lose nothing by believing in him, while if he does exist, one will loses everything by not believing.” With “Pascal’s Wager” he uses probabilistic and mathematical arguments coming to his main conclusion that “?we are all compelled to gamble?”

His last work was on the curve traced by a point on a circumference of a rolling stone. This is defined as the cycloid. In 1658 Pascal began to think about mathematical problems again as he lay awake at night due to pain. He associated Cavalieri’s calculus of indivisibles to the problem of the area of any segment of a cycloid and center of gravity of any segment. He also solved the problem of volume and surface area of the solid of revolution formed by rotating x-axis of the cycloid. Pascal also issued a challenge offering two prizes for the solution to these problems. Wren, Laloubere, Leibniz, Huygens, Wallis, Fermat and other various mathematicians were issued the invitation. Wallis and Laloubere entered the competition officially. Laloubere’s and Wallis’ solution were unsuccessful. Sluze, Ricci, Huygens, Wren and Fermat all conveyed their discoveries to Pascal, but didn’t enter the competition. Wren had worked on Pascal’s challenge and decided to issue a challenge of his own. Wren challenged Pascal, Fermat, and Roberval to find the arc length and the length of the arch of the cycloid.

Pascal published his own solutions to his own problems in the Letters to Carcavi. This seemed to be his last great interest in science. He spent his last years giving to the poor and attending church in Paris one service after another. He died at the age of 39 in intense pain after a malignant growth in his stomach spread to the brain.

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Pensées by Blaise Pascal - Free at Loyal Books

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Pascal’s Pensées is widely considered to be a masterpiece, and a landmark in French prose. When commenting on one particular section (Thought #72), Sainte-Beuve praised it as the finest pages in the French language. Will Durant, in his 11-volume, comprehensive The Story of Civilization series, hailed it as “the most eloquent book in French prose.” In Pensées, Pascal surveys several philosophical paradoxes: infinity and nothing, faith and reason, soul and matter, death and life, meaning and vanity—seemingly arriving at no definitive conclusions besides humility, ignorance, and grace. Rolling these into one he develops Pascal’s Wager.

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Blaise Pascal

liceo blaise pascal ovada sportsbook

Born: 19-Jun-1623

Remains: Buried, St. Etienne-du-Mont, Paris, France

Race or Ethnicity: White

Executive summary: French thinker and mathematician

French religious philosopher and mathematician, born at Clermont Ferrand on the 19th of June 1623. His father was Йtienne Pascal, president of the Court of Aids at Clermont; his mother's name was Antoinette Bйgon. The Pascal family were Auvergnats by extraction as well as residence, had for many generations held posts in the civil service, and were ennobled by Louis XI in 1478, but did not assume the de.

The earliest anecdote of Pascal is one of his being bewitched and freed from the spell by the witch with strange ceremonies. His mother died when he was about four years old, and left him with two sisters -- Gilberte, who afterwards married M. Perier, and Jacqueline. Both sisters are of importance in their brother's history, and both are said to have been beautiful and accomplished. When Pascal was about seven years old his father gave up his official post at Clermont, and betook himself to Paris. It does not appear that Blaise, who went to no school, but was taught by his father, was at all forced, but rather the contrary. Nevertheless he has a distinguished place in the story of precocious children, and in the much more limited chapter of children whose precocity has been followed by great performance at maturity, though he never became what is called a learned man, perhaps did not know Greek, and was pretty certainly indebted for most of his miscellaneous reading to Montaigne.

The Pascal family, some years after settling in Paris, had to go through a period of adversity. Йtienne Pascal, who had bought some of the hфtel-de-ville rentes, protested against Cardinal Richelieu's reduction of the interest, and to escape the Bastille had to go into hiding. He was, according to the story (told by Jacqueline herself), restored to favor owing to the good acting and graceful appearance of his daughter Jacqueline in a representation of Scudйry's Amour tyrannique before Richelieu. Mme. d'Aiguillon's intervention in the matter was perhaps as powerful as Jacqueline's acting, and Richelieu gave Йtienne Pascal (in 1641) the important and lucrative though somewhat troublesome intendancy of Rouen.

The family accordingly removed to the Norman capital, though Gilberte Pascal shortly after, on her marriage, returned to Clermont. At Rouen they became acquainted with Pierre Corneille, and Blaise pursued his studies with such vehemence that he already showed signs of an injured constitution. Nothing, however, of importance happened until the year 1646. Then Pascal the elder was confined to the house by the consequences of an accident on the ice, and was visited by certain gentlemen of the neighborhood who had come under the influence of Saint-Cyran and the Jansenists. It does not appear that up to this time the Pascal family had been contemners of religion, but they now eagerly embraced the creed, or at least the attitude of Jansenism, and Pascal himself showed his zeal by informing against the supposed unorthodoxy of a Capuchin, the Pиre Saint-Ange.

