BLAISE PASCAL (1623-1662), was born at Clermont Ferrand on the 19th June 1623. His father was Étienne Pascal, president of the Court of Aids at Clermont; his mother's name was Antoinette Bégon. The Pascal family were Auvergnats by extraction as well as residence, and they had for many generations held posts in the civil service. They were ennobled by Louis XI. in 1478, but, as in many other cases, no attempt seems to have been made to assume the privileged particle de. The earliest anecdote of Pascal is a singular story recorded by his niece, Marguerite Perier (the heroine of the Holy Thorn miracle), 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 (the exact date is differently stated), 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 mother having been already dead for some time, Étienne Pascal the father gave up his official post at Clermont, and betook himself to Paris for the education of his children and for his own indulgence in scientific society. 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. How, purposely kept from books, he worked out the more elementary problems of geometry for himself; how at sixteen he wrote a treatise on conic sections which Descartes refused to believe in except as the work of a master and not of a student; how he wrote treatises on acoustics at twelve, and began elaborate calculating machines when he was still a boy,—are things dwelt upon in all biographies of him. In this notice his attainments in mathematical and physical science, except those which have some special connexion with his life and history, will be dealt with separately and later.

The Pascal family, some years after settling in Paris, had to go through a period of adversity. Etienne Pascal, on leaving Clermont, had bought certain of the Hotel de Ville rentes, almost the only regular investment open to Frenchmen at the time. Richelieu reduced the interest and the investors protested, Pascal amongst them. But the great cardinal did not understand such protests, and to escape the Bastille Pascal had to go into hiding. He was, according to the story, restored to favour owing to the good acting and graceful appearance of his daughter Jacqueline in a representation of Scudery's Amour Tyrannique before Richelieu. Indeed Jacqueline, who was only fourteen, herself gives the account in a pleasant letter which is extant, and which contains an allusion to her brother's mathematical prowess. Madame d'Aiguillon's intervention in the matter was perhaps as powerful as Jacqueline's acting, and Richelieu not only relieved Etienne Pascal from the necessity of keeping out of the way, but gave him (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 Corneille, and Blaise Pascal pursued his studies with such vehemence that he already showed signs of an injured constitution. Nothing, however, of importance happened till 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 neighbourhood who had come under the influence of St 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. One of the more immediate results of this conversion has rather shocked some modern admirers of Pascal, who forget that toleration, except of the Gallio kind, is an idea which had no place in men's minds in Pascal's day. He came into contact with a Capuchin known as Pere St Ange, but whose real name was Forton, and who seems to have entertained some speculative ideas on theological points which were not strictly orthodox. Thereupon Pascal with some of his friends lodged an information against the heretic with the representative of the archbishop of Rouen. There seems to have been no lack of zeal about the accusers, but the accused made no difficulty whatever in making profession of orthodoxy, and the judge appears to have been by no means anxious to push the matter home. No doubt Pascal was perfectly sincere, and like most of his contemporaries held the opinion attributed to a great English nonconformist contemporary of his, that, while it was very shocking that men who were in the right should not be tolerated, it was almost equally shocking that men who were in the wrong should be.

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, except when physicians positively forbade study, and probably sometimes when they did so forbid, indefatigable in his mathematical work. In 1647 he published his Nouvelles Experiences 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 Descartes to Pascal is given, which, like the other information on the relations of the two, gives 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 till eleven) and to take plenty of beef tea. But the relations of Pascal with Descartes belong chiefly to the scientific achievements of the former. He had, however, other relations, both domestic and miscellaneous, which had nothing to do with science. 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 at the date above mentioned returned to Paris with the dignity of counsellor of state (his functions at Rouen having ceased), disapproved of the plan, and took both brother and sister to Clermont. Pascal stayed in Auvergne for the greater part of two years, but next to nothing is known of what he did there. Flechier, 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 who was not indifferent to society, but whose aptitude both for society and study was affected by weak health and the horse-doctoring of the time. He, his sister, and their father returned to Paris in the late autumn of 1650, and in September of the next year Etienne 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. Perhaps this difference, but more probably the mere habitual use of the well-known dialect of Port Royal, led Jacqueline to employ in reference to her brother expressions which have led biographers into most unnecessary excursions of fancy. For these they have seemed to find further warrant in similar phrases used by the Periers, mother and daughter. It has 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 Due de Roannez and others. His Discours sur les Passions de l'Amour, a striking and characteristic piece, only recently discovered and printed, has also been assigned to this period, and has been supposed to indicate a hopeless passion for Charlotte de Roannez, the duke's sister. It cannot be too decidedly said that all this is sheer romancing. The extant letters of Pascal to the lady show no trace of any affection (stronger than friendship) between them. As to Pascal's worldly life, it might be thought that only the completest ignorance of the usual dialect of the. stricter religious sects and societies (and it may be added of Port Royal in particular) could induce any one to lay much stress on that. A phrase of Jacqueline's about the " horribles attaches " which bound her brother to the world may pair off with hundreds of similar expressions from Bunyan downwards. 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. Madame 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 late and more than doubtful tradition (due to the Abbe 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 November 23, 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.

