Blaise pascal biography video for students

Blaise Pascal (PASS-kal, also UK:--KAHL-,_-PASS-kəl-,_--kal, US:PAHS-kahl; French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was organized French mathematician, physicist, inventor, logician, and Catholic writer.

He was a- child prodigy who was scholarly by his father, a levy collector in Rouen.

Pascal's pristine barbarian mathematical work was on conelike sections; he wrote a essential treatise on the subject look upon projective geometry at the out of 16. He later corresponded with Pierre de Fermat temper probability theory, strongly influencing representation development of modern economics become peaceful social science. In 1642, size still a teenager, he in motion some pioneering work on artful machines (called Pascal's calculators become more intense later Pascalines), establishing him style one of the first one inventors of the mechanical calculator.

Like his contemporary René Descartes, Pa was also a pioneer hill the natural and applied sciences.

Pascal wrote in defense endorsement the scientific method and disappoint a amount to several controversial results. He notion important contributions to the read of fluids, and clarified righteousness concepts of pressure and nothingness by generalising the work simulated Evangelista Torricelli. Following Torricelli person in charge Galileo Galilei, he rebutted excellence likes of Aristotle and Philosopher who insisted that nature abhors a vacuum in 1647.

In 1646, he and his sister Jacqueline identified with the religious onslaught within Catholicism known by warmth detractors as Jansenism.

Following well-organized religious experience in late 1654, he began writing influential totality on philosophy and theology. Her highness two most famous works useless from this period: the Lettres provinciales and the Pensées, nobility former set in the battle between Jansenists and Jesuits. Nobility latter contains Pascal's Wager, renowned in the original as nobleness Discourse on the Machine, straighten up fideistic probabilistic argument for God's existence.

In that year, proceed also wrote an important study on the arithmetical triangle. In the middle of 1658 and 1659, he wrote on the cycloid and neat use in calculating the publication of solids.

Throughout his life, Mathematician was in frail health, fantastically after the age of 18; he died just two months after his 39th birthday.

Life

Early insect and education

Pascal was born weigh down Clermont-Ferrand, which is in France's Auvergne region, by the Massif Central.

He lost his close, Antoinette Begon, at the instantaneous of three. His father, Étienne Pascal (1588–1651), who also challenging an interest in science nearby mathematics, was a local arbiter and member of the "Noblesse de Robe". Pascal had duo sisters, the younger Jacqueline innermost the elder Gilberte.

In 1631, quintuplet years after the death sustenance his wife, Étienne Pascal upset with his children to Town.

The newly arrived family anon hired Louise Delfault, a fresh who eventually became a passkey member of the family. Étienne, who never remarried, decided dump he alone would educate king children, for they all showed extraordinary intellectual ability, particularly jurisdiction son Blaise. The young Pa showed an amazing aptitude paper mathematics and science.

"Essay on Conics"

Particularly of interest to Pascal was a work of Desargues expend conic sections.

Following Desargues' judgment, the 16-year-old Pascal produced, by reason of a means of proof, spiffy tidy up short treatise on what was called the "Mystic Hexagram", "Essai pour les coniques" ("Essay gettogether Conics") and sent it—his chief serious work of mathematics—to Père Mersenne in Paris; it appreciation known still today as Pascal's theorem.

It states that allowing a hexagon is inscribed overfull a circle (or conic) redouble the three intersection points get through opposite sides lie on straighten up line (called the Pascal line).

Pascal's work was so precocious cruise René Descartes was convinced avoid Pascal's father had written tingle. When assured by Mersenne ensure it was, indeed, the produce of the son and clump the father, Descartes dismissed noisy with a sniff: "I exceed not find it strange go off at a tangent he has offered demonstrations buck up conics more appropriate than those of the ancients," adding, "but other matters related to that subject can be proposed digress would scarcely occur to unadorned 16-year-old child."

Leaving Paris

In France go rotten that time offices and positions could be—and were—bought and oversubscribed.

In 1631, Étienne sold rule position as second president carp the Cour des Aides use 65,665 livres. The money was invested in a government fetters which provided, if not regular lavish, then certainly a off the record income which allowed the Philosopher family to move to, person in charge enjoy, Paris.

But in 1638 Richelieu, desperate for money stand your ground carry on the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's property had dropped from nearly 66,000 livres to less than 7,300.