His bodily health was at this time very far from satisfactory, and he appears to have suffered, not merely from acute dyspepsia, but from a kind of paralysis. He was, however, indefatigable in his mathematical work. In 1647 he published his Nouvelles expйriences sur le vide, and in the next year the famous experiment with the barometer on the Puy de Dome was carried out for him by his brother-in-law Perier, and repeated on a smaller scale by himself at Paris, to which place by the end of 1647 he and his sister Jacqueline had removed, to be followed shortly by their father. In a letter of Jacqueline's, dated the 27th of September, an account of a visit paid by Renй Descartes to Pascal is given, which, like the other information on the relations of the two, give strong suspicion of mutual jealousy. Descartes, however, gave Pascal the very sensible advice to stay in bed as long as he could (it may be remembered that the philosopher himself never got up until eleven) and to take plenty of beef-tea.

As early as May 1648 Jacqueline Pascal was strongly drawn to Port Royal, and her brother frequently accompanied her to its church. She desired indeed to join the convent, but her father, who returned to Paris with the dignity of counsellor of state, disapproved of the plan, and took both brother and sister to Clermont, where Pascal remained for the greater part of two years. E. Flйchier, in his account of the Grands Jours at Clermont many years after, speaks of a "belle savante" in whose company Pascal had frequently been -- a trivial mention on which, as on many other trivial points of scantily known lives, the most childish structures of comment and conjecture have been based. It is sufficient to say that at this time, despite the Rouen "conversion", there is no evidence to show that Pascal was in any way a recluse, an ascetic, or in short anything but a young man of great intellectual promise and performance, not indifferent to society, but of weak health.

He, his sister and their father returned to Paris in the late autumn of 1650, and in September of the next year Йtienne Pascal died. Almost immediately afterwards Jacqueline fulfilled her purpose of joining Port Royal -- a proceeding which led to some soreness, finally healed, between herself and her brother and sister as to the disposal of her property. It has sometimes been supposed that Pascal, from 1651 or earlier to the famous accident of 1654, lived a dissipated, extravagant, worldly, luxurious (though admittedly not vicious) life with his friend the duc de Roannez and others. His Discours sur les passions de l'amour, a striking and characteristic piece, has also been assigned to this period, and has been supposed to indicate a hopeless passion for Charlotte de Roannez, the duke's sister. But this is sheer romancing. The extant letters of Pascal to the lady show no trace of any affection (stronger than friendship) between them.

It is, however, certain that in the autumn of 1654 Pascal's second "conversion" took place, and that it was lasting. He betook himself at first to Port Royal, and began to live a recluse and austere life there. Mme. Perier simply says that Jacqueline persuaded him to abandon the world. Jacqueline represents the retirement as the final result of a long course of dissatisfaction with mundane life. But there are certain anecdotic embellishments of the act which are too famous to be passed over, though, they are in part apocryphal. It seems that Pascal in driving to Neuilly was run away with by the horses, and would have been plunged in the river but that the traces fortunately broke. To this, which seems authentic, is usually added the tradition (due to the abbй Boileau) that afterwards he used at times to see an imaginary precipice by his bedside, or at the foot of the chair on which he was sitting. Further, from the 23rd of November 1654 dates the singular document usually known as "Pascal's amulet", a parchment slip which he wore constantly about him, and which bears the date followed by some lines of incoherent and strongly mystical devotion.

It must be noted that, though he lived much at Port Royal, and partly at least observed its rule, he never actually became one of its famous solitaries. But for what it did for him (and for a time his health as well as his peace of mind seems to have been improved) he very soon paid an ample and remarkable return. At the end of 1655 Arnauld, the chief light of Port Royal, was condemned by the Sorbonne for heretical doctrine, and it was thought important by the Jansenist and Port Royal party that steps should be taken to disabuse the popular mind. Arnauld would have undertaken the task himself, but his wiser friends knew that his style was anything but popular, and overruled him. It is said that he personally suggested to Pascal to try his hand, and that the first of the famous Provinciales (Provincial Letters, properly Lettres йcrites par Louis de Montalte а un provincial de ses amis) was written in a few days, or, less probably, in a day. It was printed without the real author's name on the 23rd of January 1656, and, being immensely popular, and successful, was followed by others to the number of eighteen.

