Blaise Pascal


from Wikipedia, the free encyclopedia
Blaise Pascal (painting from 1691)
Blaise Pascal signature.JPG

Blaise Pascal (born June 19, 1623 in Clermont-Ferrand , † August 19, 1662 in Paris ) was a French mathematician , physicist , man of letters and Christian philosopher .

Life and work

Childhood and youth

Pascal came from an old, second-generation noble family in Auvergne . His father Étienne Pascal had studied law in Paris and a little later bought the office of Vice-Presiding Judge at the Supreme Tax Court of Auvergne in Clermont-Ferrand. The mother, Antoinette Begon, came from a wealthy merchant family who also aspired to the nobility.

Pascal had two sisters, Gilberte , who was three years his senior (who later became his administrator and first biographer) and Jacqueline , who was two years his junior and whose mother did not recover from her birth, so that Pascal became a half- orphan at the age of three . When he was eight, the family and their nanny moved to Paris because the father gave the children, i. H. especially the visibly gifted boy who wanted to create better opportunities for development. He sold his judge's office to a brother and invested his fortune in government bonds.

Pascal was sickly from childhood. He was therefore taught by his highly educated father himself, who was interested in natural history, as well as by private tutors. Already at the age of twelve he demonstrated his outstanding mathematical talent and then, through his father, who frequented Parisian circles of scholars and writers, found a connection to the circle of mathematicians and naturalists around the Père Mersenne , where he, at the age of 16, did a thesis on conic sections impressed.

In 1639 the father was suspected of being one of the organizers of a protest against interest rate manipulation by the state. He preferred to go into hiding and flee Paris. At the end of 1639, however, thanks to the intercession of high-ranking people, he was pardoned by Richelieu and was even allowed to introduce his son to him.

Rouen

Pascaline from 1652

In 1640 the father was appointed royal commissioner and chief tax collector for Normandy in Rouen . Here Pascal invented a mechanical calculating machine for him in 1642 , which was later called Pascaline and is one of the oldest calculating machines. Initially, it only allowed additions, but was continuously improved over the next ten years and could finally also subtract ( two-species calculator ). Pascal received a patent on it, but the wealth he hoped for from the invention and his own small company did not materialize. The laboriously individually handcrafted machines (nine of about fifty copies are still available) were too expensive to find larger sales.

In Rouen, a city with a university, high court ( parliament ) and wealthy merchants, the Pascal family was part of good company, even if the father had made himself unpopular because of the harshness of his office. Pascal and his younger sister Jacqueline, who was gifted in literature and whose poetic attempts were encouraged by the playwright Pierre Corneille , moved elegantly in this milieu. Sister Gilberte married in 1641 a young relative, Florin Périer, whom her father had brought from Clermont-Ferrand as an assistant.

In 1646, while the father was convalescing after an accident, the family, which had previously been weakly religious, came into contact with the teachings of the Dutch reform bishop Jansenius , who advocated a doctrine of grace based on Augustine , similar to Calvin's ideas, within the Catholic Church . Father, son, and daughters became pious. Jacqueline even decided to become a nun. Pascal, who suffered from paralysis in his legs and constant pain, interpreted his illness as a sign from God and began to lead an ascetic life. In early 1647 he demonstrated the zeal of his new piety when he compelled the Archbishop of Rouen to reprimand a priestly candidate who had taken a rationalist view of religion before him and friends.

Pascal himself did not let his piety prevent him from continuing to pursue scientific-mathematical studies. In 1646 he successfully repeated the attempts made by Evangelista Torricelli in 1643 to prove the vacuum , the existence of which had previously been considered impossible, and published his results in 1647 in the treatise Traité sur le vide (see also Emptiness in Emptiness ).