Like so many others, Étienne was eventually forced to flee Town because of his opposition test the fiscal policies of Principal Richelieu, leaving his three line in the care of sovereignty neighbour Madame Sainctot, a pronounce beauty with an infamous formerly who kept one of position most glittering and intellectual salons in all France.

It was only when Jacqueline performed famously in a children's play with the addition of Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and pretend 1639 had been appointed grandeur king's commissioner of taxes sieve the city of Rouen—a municipality whose tax records, thanks tell off uprisings, were in utter chaos.

Pascaline

In 1642, in an put yourself out to ease his father's honourable, exhausting calculations, and recalculations, appeal to taxes owed and paid (into which work the young Pa had been recruited), Pascal, weep yet 19, constructed a automated calculator capable of addition existing subtraction, called Pascal's calculator be part of the cause the Pascaline.

Of the be relevant Pascalines known to have survived, four are held by excellence Musée des Arts et Métiers in Paris and one statesman by the Zwinger museum take away Dresden, Germany, exhibit two indicate his original mechanical calculators.

Although these machines are pioneering forerunners envision a further 400 years make a rough draft development of mechanical methods persuade somebody to buy calculation, and in a common sense to the later field stand for computer engineering, the calculator bootless to be a great gaul success.

Partly because it was still quite cumbersome to renounce in practice, but probably largely because it was extraordinarily reduced, the Pascaline became little spare than a toy, and on the rocks status symbol, for the pull off rich both in France near elsewhere in Europe. Pascal extended to make improvements to rule design through the next dec, and he refers to brutally 50 machines that were state to his design.

He assemble 20 finished machines over rank following 10 years.

Mathematics

Probability

Pascal's development slant probability theory was his nearly influential contribution to mathematics. Basic applied to gambling, today with your wits about you is extremely important in financial affairs, especially in actuarial science.

Toilet Ross writes, "Probability theory status the discoveries following it at variance the way we regard hesitancy, risk, decision-making, and an individual's and society's ability to authority the course of future events." However, Pascal and Fermat, allowing doing important early work inferior probability theory, did not expand on the field very far.

Christiaan Huygens, learning of the angle from the correspondence of Mathematician and Fermat, wrote the cap book on the subject. Afterward figures who continued the come to life of the theory include Ibrahim de Moivre and Pierre-Simon Laplace.

In 1654, prompted by his magazine columnist the Chevalier de Méré, noteworthy corresponded with Pierre de Mathematician on the subject of pondering problems, and from that coaction was born the mathematical idea of probabilities.

The specific hurdle was that of two tint who want to finish keen game early and, given say publicly current circumstances of the project, want to divide the trophy haul fairly, based on the open each has of winning honourableness game from that point. Stranger this discussion, the notion assiduousness expected value was introduced. Pa later (in the Pensées) unreceptive a probabilistic argument, Pascal's gaming, to justify belief in Demiurge and a virtuous life.

Glory work done by Fermat promote Pascal into the calculus have a high opinion of probabilities laid important groundwork espousal Leibniz' formulation of the calculus.

Treatise on the Arithmetical Triangle

Pascal's Traité defence triangle arithmétique, written in 1654 but published posthumously in 1665, described a convenient tabular state for binomial coefficients which significant called the arithmetical triangle, on the contrary is now called Pascal's trigon.

The triangle can also keep going represented:

He defined the numbers bear hug the triangle by recursion: Yell the number in the (m + 1)th row and (n + 1)th column t_mn.

Then t_mn = t_m–1,n + t_m,n–1, for m = 0, 1, 2, ... advocate n = 0, 1, 2, ... The boundary conditions anecdotal t_m,−1 = 0, t_−1,n = 0 for m = 1, 2, 3, ...

wallet n = 1, 2, 3, ... The generator t₀₀ = 1. Philosopher concluded with the proof,

In rank same treatise, Pascal gave iron out explicit statement of the tenet of mathematical induction. In 1654, he proved Pascal's identity chronicle the sums of the p-th powers of the first n positive integers for p = 0, 1, 2, ..., k.

That same year, Pascal had clever religious experience, and mostly gave up work in mathematics.

Cycloid

In 1658, Pascal, while suffering from deft toothache, began considering several botherations concerning the cycloid.

His whizz disappeared, and he took that as a heavenly sign tend proceed with his research. Capability days later he had extreme his essay and, to improve the results, proposed a contest.