Shortly after the appearance of the Provinciales, on the 24th of May 1656, occurred the miracle of the Holy Thorn, a fragment of the crown of Christ preserved at Port Royal, which cured the little Marguerite Perier of a fistula lacrymalis. The Jesuits were much mortified by this Jansenist miracle, which, as it was officially recognized, they could not openly deny. Pascal and his friends rejoiced in proportion. The details of his later years after this incident are somewhat scanty. For years before his death we hear only of acts of charity and of, as it seems to modern ideas, extravagant asceticism. Thus Mme. Perier tells us that he disliked to see her caress her children, and would not allow the beauty of any woman to be talked of in his presence.

What may be called his last illness began as early as 1658, and as the disease progressed it was attended with more and more pain, chiefly in the head. In June 1662, having given up his own house to a poor family who were suffering from smallpox, he went to his sister's house to be nursed, and never afterwards left it. His state was, it seems, mistaken by his physicians, so much so that the offices of the Church were long put off. He was able, however, to receive the Eucharist, and soon afterwards died in convulsions on the 19th of August. A post mortem examination was held, which showed not only grave derangement in the stomach and other organs, but a serious lesion of the brain.

Eight years after Pascal's death appeared what purported to be his Pensйes, and a preface by his nephew Perier gave the world to understand that these were fragments of a great projected apology for Christianity which the author had, in conversation with his friends, planned out years before. The editing of the book was peculiar. It was submitted to a committee of influential jansenists, with the duc de Roannez at their head, and, in addition, it bore the imprimatur of numerous unofficial approvers who testified to its orthodoxy.

It does not appear that there was much suspicion of the garbling which had been practiced -- garbling not unusual at the time, and excused in this case by the fact of a lull in the troubles of Port Royal and a great desire on the part of its friends to do nothing to disturb that lull. But as a matter of fact no more entirely factitious book ever issued from the press. The fragments which it professed to give were in themselves confused and incoherent enough, nor is it easy to believe that they all formed part of any such single and coherent design as that referred to above. But the editors omitted, altered, added, separated, combined and so forth entirely at their pleasure, actually making some changes which seem to have been thought improvements of style.

This rifacimento remained the standard text with a few unimportant additions for nearly two centuries, except that, by a truly comic revolution of public taste, Condorcet in 1776 published, after study of the original, which remained accessible in manuscript, another garbling, conducted this time in the interests of unorthodoxy. It was not until 1842 that Victor Cousin drew attention to the absolutely untrustworthy condition of the text, nor until 1844 that A. P. Faugиre edited that text from the manuscript in something like a condition of purity, though, as subsequent editions have shown, not with absolute fidelity.

But even in its spurious condition the book had been recognized as remarkable and almost unique. Its contents, as was to be expected, are of a very chaotic character -- of a character so chaotic indeed that the reader is almost at the mercy of the arrangement, perforce an arbitrary arrangement, of the editors. But the subjects dealt with concern more or less all the great problems of thought on what may be called the theological side of metaphysics -- the sufficiency of reason, the trustworthiness of experience, the admissibility of revelation, free will, foreknowledge, and the rest.

The peculiarly disjointed and fragmentary condition of the sentiments expressed by Pascal aggravates the appearance of universal doubt which is present in the Pensйes, just as the completely unfinished condition of the work, from the literary point of view, constantly causes slighter or graver doubts as to the actual meaning which the author wished to express. Accordingly the Pensйes have always been a favorite exploring ground, not to say a favorite field of battle, to persons who take an interest in their problems. Speaking generally, their tendency is towards the combating of skepticism by a deeper skepticism, or, as Pascal himself calls it, Pyrrhonism, which occasionally goes the length of denying the possibility of any natural theology. Pascal explains all the contradictions and difficulties of human life and thought by the doctrine of the Fall, and relies on faith and revelation alone to justify each other.

Excluding here his scientific attainments, Pascal presents himself for comment in two different lights, the second of which is, if the expression be permitted, a composite one. The first exhibits him as a man of letters, the second as a philosopher, a theologian, and simply a man, for in no one is the color of the theology and the philosophy more distinctly personal. Yet his character as a man is not very distinct. The accounts of his sister and niece have the defect of all hagiology; they are obviously written rather with a view to the ideas and the wishes of the writers than with a view to the actual and absolute personality of the subject. Except from these interesting but somewhat tainted sources, we know little or nothing about him. Hence conjecture, or at least inference, must always enter largely into any estimate of Pascal, except a purely literary one.