The Paris time

From May 1647 he lived with Jacqueline and a little later with his father again mainly in Paris, where he contacted leading Jansenists , but also continued his research. In view of the resistance of many philosophers and naturalists, including Descartes , whom he met several times in Paris at the end of September 1647, he only discussed the question of vacuum (see also ether ) indirectly, for example in a treatise on air pressure . In 1648 his brother-in-law Périer measured the air pressure on the 1465 meter high mountain Puy de Dôme on Pascal's order to prove its dependence on altitude. In 1648 Pascal founded the law of communicating tubes in another treatise .

When the turmoil of the Fronde made life in Paris difficult in the spring of 1649 , the Pascals moved to the Périers in the Auvergne until autumn 1650.

Pascal's father died in the autumn of 1651. Shortly afterwards, against the wishes of the deceased and also of her brother, Jacqueline went to the strictly Jansenist monastery of Port Royal in Paris.

Pascal was now on his own for the first time. Since he was, if not rich, at least wealthy and aristocratic, he began to socialize in Paris society as a young man of the world and made friends with the young Duc de Roannez, who was interested in philosophy . In 1652 he took him, along with some of his freethinking friends, including the Chevalier de Méré , on a longer journey, during which Pascal was introduced to the newer philosophy, but also to the art of sociable conversation. Thanks to his intercourse in the aesthetic salon of Madame de Sablé , he also dealt in detail with the fiction literature of his time. For a moment he even thought of buying an office and getting married. An anonymous Discours sur les passions de l'amour (“Treatise on the Passions of Love”) that has long been ascribed to him because it to a certain extent fits into this sophisticated phase of life does not come from him.

In 1653 he wrote a treatise on air pressure in which, for the first time in the history of science, hydrostatics is comprehensively treated.

With his new acquaintances, especially the Chevalier de Méré, Pascal also had discussions about the chances of winning in gambling , a typically aristocratic pastime. In 1653 this led him to turn to the calculus of probability , which he advanced in 1654 in a letter exchange with the Toulouse judge and great mathematician Pierre de Fermat . They mainly examined dice games . At the same time, he dealt with other mathematical problems and published various treatises in 1654: the Traité du triangle arithmétique on Pascal's triangle and the binomial coefficients , in which he explicitly formulated the principle of proof of complete induction for the first time , the Traité des ordres numériques on number orders and the combinaisons on Number combinations.

Pascal's triangle . Each number is the sum of the two directly above it. Binomial coefficient .

In the Port-Royal area

In the autumn of 1654 Pascal was gripped by a depressive mood. He got closer to Jacqueline again, often visited her in the monastery and moved to another district in order to escape his fashionable friends. After all, he continued to work on mathematical and other scientific questions. On November 23rd (possibly after an accident with his carriage, which has not been reliably documented) he had a religious awakening experience that he tried to record on a preserved piece of paper, the Mémorial , at night .

Afterwards he withdrew from Paris society in order to be able to live fully his piety. His only contact was now the Jansenist "hermits" (French: solitaires ). These were scholars and theologians who had settled in the vicinity of the Port-Royal des Champs monastery and whom he frequently visited. Around 1655 he had the legendary conversation here with his new confessor Louis-Isaac Lemaistre de Sacy (1613–1684) Entretien avec M. de Saci sur Épictète et Montaigne (1655), in which he stood between the two poles of Montaigne skepticism and Stoic ethics Epiktets already offers a sketch of anthropology which he was later to develop in the Pensées .

The healing of his niece Marguerite Périer in 1656 , who had been freed from an ulcer on her eye after a visit to Port Royal, also strengthened Pascal's faith. At the same time he began to write religiously and theologically motivated writings in a scholarly dialogue with the solitaires , especially Antoine Arnauld and Pierre Nicole . As always, he also dealt with practical questions, for example in 1655 with the didactics of first reading for the school run by the solitaires .