But, whatever may have been the immediate cause of Pascal's conversion and (for a time) domestication at Port Royal, it certainly had no evil effect on his intellectual or literary powers. Indeed, if he had been drowned at Neuilly he would hardly be thought of now as anything but an extraordinarily gifted man of science. It must also 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 the most ample and remarkable return that any man of letters ever paid to any institution. At the end of 1655 Arnauld, the chief light of Port Royal, was condemned by the Sorbonne for heretical doctrine in a letter which he had published on the question of the famous five propositions attributed to Jansen, and, as much was made of this condemnation, it was thought important by the Jansenist and Port Royal party that steps should be taken to disabuse the popular mind on the whole controversy. 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 Provincial Letters (properly Lettres Ecrites par Louis de Montalte à un Provincial de ses Amis) was written in a few days, or, less probably, in a day. It was printed on the 23d January 1656, and, being immensely popular and successful, was followed by others to the number of eighteen. The method and facts may have been partly taken from a book on the moral theology of the Jesuits published some years earlier, and attributed in part at least to Arnauld.

In the Provinciales Pascal, who it must be remembered published under a strict incognito, denies that he belongs to Port Royal, and in fact, though during the last years of his life he was wholly devoted to its interests, he was never a regular resident there, and usually abode in his own house at Paris. Shortly after the appearance of the Provinciales, on May 24, 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. But the details of his later years after this incident are somewhat scanty, and as recorded by his sister and niece they tell of increasing ill health, and of ascetic practices and beliefs increasing still more. One curious incident, contrasting equally with this state of things and with Pascal's studious character and renown, is what Madame Perier calls "l'affaire des carrosses," a scheme of the Due de Roannez and others for running omnibuses in Paris, which was actually carried out, of which Pascal was in some sort manager, and from which he derived some profit. This, however, is an exception. Otherwise, for years before his death, we hear only of acts of charity and of, as it seems to modern ideas, extravagant asceticism. Thus Madame 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, after which year he never seems to have enjoyed even tolerable health, 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 small-pox, and being unwilling that his sister should expose herself to infection, he went to her house to be nursed, and never afterwards left it. His state was, it seems, mistaken by his physicians, who to the last maintained that there was little danger— 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 August 19th. 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, in a small volume, the book which has given most trouble to all students of Pascal, and most pleasure to some of them. It purported to be Pascal's Pensées, 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 Due 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 practised,—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. As an instance of their anxiety to avoid offence, it may be noticed that they rejected, apparently as too outspoken, Madame Perier's invaluable life of her brother, which was written to accompany the second edition of the Pensées, but did not actually appear with them till 1684. 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 till 1842 that Victor Cousin drew attention to the absolutely untrustworthy condition of the text, nor till 1844 that M. Faugére edited that text from the MS. 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 Pensées, just as the completely unfinished condition, from the literary point of view, of the work constantly causes slighter or graver doubts as to the actual meaning which the author wished to express. Accordingly the Pensées have always been a favourite exploring ground, not to say a favourite field of battle, to persons who take an interest in their problems. Speaking generally, their tendency is towards the combating of scepticism by a deeper scepticism, 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. Comparison of the Pensées with the Provinciales is, considering the radical differences of state (the one being a finished work deliberately issued from the master's hands, the other not even a rough draught, scarcely even "heads" or "outlines," but a collection of loose and uncorrected notes settled neither as to the exact form of each nor as to the relation of each to any whole), impossible. But it may be said that no one can properly perceive how great a man of letters Pascal was from the Pensées alone, and that no one can perceive how deep if not wide a thinker he was from the Provinciales alone. An absolute preference of either argues a certain onesidedness in the relative estimate of matter and form. The wiser mind distinctly prefers both, and recognizes that if either were lacking the greatness of Pascal would fail to be perceived, or at least to be perceived fully.