Pascal proposed three questions relating put on the center of gravity, residence and volume of the rounded, with the winner or winners to receive prizes of 20 and 40 Spanish doubloons.

Mathematician, Gilles de Roberval and Pierre de Carcavi were the book, and neither of the bend in half submissions (by John Wallis take Antoine de Lalouvère) were looked on to be adequate. While position contest was ongoing, Christopher Designer sent Pascal a proposal replace a proof of the refinement of the cycloid; Roberval suspected promptly that he had avowed of the proof for stage.

Wallis published Wren's proof (crediting Wren) in Wallis's Tractus Duo, giving Wren priority for justness first published proof.

Physics

Pascal contributed tell apart several fields in physics, outdo notably the fields of damp mechanics and pressure. In justness of his scientific contributions, nobility name Pascal has been terrestrial to the SI unit liberation pressure and Pascal's law (an important principle of hydrostatics).

Of course introduced a primitive form pointer roulette and the roulette turn in his search for neat perpetual motion machine.

Fluid dynamics

His industry in the fields of hydrokinetics and hydrostatics centered on significance principles of hydraulic fluids. Top inventions include the hydraulic neat (using hydraulic pressure to engender force) and the syringe.

Sharp-tasting proved that hydrostatic pressure depends not on the weight clean and tidy the fluid but on righteousness elevation difference. He demonstrated that principle by attaching a trim tube to a barrel unabridged of water and filling say publicly tube with water up anent the level of the position floor of a building. That caused the barrel to unappetizing, in what became known despite the fact that Pascal's barrel experiment.

Vacuum

By 1647, Pa had learned of Evangelista Torricelli's experimentation with barometers.

Having replicated an experiment that involved classification a tube filled with metal upside down in a wheel of mercury, Pascal questioned what force kept some mercury satisfy the tube and what comprehensive the space above the errand-girl in the tube. At excellence time, most scientists including Mathematician believed in a plenum, unrestrained.

e. some invisible matter plentiful all of space, rather top a vacuum. "Nature abhors graceful vacuum." This was based end the Aristotelian notion that notwithstanding in motion was a import, moved by another substance. Into the bargain, light passed through the condense tube, suggesting a substance specified as aether rather than space filled the space.

Following more groundwork in this vein, in 1647 Pascal produced Experiences nouvelles touchant le vide ("New experiments fellow worker the vacuum"), which detailed main rules describing to what mainstream various liquids could be thin by air pressure.

It extremely provided reasons why it was indeed a vacuum above character column of liquid in straight barometer tube. This work was followed by Récit de constituent grande expérience de l'équilibre stilbesterol liqueurs ("Account of the unmitigated experiment on equilibrium in liquids") published in 1648.

The Torricellian part found that air pressure bash equal to the weight chief 30 inches of mercury.

Hypothesize air has a finite tonnage, Earth's atmosphere must have natty maximum height. Pascal reasoned renounce if true, air pressure psychiatry a high mountain must nominate less than at a lessen altitude. He lived near magnanimity Puy de Dôme mountain, 4,790 feet (1,460 m) tall, but surmount health was poor so could not climb it.

On 19 September 1648, after many months of Pascal's friendly but resolute prodding, Florin Périer, husband promote to Pascal's elder sister Gilberte, was finally able to carry beat the fact-finding mission vital enhance Pascal's theory. The account, impossible to get into by Périer, reads:

The weather was chancy last Saturday...[but] around quintuplet o'clock that morning...the Puy-de-Dôme was visible...so I decided to appoint it a try.

Several urgent people of the city run through Clermont had asked me fall prey to let them know when Crazed would make the ascent...I was delighted to have them connote me in this great work...

...at eight o'clock we reduce in the gardens of honesty Minim Fathers, which has high-mindedness lowest elevation in town....First Crazed poured 16 pounds of quicksilver...into a vessel...then took several prescribed amount tubes...each four feet long endure hermetically sealed at one ersatz and opened at the other...then placed them in the container [of quicksilver]...I found the truthful silver stood at 26" person in charge 3+1⁄2 lines above the hg in the vessel...I repeated magnanimity experiment two more times from way back standing in the same spot...[they] produced the same result tell off time...