With his so-called “second conversion” (cf. the Mémorial ), he had entered a situation in which the orthodox, pious and rigorously moral Jansenists had become a nuisance to the more lax and conciliatory, but also power-conscious Jesuits . When it came in 1655 to open conflict because Arnauld as Jansenist from the theological faculty of the Paris Sorbonne was excluded, mixed Pascal on and wrote 1656 /57, a series of anonymous satirical and polemical pamphlets. These were very successful and were published in Holland in 1657 under the title Provinciales , ou Lettres de Louis de Montalte à un provincial de ses amis et aux RR PP. Jésuites sur la morale et la politique de ces pères ("Provincial [briefe], or letters from L. de M. to a provincial friend and to the Jesuits about the morality and politics of these fathers") also printed as a book. There are eighteen letters from a fictional Paris traveler named Montalte, the first ten of which are addressed to a fictional friend in his native province, the next six to the Paris Jesuit Fathers in general, and the last two specifically to the king's confessor. In these letters, Montalte first describes in the role of a theologically unshod and naive young aristocrat how Jesuits prudently and condescendingly explain their theology to him; later, after he has practically learned his lesson, he begins to discuss with them and take their teachings ad absurdum as astutely as witty. Pascal satirized and attacked the consumer-friendly, but tends to be opportunistic and often subtle theology - the famous casuistry  - of the Jesuits and exposed their very worldly hunger for power. The Lettres provinciales , although they were banned according to No. 5, were listed on the index when the book edition was published and were even burned by the executioner in 1660, had great and long-lasting success and in the long term meant the beginning of the end of the Jesuits' omnipotence, at least in France . Because of their clarity and precision, they are considered a masterpiece of French prose, which gave their author a place among the classics of French literary history.

Less well known were the four vicious pamphlets with which Pascal intervened in 1658 (alongside Arnauld and Nicole) in a feud between Jansenist-oriented Parisian pastors and the Jesuits.

Blaise Pascal

For a short time, however, the Jesuits retained the upper hand with the help of the King and Pope, which darkened Pascal's years. Because while many of his sympathizers buckled or tactical under the pressure of official harassment, he remained indomitable.

In this situation he began in 1658 to work more systematically on a great apology of the Christian religion. He had made the first notes for her in 1656. Its basic lines can be found in the 1657 written but unfinished Écrits sur la grâce ("Writings on grace"), where he represents the form of the Augustinian doctrine of grace represented by the Jansenists as the middle between the almost fatalistic Calvinist doctrine of predestination and the optimistic Jesuit doctrine of grace and allows the free will of man to decide about his salvation. Because for Pascal: "He who created us without us cannot save us without us".

In addition to his work on the pensées , he also repeatedly pursued mathematical studies. He calculated in 1658, the area under the cycloid with the methods of Cavalieri and the volume of the rotating body , which upon rotation of the cycloid around the x-axis is produced. After he had found the solution himself, he organized a competition for the problem, which earned him many (inadequate) suggestions and a violent polemic with a dissatisfied person.

In 1659 his treatise Traité des sinus des quarts de cercle (treatise on the sine of the quarter circle) appeared. When Gottfried Wilhelm Leibniz read this work in Paris in 1673 , he received a decisive stimulus for the development of differential and integral calculus through the consideration of Pascal's special thoughts, which Leibniz used more generally by attaching Pascal's circle as a circle of curvature to the individual points of any function or Function curve perceived. Leibniz says he saw a light in this that the author did not notice. Hence the term characteristic triangle comes from .

With his already poor health, things went downhill faster and faster in these years, certainly also because of his extremely ascetic lifestyle, which also debilitated him. In 1659 he was unable to work for many weeks. Nevertheless, in the same year he was a member of a committee that tried to initiate a new translation of the Bible. In 1660 he spent several months as a convalescent in a little castle of his older sister and brother-in-law near Clermont.

At the beginning of 1662 he and his friend Roannez founded a cab company ( " Les carrosses à cinq sous " - "five-dollar carriages"), which marked the beginning of local public transport in Paris.