Excluding his scientific attainments, which, as has been noted above, will be the subject of separate notice, 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 a man. If this last combination seems to be audacious or clumsy, it can only be said that in hardly any thinker are theological thoughts, and thoughts more strictly to be called philosophical or metaphysical, so intimately, so inextricably blended as in Pascal, and that in none is the colour of the theology and the philosophy more distinctly personal. This latter fact adds to the difficulty of the problem ; for, though Pascal has written not a little, and though a vast amount has been written about him, it cannot be said that his character as a man, not a writer, is very distinct.

The accounts of his sister and niece have the defect of all hagiology (to use the term with no disrespectful intention) ; 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 unanimity of eulogy as to the style of this wonderful book has sometimes tempted foreigners, who feel or affect to feel an inability to judge for themselves, into a kind of scepticism for which there is absolutely no ground. 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 practised, and in which they have furnished a model to generation after generation without being surpassed by any of the works to which they have shown the way. 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 splendour, and which no lapse of time, affecting as that lapse has already done to a great extent the attraction of the subjects themselves, can ever impair. The tools of phrase and diction by which this triumph is achieved were not in all cases of Pascal's invention—Descartes and Corneille had been beforehand with him to some extent—but many of them were actually new, and all were newly and more skilfully applied. Nor perhaps is this literary art really less evident in the Pensées, though it is less clearly displayed, owing to the fragmentary or rather chaotic condition of the work, and partly also to the fact that the subject here for many readers and in many places claims attention almost to the disregard of the form. The vividness and distinction of Pascal's phrase, his singular faculty of inserting in the gravest and most impassioned meditation what may be almost called quips of thought and diction without any loss of dignity, the intense earnestness of meaning weighting but not confusing the style, all appear here, and some of them appear as they have no chance of appearing in at least the earlier Provinciales.

No such positive statements as these are, however, possible as to the substance of the Pensées and the attitude of their author towards "les grands sujets." In the space and circumstances of the present notice nothing more can be attempted than a summary of the opinions hitherto advanced on the subject, and an indication of the results which may seem most probable to unprejudiced inquirers who possess a fair knowledge of and interest in the problems concerned. 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 sceptic 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. In these as in all other matters the first requisite seems to be to clear the mind of prepossession and commonplace. It has already been hinted that far too much stress may be laid on the description of Pascal by his family as a converted sinner, and it may be added that at least as much stress has been laid on the other side on the notion of him as of a clear-headed materialist and expert in positive science, who by ill-health, overwork, and family influence was persuaded to adopt, half against his will, supernaturalist opinions. An unbiassed 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 scepticism; least of all was he a freethinker in disguise. He appears, as far as can be judged from the fragments of his Pensées, to have seized much more firmly and fully than has been usual for two centuries at least 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. The emotion, amounting to passion, which he displays in conducting this campaign, and the superfluous energy of his debate on numerous points which, for instance, such a man as Berkeley was content to leave in the vague must be traced to temperament, aggravated no doubt by his extreme intellectual activity, by ill health, and by his identification comparatively late in life and under peculiar circumstances with a militant and so to speak sectarian form of religious or ecclesiastical belief. 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." But the very worst method that can be taken for dealing with these contradictions is to assume, as his critics on one side too often do, that so clever a man as Pascal could not possibly be a convinced acceptor of dogmatic Christianity, or to assume, as too many of his critics on the other do, that so pious and orthodox a man as Pascal could not entertain any doubts or see any difficulties in reference to dogmatic Christianity. He had taken to the serious contemplation of theological problems comparatively late; for the Rouen escapade noted above is merely a specimen of the kind of youthful intolerance which counts for nothing when justly viewed. 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 Entretien with Sacy on the subject (the restoration of which to its proper form is one of the most valuable results of recent criticism) leaves no doubt possible as to the source of his "Pyrrhonian " method. The atmosphere of somewhat heated devotion in which he found himself when he retired to Port Royal must naturally count for something in the direction and expression of his thoughts ; his broken health for something more. It is unfortunately usual with societies like Port Royal to generate a kind of mist and mirage which deceives and distorts even the keenest sight that looks through their eyes. But it is impossible for any one who takes Pascal's Pensées simply as he finds them in connexion 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. Excursions into the field beyond formularies were necessary to him, and he made them freely ; but there is no evidence that these excursions tempted him to remain outside, and it appears particularly erroneous to take his celebrated "wager" thoughts (the argument that, as another world and its liabilities, if accepted, imply no loss and much possible gain, they should be accepted) as an evidence of weakened belief or a descent from rational religion. It is of the essence of an active mind like Pascal's to explore and state all the arguments of whatever degree of goodness which make for or make against the conclusion it is investigating, and this certainly is neither the least obvious nor the weakest of the arguments which must have presented themselves to him.