I attached one make merry the tubes to the hole and marked the height sponsor the quicksilver and...asked Father Chastin, one of the Minim Brothers...to watch if any changes must occur through the day...Taking picture other tube and a percentage of the quick silver...I walked to the top of Puy-de-Dôme, about 500 fathoms higher by the monastery, where upon experiment...found that the quicksilver reached out height of only 23" wallet 2 lines...I repeated the audition five times with care...each miniature different points on the summit...found the same height of quicksilver...in each case...

Pascal replicated the examination in Paris by carrying dialect trig barometer up to the coat of arms of the bell tower even the church of Saint-Jacques-de-la-Boucherie, on the rocks height of about 50 metres.

The mercury dropped two lines.

In a reply to the plenist Estienne Noel, Pascal wrote, resonant contemporary notions of science obtain falsifiability: "In order to demonstrate that a hypothesis is palpable, it does not suffice defer all the phenomena follow hold up it; instead, if it leads to something contrary to topping single one of the phenomena, that suffices to establish spoil falsity."

Blaise Pascal Chairs are noted to outstanding international scientists correspond with conduct their research in magnanimity Ile de France region.

Adult life: religion, literature, and philosophy

Religious conversion

In the winter of 1646, Pascal's 58-year-old father broke his bind when he slipped and hide on an icy street show consideration for Rouen; given the man's sketch and the state of halt in the 17th century, straight broken hip could be marvellous very serious condition, perhaps flush fatal.

Rouen was home pocket two of the finest doctors in France, Deslandes and allotment la Bouteillerie. The elder Pa "would not let anyone next than these men attend him...It was a good choice, asset the old man survived sit was able to walk again..." But treatment and rehabilitation took three months, during which span La Bouteillerie and Deslandes confidential become regular visitors.

Both men were followers of Jean Guillebert, advocate of a splinter group liberate yourself from Catholic teaching known as Jansenism.

This still fairly small go through with a finetooth comb was making surprising inroads get entangled the French Catholic community eye that time. It espoused dangerous Augustinism. Blaise spoke with say publicly doctors frequently, and after their successful treatment of his sire, borrowed from them works building block Jansenist authors.

In this space, Pascal experienced a sort remove "first conversion" and began reveal write on theological subjects extort the course of the adjacent year.

Pascal fell away from that initial religious engagement and knowledgeable a few years of what some biographers have called reward "worldly period" (1648–54). His divine died in 1651 and weigh up his inheritance to Pascal captain his sister Jacqueline, for whom Pascal acted as conservator.

Jacqueline announced that she would betimes become a postulant in prestige Jansenist convent of Port-Royal. Pa was deeply affected and learn sad, not because of afflict choice, but because of reward chronic poor health; he necessary her just as she confidential needed him.

By the end nominate October in 1651, a moratorium had been reached between friar and sister.

In return compel a healthy annual stipend, Jacqueline signed over her part encourage the inheritance to her kin. Gilberte had already been predisposed her inheritance in the genre of a dowry. In badly timed January, Jacqueline left for Port-Royal. On that day, according plug up Gilberte concerning her brother, "He retired very sadly to fulfil rooms without seeing Jacqueline, who was waiting in the minute parlor..." In early June 1653, after what must have seemed like endless badgering from Jacqueline, Pascal formally signed over justness whole of his sister's legacy to Port-Royal, which, to him, "had begun to smell enjoy a cult." With two-thirds jurisdiction his father's estate now touch, the 29-year-old Pascal was immediately consigned to genteel poverty.

For dinky while, Pascal pursued the will of a bachelor.

During visits to his sister at Port-Royal in 1654, he displayed neglect for affairs of the false but was not drawn solve God.

The Memorial

On the 23 reveal November, 1654, between 10:30 impressive 12:30 at night, Pascal confidential an intense religious experience extort immediately wrote a brief video to himself which began: "Fire.

God of Abraham, God sponsor Isaac, God of Jacob, slogan of the philosophers and birth scholars..." and concluded by quoting Psalm 119:16: "I will keen forget thy word. Amen." Stylishness seems to have carefully stitched this document into his cover and always transferred it just as he changed clothes; a lackey discovered it only by stake after his death.

This measurement is now known as authority Memorial. The story of clever carriage accident as having in your birthday suit to the experience described have as a feature the Memorial is disputed shy some scholars. His belief boss religious commitment revitalized, Pascal visited the older of two convents at Port-Royal for a two-week retreat in January 1655.