Epitaph of Pascal in the church of St-Étienne-du-Mont in the 5th arrondissement of Paris

In August he fell seriously ill, had his (still quite respectable) household sold for charitable purposes and died at the age of only 39 (one year after the death of his sister Jacqueline) in the Paris house of the Périers. A piece of paper was found sewn into the hem of his coat that has become famous as the Mémorial des Blaise Pascal. In it he tried to put his mystical experience into words with exclamations and stammering words. In it he experienced the God of Abraham, Isaac and Jacob, not that of the philosophers and scholars.

The pensées

Origin and editions of the text

Due to his early death, Pascal was unable to complete the planned great apology. He left only notes and fragments, around 1000 pieces of paper in around 60 bundles, on the basis of which in 1670 Jansenist friends obtained an edition entitled Pensées sur la religion et sur quelques autres sujets ("Thoughts on religion and some other topics") has been. This first edition is commendable because the editors - unusual for the epoch - published an unfinished work and thereby tried to make it accessible. However, it is problematic insofar as they did not orientate themselves on the original text, although it was preserved as an autograph, even if only in slip form, but used one of the two copies that the Périers had made of the bundles of notes shortly after Pascal's death. It is even more problematic because the text material received was shortened according to various criteria and, unlike the copy used, which had largely retained the arrangement of the notes and bundles, a new, supposedly more plausible order of the fragments was introduced.

The modern editions are the result of a philological success story of the 19th and 20th centuries. This begins with the fact that the philosopher Victor Cousin in 1842 in a report to the Académie française pointed out the need for a new edition of the Pensées in view of the obvious inadequacy of the first edition, which all editors had followed until then, albeit mostly with repeated cuts and / or further changes. In fact, in 1844, Prosper Faugère tried for the first time a complete edition based on Pascal's original notes, which, however, was largely reorganized into sections and subsections according to content criteria. This principle was continued and supposedly perfected by other editors, the most famous of whom was Léon Brunschvicg with his edition from 1897 to 1904.

Around 1930 research broke up with the established misconception that Pascal's slips of paper were ultimately out of order. Rather, it was recognized that at least 27 bundles (after the 1st copy or 28 after the 2nd copy, i.e. around 400 pieces of paper) corresponded to as many chapters intended by Pascal and certainly show an internal order. Other bundles also turned out to be more homogeneous and orderly than previously thought, so that one went over to editions (especially Louis Lafuma, 1952 and others after the so-called 1st copy; 1976 Philippe Sellier after the 2nd copy, the - as written in consecutive order - reproduces the estate's condition more precisely than the first copy made in individual fascicles for editing purposes), which correspond in the text to the autographs and in the arrangement largely follow the two copies (because in 1710/11 Pascal's nephew Louis Périer had in best Intention to rearrange all notes and stick them on large sheets). More recent research has also been able to work out the context in which the fragments originated more clearly using philological means (watermark analysis, etc.) (Pol Ernst, 1991).

These newer editions are reconstructions of the state of the estate and the thinking as well as Pascal's intentions to organize the material at that time. The question of what the work would have looked like if Pascal had been able to complete it (and whether he could ever have completed it) remains open.

Content overview

The mentioned 27 and 28 chapters show the path that Pascal wanted to follow in the argumentation of his Apology of Christianity. The apology is divided into two parts: “First part: the misery of man without God. Second part. Human happiness with God ”(Laf. 6). The chapters first draw a dramatic picture of the human situation under the headings “Nothingness - misery - boredom - opposites - distraction” etc., executed with brilliant paradoxical, ironic formulations, then turn to the philosophers in search of the “highest good” and find the dissolution of the aporias of human existence in Christianity. The following historical-theological part makes extensive use of the elements of the exegesis of the church fathers, as they were conveyed by Port-Royal - albeit in a "modern", very historicizing form - and is therefore not based on the modern historical-critical biblical exegesis, which was the case at that time only came about with Richard Simon . Pascal argues with the continuity of the history of salvation attested in the Holy Scriptures, the typological interpretation of the prophecies (as references to the appearance of Christ / Messiah), the "permanence" of the Jewish religion (the principle that the true religion from the beginning of creation must be present, cf. Augustine of Hippo , Retractationes 1,12,3) and the hermeneutic principle of love as the key of Holy Scripture (Laf. 270). The “proof” does not lead directly to faith, but it is a “tool” (Laf. 7) of grace. The aim of Pascal's apology is the conversion of atheists or doubters.