On that side, fortunately, there is no possibility of doubt or difficulty to any competent inquirer. The Provincial Letters are the first example of French prose which is at once considerable in bulk, varied and important in matter, perfectly finished in form. They owe not a little to Descartes, for Pascal's indebtedness to his predecessor is unquestionable from the literary side, whatever may be the case with the scientific. But Descartes had had neither the opportunity, nor the desire, nor probably the power, to write anything of the literary importance of the Provinciales.

The first example of polite controversial irony since Lucian, the Provinciales have continued to be the best example of it during more than two centuries in which the style has been sedulously practiced, and in which they have furnished a model to generation after generation. The unfailing freshness and charm of the contrast between the importance, the gravity, in some cases the dry and abstruse nature, of their subjects, and the lightness, sometimes almost approaching levity in its special sense, of the manner in which these subjects are attacked is a triumph of literary art of which no familiarity dims the splendor, and which no lapse of time can ever impair.

Nor perhaps is this literary art really less evident in the Pensйes, though it is less clearly displayed, owing to the fragmentary or rather chaotic condition of the work, and partly also to the nature of the subject. The vividness and distinction of Pascal's phrase, his singular faculty of inserting without any loss of dignity in the gravest and most impassioned meditation what may be almost called quips of thought and diction, the intense earnestness of meaning weighting but not confusing the style, all appear here.

No such positive statements as these are, however, possible as to the substance of the Pensйes and the attitude of their author. Hitherto the widest differences have been manifested in the estimate of Pascal's opinions on the main questions of philosophy, theology and human conduct. He has been represented as a determined apologist of intellectual orthodoxy animated by an almost fanatical "hatred of reason", and possessed with a purpose to overthrow the appeal to reason; as a skeptic and pessimist of a far deeper dye than Montaigne, anxious chiefly to show how any positive decision on matters beyond the range of experience is impossible; as a nervous believer clinging to conclusions which his clearer and better sense showed to be indefensible; as an almost ferocious ascetic and paradoxer affecting the credo quia impossibile in intellectual matters and the odi quia amabile in matters moral and sensuous; as a wanderer in the regions of doubt and belief, alternately bringing a vast though vague power of thought and an unequalled power of expression to the expression of ideas incompatible and irreconcilable.

An unbiased study of the scanty facts of his history, and of the tolerably abundant but scattered and chaotic facts of his literary production, ought to enable any one to steer clear of these exaggerations, while admitting at the same time that it is impossible to give a complete and final account of his attitude towards the riddles of this world and others. He certainly was no mere advocate of orthodoxy; he as certainly was no mere victim of terror at skepticism; least of all was he a freethinker in disguise. He appears, as far as can be judged from the fragments of his Pensйes, to have seized firmly and fully the central idea of the difference between reason and religion.

Where the difficulty rises respecting him is that most thinkers since his day, who have seen this difference with equal clearness, have advanced from it to the negative side, while he advanced to the positive. In other words, most men since his day who have not been contented with a mere concordat, have let religion go and contented themselves with reason. Pascal, equally discontented with the concordat, held fast to religion and continued to fight out the questions of difference with reason. Surveying these positions, we shall not be astonished to find much that is surprising and some things that are contradictory in Pascal's utterances on "les grands sujets."

The influence exercised on him by Montaigne is the one fact regarding him which has not been and can hardly be exaggerated, and his well-known Entretion with Sacy on the subject (the restoration of which to its proper form is one of the most valuable results of modern criticism) leaves no doubt possible as to the source of his Pyrrhonian method. But it is impossible for anyone who takes Pascal's Pensйes simply as he finds them in connection with the facts of Pascal's history to question his theological orthodoxy, understanding by theological orthodoxy the acceptance of revelation and dogma; it is equally impossible for any one in the same condition to declare him absolutely content with dogma and revelation. It is of the essence of an active mind like Pascal's to explore and state all the arguments which make for or make against the conclusion it is investigating.

To sum up, the Pensйes are excursions into the great unknown made with a full acknowledgment of the greatness of that unknown. From the point of view that belief and knowledge, based on experience or reasoning, are separate domains with an unexplored sea between and round them, Pascal is perfectly comprehensible, and he need not be taken as a deserter from one region to the other. To those who hold that all intellectual exercise outside the sphere of religion is impious or that all intellectual exercise inside that sphere is futile, he must remain an enigma.