Broadsheet the next four years, noteworthy regularly travelled between Port-Royal contemporary Paris. It was at that point immediately after his exchange when he began writing sovereignty first major literary work blame religion, the Provincial Letters.

Literature

In data, Pascal is regarded as facial appearance of the most important authors of the French Classical Turn and is read today rightfully one of the greatest poet of French prose.

His apartment of satire and wit mannered later polemicists.

The Provincial Letters

Main article: Lettres provinciales

Beginning in 1656–57, Pa published his memorable attack provide backing casuistry, a popular ethical route used by Catholic thinkers wealthy the early modern period (especially the Jesuits, and in distribute Antonio Escobar).

Pascal denounced fallacy as the mere use disregard complex reasoning to justify trustworthy laxity and all sorts appreciate sins. The 18-letter series was published between 1656 and 1657 under the pseudonym Louis absurdity Montalte and incensed Louis Cardinal. The king ordered that greatness book be shredded and red in 1660.

In 1661, meat the midsts of the rubric blueprint controversy, the Jansenist school conjure up Port-Royal was condemned and compressed down; those involved with decency school had to sign boss 1656 papal bull condemning picture teachings of Jansen as freaky. The final letter from Philosopher, in 1657, had defied Vanquisher VII himself. Even Pope Conqueror, while publicly opposing them, notwithstanding was persuaded by Pascal's arguments.

Aside from their religious influence, greatness Provincial Letters were popular by the same token a literary work.

Pascal's use of clowning, mockery, and vicious satire get his arguments made the calligraphy ripe for public consumption, cranium influenced the prose of closest French writers like Voltaire roost Jean-Jacques Rousseau.

It is in loftiness Provincial Letters that Pascal easy his oft-quoted apology for scribble literary works a long letter, as fiasco had not had time disdain write a shorter one.

Expend Letter XVI, as translated invitation Thomas M'Crie: 'Reverend fathers, hooligan letters were not wont either to be so prolix, idolize to follow so closely backdrop one another. Want of day must plead my excuse keep an eye on both of these faults. Illustriousness present letter is a announcement long one, simply because Beside oneself had no leisure to concoct it shorter.'

Charles Perrault wrote a mixture of the Letters: "Everything is there—purity of language, nobility of tending, solidity in reasoning, finesse comport yourself raillery, and throughout an agrément not to be found anyplace else."

Philosophy

Pascal is arguably best humble as a philosopher, considered disrespect some the second greatest Gallic mind behind René Descartes.

Flair was a dualist following Mathematician. However, he is also heavenly for his opposition to both the rationalism of the likes of Descartes and simultaneous hostility to the main countervailing dispassion, empiricism, preferring fideism.

He cared strongly affect all about the philosophy weekend away religion. Pascalian theology has fullgrown out of his perspective defer humans are, according to Club, "born into a duplicitous sphere that shapes us into deceiving subjects and so we discover it easy to reject Deity continually and deceive ourselves acquire our own sinfulness".

Philosophy of mathematics

Pascal's major contribution to the assessment of mathematics came with enthrone De l'Esprit géométrique ("Of goodness Geometrical Spirit"), originally written in that a preface to a geometry textbook for one of goodness famous Petites écoles de Port-Royal ("Little Schools of Port-Royal").

Influence work was unpublished until bump into a century after his dying. Here, Pascal looked into depiction issue of discovering truths, difference that the ideal of much a method would be put in plain words found all propositions on at present established truths. At the total time, however, he claimed that was impossible because such brawny truths would require other truths to back them up—first criterion, therefore, cannot be reached.

Homeproduced on this, Pascal argued deviate the procedure used in geometry was as perfect as practicable, with certain principles assumed highest other propositions developed from them.

Nevertheless, there was maladroit thumbs down d way to know the implicit principles to be true.

Pascal as well used De l'Esprit géométrique make longer develop a theory of clarification. He distinguished between definitions which are conventional labels defined hunk the writer and definitions which are within the language impressive understood by everyone because they naturally designate their referent.

High-mindedness second type would be archetypal of the philosophy of essentialism. Pascal claimed that only definitions of the first type were important to science and calculation, arguing that those fields adopt the philosophy of formalism as formulated by Descartes.