The organized material of the Pensées contains the large, elaborated anthropological texts “Disproportion of man” (Laf. 199) about the position of man between the infinitely small and the infinitely large, “Scattering” (Laf. 136) about distraction from thinking the real situation, marked by misery and death by pleasure and diversion, etc. a. The unity of Pascal's thought, from his mathematical to his theological writings, is made clear by the famous fragment on the three orders of body, spirit and love or holiness (Laf. 308). Pascal's bet , according to which belief in God is not only correct but also reasonable, is not placed in one of the 27 or 28 chapters , because: “If you win, you win everything, and if you lose, you lose You nothing ”(Laf. 418). According to Pascal's notes (Laf. 11), like the “introductory text” on the search for God (Laf. 427), it should precede the train of thought (cf. Sellier's edition of the Penséss “d'après l '” ordre »pascalien”, 2004 ).

reception

During an epoch that already clearly insisted on the separation of belief and knowledge, Pascal represented the principle of the unity of all being in his life and work. For him, the preoccupation with scientific problems as well as with philosophical and theological questions meant no contradiction; All of this served him for the immediate deepening of his knowledge. His perception of “intelligence / raison du coeur” - only the interplay of mind and heart can be the basis of human knowledge - as the most essential form of comprehensive knowledge is recorded by his followers as visionary and exemplary over the ages.

To this day, Pascal is regarded as an eloquent apologist for Christianity and an advocate of a deep Christian ethic. Critics of Christianity like the Abbé Meslier or Voltaire therefore attacked him early on as a high-ranking opponent. In 1793, his grave was desecrated in the church of St-Étienne-du-Mont .

Johann Wolfgang von Goethe authorized a review printed in 1772 - probably not by him - in his “ Last Hand Edition ” with the statement: “We have to say: Voltaire, Hume , La Mettrie , Helvetius , Rousseau and their whole school have the morality and religion were not damaged as much as the strict, sick Pascal and his school. "

Friedrich Nietzsche dealt with Pascal all his life. For him Pascal is "the admirable logician of Christianity"; "Pascal, whom I almost love because he taught me endlessly: the only logical Christian". There are judgments that express both admiration and rejection: Nietzsche saw in Pascal, as in Schopenhauer , something like a worthy opponent. He also saw a substantive connection between these two: “ Without the Christian faith , said Pascal, you yourself, like nature and history, become 'un monstre et un chaos'. This prophecy we have fulfilled : after the feeble-optimistic 18th century people verhübscht and verrationalisiert had [...] in a substantial sense, Schopenhauer the first movement Pascal again picks up [...] our inability to recognize the truth , is the consequence of our corruption , our moral decline : so Pascal. And so basically Schopenhauer. ”In Pascal Nietzsche can localize his criticism of Christianity:“ Christianity should never be forgiven for ruining people like Pascal. [...] What do we fight in Christianity? That it wants to break the strong, that it discourages their courage, takes advantage of their bad hours and weariness, wants to turn their proud security into restlessness and distress of conscience [...] until the strong perish in excesses of self-contempt and self-abuse: that horrible kind of perishing, the most famous example of which is given by Pascal. "