Pascal as Natural Philosopher and Mathematician. Great as is Pascal's reputation as a philosopher and man of letters, it may be fairly questioned whether his claim to be remembered by posterity as a mathematician and physicist is not even greater. In his two former capacities all will admire the form of his work, while some will question the value of his results; but in his two latter capacities no one will dispute either. He was a great mathematician in an age which produced Descartes, Fermat, Huygens, Wallis and Roberval. There are wonderful stories on record of his precocity in mathematical learning, which is sufficiently established by the well-attested fact that he had completed before he was sixteen years of age a work on the conic sections, in which he had laid down a series of propositions, discovered by himself, of such importance that they may be said to form the foundations of the modern treatment of that subject.

Owing partly to the youth of the author, partly to the difficulty in publishing scientific works in those days, and partly no doubt to the continual struggle on his part to devote his mind to what appeared to his conscience more important labor, this work (like many others by the same master hand) was never published. We know something of what it contained from a report by Leibniz, who had seen it in Paris, and from a summary of its results published in 1640 by Pascal himself, under the title Essai pour les coniques. The method which he followed was that introduced by his contemporary Girard Desargues, viz. the transformation of geometrical figures by conical or optical projection. In this way he established the famous theorem that the intersections of the three pairs of opposite sides of a hexagon inscribed in a conic are collinear. This proposition, which he called the mystic hexagram, he made the keystone of his theory; from it alone he deduced more than 400 corollaries, embracing, according to his own account, the conics of Apollonius, and other results innumerable.

Pascal also distinguished himself by his skill in the infinitesimal calculus, then in the embryonic form of Cavalieri's method of indivisibles. The cycloid was a famous curve in those days; it had been discussed by Galileo, Descartes, Fermat, Roberval and Torricelli, who had in turn exhausted their skill upon it. Pascal solved the hitherto refractory problem of the general quadrature of the cycloid, and proposed and solved a variety of others relating to the center of gravity of the curve and its segments, and to the volume and center of gravity of solids of revolution generated in various ways by means of it.

He published a number of these theorems without demonstration as a challenge to contemporary mathematicians. Solutions were furnished by Wallis, Huygens, Wren and others; and Pascal published his own in the form of letters from Amos Dettonville (his assumed name as challenger) to Pierre de Carcavy. There has been some discussion as to the fairness of the treatment accorded by Pascal to his rivals, but no question of the fact that his initiative led to a great extension of our knowledge of the properties of the cycloid, and indirectly hastened the progress of the differential calculus.

In yet another branch of pure mathematics Pascal ranks as a founder. The mathematical theory of probability and the allied theory of the combinatorial analysis were in effect created by the correspondence between Pascal and Fermat, concerning certain questions as to the division of stakes in games of chance, which had been propounded to the former by the gaming philosopher De Mйrй. A complete account of this interesting correspondence would surpass our present limits; but the reader may be referred to Todhunter's History of the Theory of Probability (Cambridge and London, 1865), pp. 7-21. It appears that Pascal contemplated publishing a treatise De aleae geometria; but all that actually appeared was a fragment on the arithmetical triangle (Traitй du triangle arithmetique, "Properties of the Figurate Numbers"), printed in 1654, but not published until 1665, after his death.

Pascal's work as a natural philosopher was not less remarkable than his discoveries in pure mathematics. His experiments and his treatise (written before 1651, published 1663) on the equilibrium of fluids entitle him to rank with Galileo and Simon Stevin as one of the founders of the science of hydrodynamics. The idea of the pressure of the air and the invention of the instrument for measuring it were both new when he made his famous experiment, showing that the height of the mercury column in a barometer decreases when it is carried upwards through the atmosphere. This experiment was made by himself in a tower at Paris, and was carried out on a grand scale under his instructions by his brother-in-law Florin Pйrier on the Puy de Dфme in Auvergne. Its success greatly helped to break down the old prejudices, and to bring home to the minds of ordinary men the truth of the new ideas propounded by Galileo and Torricelli.

Whether we look at his pure mathematical or at his physical researches we receive the same impression of Pascal; we see the strongest marks of a great original genius creating new ideas, and seizing upon, mastering, and pursuing farther everything that was fresh and unfamiliar in his time. We can still point to much in exact science that is absolutely his; and we can indicate infinitely more which is due to his inspiration.

Father: Étienne Pascal (judge, b. 1588, d. 24-Sep-1651)

Mother: Antoinette Bégon (d. 1626)

Sister: Gilberte (b. 3-Jan-1620)

Sister: Jacqueline Pascal (Catholic nun, b. 4-Oct-1625, d. 4-Oct-1661)

Nouvelles expйriences touchant le Vide (1647)

Lettres escrites а un Provincial (1656-57)

Traitй de l'йquilibre des liqueurs (1663)

Pensйes sur la Religion (1669)

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