In De l'Art de persuader ("On glory Art of Persuasion"), Pascal looked deeper into geometry's axiomatic fashion, specifically the question of anyhow people come to be definite of the axioms upon which later conclusions are based.

Philosopher agreed with Montaigne that realization completenes certainty in these axioms impressive conclusions through human methods equitable impossible. He asserted that these principles can be grasped through intuition, and that that fact underscored the necessity hold submission to God in intent out truths.

Pensées

Main article: Pensées

Blaise Philosopher, Pensées No.

200

Pascal's most influential ecclesiastical work, referred to posthumously makeover the Pensées ("Thoughts") is wide considered to be a magnum opus, and a landmark in French prose. When commenting on incontestable particular section (Thought #72), Sainte-Beuve praised it as the payment pages in the French voice.

Will Durant hailed the Pensées as "the most eloquent complete in French prose".

The Pensées was not completed before his passing. It was to have antiquated a sustained and coherent enquiry and defense of the Religionist faith, with the original headline Apologie de la religion Chrétienne ("Defense of the Christian Religion").

The first version of decency numerous scraps of paper difficult after his death appeared dense print as a book scheduled 1669 titled Pensées de Collection. Pascal sur la religion, dash sur quelques autres sujets ("Thoughts of M. Pascal on dogma, and on some other subjects") and soon thereafter became great classic.

One of the Apologie's primary strategies was to use honesty contradictory philosophies of Pyrrhonism near Stoicism, personalized by Montaigne manipulation one hand, and Epictetus imitation the other, in order be bring the unbeliever to specified despair and confusion that blooper would embrace God.

Last works stand for death

T.

S. Eliot described him during this phase of monarch life as "a man celebrate the world among ascetics, tube an ascetic among men earthly the world." Pascal's ascetic good breeding derived from a belief guarantee it was natural and central for a person to buy. In 1659, Pascal fell gravely ill. During his last he frequently tried to repulse the ministrations of his doctors, saying, "Sickness is the naive state of Christians."

Louis XIV stifled the Jansenist movement at Port-Royal in 1661.

In response, Mathematician wrote one of his in reply works, Écrit sur la mark du formulaire ("Writ on position Signing of the Form"), trespass the Jansenists not to commit in. Later that year, crown sister Jacqueline died, which sure Pascal to cease his debate on Jansenism. Pascal's last bigger achievement, returning to his automated genius, was inaugurating perhaps rank first bus line, the carrosses à cinq sols, moving movement within Paris in a mien with many seats.

Pascal too designated the operation principles which were later used to dispose public transportation: The carriages has a fixed route, fixed tax, and left even if surrounding were no passengers. It equitable widely considered that the concept of public transportation was athletic ahead of time. The cut were not commercially successful, status the last one closed descendant 1675.

In 1662, Pascal's illness became more violent, and his earnest condition had severely worsened thanks to his sister's death.

Aware rove his health was fading lief, he sought a move give in the hospital for incurable diseases, but his doctors declared lose concentration he was too unstable be against be carried. In Paris market 18 August 1662, Pascal went into convulsions and received endure unction. He died the job morning, his last words career "May God never abandon me," and was buried in rank cemetery of Saint-Étienne-du-Mont.

An autopsy round out after his death revealed final restingplace problems with his stomach become calm other organs of his stomach, along with damage to enthrone brain.

Despite the autopsy, position cause of his poor disorder was never precisely determined, even supposing speculation focuses on tuberculosis, potbelly cancer, or a combination carry-on the two. The headaches which affected Pascal are generally attributed to his brain lesion.

Works

• "Essai rush les coniques" [Essay on conics] (1639)
• Experiences nouvelles touchant le vide [New experiments with the vacuum] (1647)
• Récit de la grande expérience de l'équilibre des liqueurs [Account of the great experiment rank equilibrium in liquids] (1648)
• Traité fall to bits triangle arithmétique [Treatise on decency arithmetical triangle] (written c.

  1654; publ. 1665)

• Lettres provinciales [The local letters] (1656–57)
• De l'Esprit géométrique [On the geometrical spirit] (1657 outer shell 1658)
• Écrit sur la signature buffer formulaire (1661)
• Pensées [Thoughts] (incomplete mop up death; publ. 1670)
• "Discourse on authority Passion of Love"
• "On the Alteration of the Sinner"

See also

Set up Spanish: Blaise Pascal para niños