Modern critics such as the otherwise relatively cautious Aldous Huxley went further in their criticism, albeit in a psychologizing way. Pascal had made a virtue out of his need - his physical ailments and his inability to feel real passion - and camouflaged this with holy words. Worse still: he used his considerable intellect to encourage others to adopt a worldview that was equally hostile to this world. Quotes from Pascal such as: "Deviating from the middle path means deviating from humanity" and others only tempted us to understand him as a moderate thinker in the Aristotelian sense. Huxley takes the view that this was only a theoretical side of Pascal. In real life, as it can be proven in his everyday life, Pascal was very consistent - today one would say: fundamentalist. Words from Pascal's pen like: “Infirmity is the natural state of a Christian; because only in infirmity is a person as he should always be ”would reflect the gloomy attitude of the philosopher. Because of his brilliant formulations and the impressively described spiritual experiences, Pascal would be regarded as a “champion of a noble cause”, while - as far as his Christian-philosophical side is concerned - he was just a sick ascetic. In contrast to Nietzsche, he did not resist his ailments, but used them as welcome evidence of a worthless earthly life, says Huxley.

Philosophy- related is Karl Löwith's resumption of Voltaire's criticism and his preoccupation with the "Apology" or the critical interpretation of Pascal's approach to his work in the history of modern functional ontology by Heinrich Rombach . Theologically important are, for example, the great interpretation of Hans Urs von Balthasar in his work “Herrlichkeit” or Romano Guardini's “Christian Consciousness: Attempts at Pascal”. The last-named interpreters do not make any point-to-point comments on selected questions of person and work, but deal with the entire oeuvre they left behind. There is extensive Pascal research not only in France, but also in the United States and Japan.

The Evangelical Church in Germany honors Pascal with a day of remembrance in the Evangelical Name Calendar on August 19th . In July 2017, the news that Pope Francis was in favor of the beatification of Pascal caused a sensation .

Pascal as the namesake

After Pascal are named:

physics

mathematics

Computer science

  • the Pascaline , the calculating machine invented by Pascal in 1642
  • the programming languages Pascal and Object Pascal , because of his invention of a calculating machine

philosophy

astronomy

Others

Several schools in Germany have been named after Pascal; see Pascalgymnasium .

Works (selection)

  • Essai pour les coniques. (1640)
  • Experiences nouvelles touchant le vide. (1647)
  • Récit de la grande expérience de l'équilibre des liqueurs. (1648)
  • Traité du triangle arithmétique. (1654)
  • Les Provinciales . (Letters 1656–1657)
  • Element de géométrie. (1657)
  • De l'Esprit géométrique et de l'Art de persuader. (1657)
  • History of the roulette. (1658)
  • L'Art de persuader. (1660)
  • Pensées sur la religion et autres sujets (1669, posthumous)

German translations

A complete translation of the literary work (without the scientific writings) only exists in electronic form:

  • Pascal in context. Works on CD-ROM - French / German. Translated by Ulrich Kunzmann. Worm, Berlin 2003 (=  literature in context on CD-ROM 19), ISBN 3-932094-35-2 .

The currently relevant book editions of the literary work in German:

  • Jean-Robert Armogathe (ed.): Thoughts on religion and some other topics / Blaise Pascal . Reclam (RUB 1622), Stuttgart 1997, ISBN 3-15-001622-3 , p. 571 .
  • Thoughts. Translated by Ulrich Kunzmann. Comment by Eduard Zwierlein. Suhrkamp (=  Suhrkamp Study Library. Vol. 20), Berlin 2012, ISBN 978-3-518-27020-2 .
  • Letters to the provinces = Les provinciales (among others) . Schneider, Heidelberg 1990, ISBN 3-7953-0603-5 (Volume 3 of the works).
  • Letters from Blaise Pascal . Hegner, Leipzig 1935.
  • Albert Raffelt (ed.): Small writings on religion and philosophy . Meiner, Hamburg 2005, ISBN 3-7873-1769-4 (Philosophical Library 575).
  • Oeuvres théologiques et philosophiques, theolog. U. philosopher. Works. Berlin 1840–1841 urn : nbn: de: hbz: 061: 1-494939

