Word Finder - pascal

definition

In the International System of Units, the derived unit of pressure and stress; one newton per square metre. Symbol: Pa.

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.

In that case, all who accept a revelation without professing to understand its content would require to be ranked as mystics; the fierce sincerity of Tertullian's credo quia ab-' surdum, Pascal's reconciliation of contradictions in Jesus Christ, and Bayle's half-sneering subordination of reason to faith would all be marks of this standpoint.

Twelve years after the Areopagitica appeared Pascal's Provincial Letters (1656-16J7).

Thus Nicomedes invented the conchoid; Diodes the cissoid; Dinostratus studied the quadratrix invented by Hippias; all these curves furnished solutions, as is also the case with the trisectrix, a special form of Pascal's limacon.

These are the two points on which Pascal's thought turns.

Daniel also wrote a by no means successful reply to Pascal's Provincial Letters, entitled Entretiens de Cleanthe provinciales (1694); two treatises on the Cartesian theory as to the intelligence of the lower animals, and other works.

It is, however, certain that in the autumn of 1654 Pascal's second "conversion" took place, and that it was lasting.

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.

Eight years after Pascal's death appeared what purported to be his Pensees, 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.

Accordingly the Pensees 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.

Hence conjecture, or at least inference, must always enter largely into any estimate of Pascal, except a purely literary one.

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 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.

Hitherto the widest differences have been manifested in the estimate of Pascal's opinions on the main questions of philosophy, theology and human conduct.

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 it is impossible for anyone who takes Pascal's 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.

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.

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.

There are few writers who are more in need than Pascal of being fully and competently edited.

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.

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.

Pascal also distinguished himself by his skill in the infinitesimal calculus, then in the embryonic form of Cavalieri's method of indivisibles.

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.

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.

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.

It appears that Pascal contemplated publishing a treatise De aleae geometria; but all that actually appeared was a fragment on the arithmetical triangle (Traite du triangle arithmetique, " 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.

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.

He also published a small work, The Christ of the Gospels and the Christ of History, in which the views of Renan on the gospel history were dealt with; a monograph on Pascal for Blackwood's Foreign Classics series; and a little work, Beginning Life, addressed to young men, written at an earlier period.

The first mentioned of these was severely criticised by Pascal in the fifth and sixth of his Provincial Letters, as tending to inculcate a loose system of morality.

Muller (1884 and 1893), C. Pascal, Studi sugli scrittori Latini (1900); see also Mommsen, History of Rome, bk.

Lang, Myth, Ritual and Religion (1899); C. Pascal, Studii di antichita e mitologia (1896), who sees in Lycaon a god of death honoured by human sacrifice; Ed.

Later satires in an epistolary form are Pascal's Provincial Letters, Swift's Drapier Letters, and the Letters of Junius.

Wissowa, Religion and Kultus der Romer, p. 355 seq.; monograph by Wackermann (Hanau, 1888); C. Pascal, Studii di antichita e mitologia (1896).

Rouse's The Year's Work in Classical Studies (1907); C. Pascal, Studii di antichitd e Mitologia (1896).

From the Fortune des Rougon to the Docteur Pascal (1893) there are some twenty novels in the Rougon-Macquart series, the second half of which includes the powerful novels Germinal (1885) and La Terre (1888).

Blaise Pascal determined the area of the section made by any line parallel to the base and the volumes and centres of gravity of the solids generated by revolving the curve about its axis and base.

Having established his priority, Pascal published his investigations, which occasioned a great sensation among his contemporaries, and Wallis was enabled to correct his methods.

Applying to the French classics the rigorous method used with regard to the texts of the middle ages, he published the of Pascal, revised with the original manuscript (1887-1889), and the Provinciales (1891), edited with notes.

As the results of his work in this line, we have, besides the Des Pensees de Pascal, 1842, Etudes sur les femmes et la societe du X VII e siècle, 1853.

He has sketched Jacqueline Pascal (1844), Madame de Longueville (18J3), the marquise de Sable (1854), the duchesse de Chevreuse (1856), Madame de Hautefort (1856).

Pascal, Repertorio di matematiche superiori, ii.

The results to which this Probabilism, applied with an earnest desire to avoid dangerous rigour, led in the 17th century were revealed to the world in the immortal Lettres provinciales of Pascal.

Vinet's Chrestomathie francaise (1829), his Etudes sur la litterature francaise au XIX me siècle (1849-51), and his Histoire de la litterature francaise au X VIII me siecle, together with his Etudes sur Pascal, Etudes sur les moralistes aux X VIme ei X VII me siecles, Histoire de la predication parmi les Reformes de France and other kindred works, gave evidence of a wide knowledge of literature, a sober and acute literary judgment and a distinguished faculty of appreciation.

If five points be given, Pascal's theorem affords a solution; if five tangents, Brianchon's theorem is employed.

The extraordinary advances made by him in this branch of knowledge were owing to his happy method of applying mathematical analysis to physical problems. As a pure mathematician he was, it is true, surpassed in profundity by more than one among his pupils and contemporaries; and in the wider imaginative grasp of abstract geometrical principles he cannot be compared with Fermat, Descartes or Pascal, to say nothing of Newton or Leibnitz.

In 1656 Arnauld was deprived of his degree, in spite of Pascal's Provincial Letters (1656-1657), begun in an attempt to save him (see Pascal; Casuistry).

Desargues has a special claim to fame on account of his beautiful theorem on the involution of a quadrangle inscribed in a conic. Pascal discovered a striking property of a hexagon inscribed in a conic (the hexagrammum mysticum); from this theorem Pascal is said to have deduced over 400 corollaries, including most of the results obtained by earlier geometers.