In ecclesiastical questions as distinguished from theological Pascal appears to have been an ardent Jansenist, adopting without very much discrimination the stand-point of his friends and religious directors Sacy, Arnauld, Singlin, and others. In one point he went beyond them, boldly disputing the infallibility of the pope, and hinting not obscurely at the propriety of agitation against erroneous papal decisions. The Jansenists as a body could not muster courage to adopt this attitude, But it is not easy to discuss isolated points of this kind here ; indeed their discussion belongs more properly to the general subject of Jansenism, and the history of Port Royal.

To sum up, the interest and value of the Pensées is positively diminished if they are taken as gropings after self-satisfaction or feeble attempts at freethinking. They are excursions into the great unknown made with a full acknowledgment of the greatness of that unknown, but with no kind of desire for something more known than the writer's own standpoint. If to any one else they communicate such a desire that is not Pascal's fault ; and, if it seems to any one that without such a desire they could not have been indulged in, that comes mainly from an alteration of mental attitude, and from a want of familiarity with the mental attitude of Pascal's own time. 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.

There are few writers who are more in need than Pascal of being fully and competently edited. The chief nominally complete edition at present in existence is that of Bossut (1779, 5 vols., and since reprinted), which not only appeared before any attempt had been made to restore the true text of the Pensées, but is in other respects quite inadequate. The edition of Lahure, 1858, is not much better, though the Pensées appear in their more genuine form. An edition has been long promised for the excellent collection of Les Grands Écrivains de la France; it has been understood to be under the charge of M. Faugére. Meanwhile, with the exception of the Provinciales (of which there are numerous editions, no one much to be preferred to any other, for the text is undisputed and the book itself contains almost all the exegesis of its own contents necessary), Pascal can be read only at a disadvantage. There are four chief editions of the true Pensées: that of M. Faugére (1844), the editio princeps; that of M. Havet (1852, 1867, and 1881), on the whole the best; that of M. Victor Rochet (1873), good, but arranged and edited with the deliberate intention of making Pascal first of all an orthodox apologist; and that of M. Molinier (1877-79), a carefully edited and interesting text, the important corrections of which have been introduced into M. Havet's last edition. Unfortunately, none of these can be said to be exclusively satisfactory. The minor works must chiefly be sought in Bossut or reprints of him. Works on Pascal are innumerable: Sainte-Beuve's Port Royal, Cousin's writings on Pascal and his Jacqueline Pascal, and the essays of the editors of the Pensées just mentioned are the most noteworthy. Principal Tulloch has contributed a useful little monograph to the series of Foreign Classics for English Readers (Edinburgh and London, 1878). (G. SA.)

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 labour, this work (like many others by the same master-hand) was never published. We know something of what it contained from a report by Leibnitz, who had seen it in Paris, and from a resume 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 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 four hundred corollaries, embracing, according to his own account, the conies 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 centre of gravity of the curve and its segments, and to the volume and centre 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 M. Cercavi. 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 Mere. 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 ("Properties of the Figurate Numbers") printed in 1654, but not published till 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 1653, published 1662) on the equilibrium of fluids entitle him to rank with Galileo and Stevinus 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 in the first place by himself in a tower at Paris, and was afterwards carried out on a grand scale under his instructions by his brother-in-law Perier on the Puy de Dome 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. After the lapse of more than two hundred years, 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. (G. CH.)






The above article was written by two authors:
-- 1st section: Pascal's Life and his Religious and Philosophical Beliefs and Works
George Saintsbury, M.A.

and

-- 2nd section: Pascal as Natural Philosopher and Mathematician
Prof. George Chrystal.