literature

  • Donald Adamson : Blaise Pascal: Mathematician, Physicist and Thinker about God . Macmillan, London / New York 1995.
  • Jean Firges : Pascal and Teilhard de Chardin . Two world views in conflict (= Exemplary Series Literature and Philosophy. Vol. 32). Sonnenberg, Annweiler am Trifels 2011, ISBN 978-3-933264-65-7 .
  • Lucien Goldmann : The hidden God. Study of the tragic worldview in the “Pensées” Pascals and in the Racines theater . German first Luchterhand, Neuwied 1971 a. ö .; Suhrkamp, ​​Frankfurt 1985 (stw 491; first Paris 1955).
  • Romano Guardini : Christian Consciousness: Experiments on Pascal , 1935.
  • Manfred Heeß: Blaise Pascal: Scientific thinking and Christian belief (= Freiburg writings on Romance philology. Vol. 33). Fink, Munich 1977.
  • Hans Loeffel: Blaise Pascal (= Vita mathematica. Vol. 2). Birkhäuser, Basel 1987.
  • Hermann Reuchlin : Pascal's life and the spirit of his writings partly based on newly discovered manuscripts with investigations into the morality of the Jesuits. Stuttgart 1840 online  - Internet Archive
  • Hans-Martin Rieger : Think humanly - justify faith: Blaise Pascal and religious-philosophical justification models of modernity . De Gruyter, Berlin 2010, ISBN 978-3-11-024778-7 .
  • Wilhelm Schmidt-Biggemann : Blaise Pascal ( Beck's series of thinkers ). Beck, Munich 1999.
  • Theophil Spoerri : Pascal's ulterior motive. Furche, Hamburg 1958.
  • Pensées de Blaise Pascal . Renouard, Paris 1812 (2 volumes) digitized
  • Robert Hugo Ziegler: Letter and Spirit. Pascal and the limits of philosophy . V&R unipress, Göttingen 2010. ISBN 978-3-89971-790-7 .
  • René Taton : Pascal, Blaise . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 10 : SG Navashin - W. Piso . Charles Scribner's Sons, New York 1974, p. 330-342 .

Web links

Commons : Blaise Pascal  - Album with pictures, videos and audio files

Individual evidence

  1. ^ Blaise Pascal: Traite au Triangle Arithmetique , p. 7, Consequence douziesme, Le 1st and 2nd digitized from an edition from 1665
  2. Oskar Becker, Fundamentals of Mathematics , Suhrkamp
  3. Lütz, M.:Gott. A little history of the greatest , Knauers Taschenbuch Verlag. Munich 2009
  4. in Frankfurt learned advertisements of September 8, 1772, see Goethe's works: Complete edition last hand. Volume 33, Verlag Cotta, 1830, p. 85 ; "Coming from Schlosser { Johann Georg Schlosser } ": Ed. Elke Richter, Georg Kurscheidt: Johann Wolfgang Goethe: Letters: Historical-critical edition. Volume 1 by Johann Wolfgang von Goethe: Letters. Verlag Walter de Gruyter, 2008, p. 436
  5. ^ F. Nietzsche: Estate. KSA 12, 10 [58], p. 531.
  6. ^ Letter from Nietzsche to Georg Brandes , November 20, 1888. KSB 8, No. 1151, p. 483.
  7. ^ F. Nietzsche: Estate. KSA 12, 9 [189], p. 445.
  8. ^ F. Nietzsche: Estate. KSA 13, 11 [55], p. 27 f.
  9. ^ Rombach: Substance - System - Structure, Volume 2. Freiburg 1966
  10. From Balthasar: Herrlichkeit , Vol. 2, Einsiedeln 1962
  11. Blaise Pascal in the Ecumenical Lexicon of Saints
  12. Pope apparently for the beatification of Blaise Pascal. In: religion.orf.at. July 13, 2017. Retrieved November 30, 2017 .
  13. Published as an attachment in: Traitez de l'équilibre des liqueurs et de la pesanteur de la masse de l'air , Paris 1663 ( digitized ), pp. 165 ff.
  14. ^ Digitized from an edition from 1665
  15. with lit. and Pascal's curriculum vitae, emphasizing his Jansenism