text: Berlin

text: Oels

text: Silesia

text: Prussian

text: lieutenant colonel

text: Prussian Army

text: 10th Prussian Fusilier Battalion

text: Kingdom of Prussia

text: order of merit

text: Knight

text: Pour le Mérite

text: Prussian Army

text: Oels

text: Silesia

text: Prussian

text: Lieutenant General

text: King

text: Frederick the Great

text: Frederick the Great

text: Drost

text: Castellan

text: County of Mark

text: Castellan

text: ("Drost")

text: Neuenrade

text: Prussian

text: Regiment

text: 23rd Prussian Infantry Regiment

text: Schweidnitz

text: Seven Years' War

text: Battle of Freiberg

text: Seven Years' War

text: 28th Prussian Infantry Regiment

text: Brieg

text: Silesia

text: major

text: Battalion

text: 15th Füsilier Battalion

text: Löwenberg

text: Silesia

text: Kingdom of Prussia

text: order of merit

text: Pour le Mérite

text: battalion commander

text: 10th Füsilier Battalion

text: Neumarkt

text: Silesia

text: Rhine Campaigns

text: lieutenant colonel

text: Frederick William III of Prussia

text: Coat of Arms

text: escutcheon

text: field

text: divided

text: argent

text: tincture

text: gules

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text: sinople

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text: Count

text: coronet

text: helmut

text: escutcheon

text: crested

text: or

text: fleur-de-lis

text: or

text: lions

text: supporting

text: escutcheon

text: Motto

text: Heraldic Symbolism

text: lion

text: tower

text: mullets

text: rose

text: fleur-de-lis

text: France

text: coronet

text: Count

text: coronet

text: rank

text: count

text: Foix

text: Béarn

text: Middle Ages

text: King

text: Frederick the Great

text: Regimentschef

text: 23rd Prussian Infantry Regiment

text: Kingdom of Prussia

text: order of merit

text: Pour le Mérite

text: Order of the Black Eagle

text: Canon

text: Havelberg

text: Castellan

text: County of Mark

text: Lord

text: Seneschal

text: Zinna

text: "Ober-Collegium Sanitatis"

text: Lieutenant governor

text: Breslau

text: French Cathedral in Berlin

text: Baron

text: Sardinia

text: Prussian

text: Major General

text: Baron

text: Berlin

text: Huguenot

text: Oels

text: Silesia

text: Oels

text: Breslau

text: Herr

text: Herr

text: Berlin

text: Breslau

text: Silesia

text: Prussian

text: Major

text: Knight

text: Iron Cross

text: Knight

text: Prussian

text: Prussian

text: Chamberlain

text: Castellan

text: County of Mark

text: Brieg

text: Silesia

text: Imperial Russian Army

text: lieutenant colonel

text: adjutant

text: Imperial Russian Army

text: Infantry

text: General

text: Loggin Osipovitch Roth

text: Kingdom of Prussia

text: order of merit

text: Knight

text: Pour le Mérite

text: Brieg

text: Silesia

text: Rawicz

text: Posen

text: Prussian

text: Major

text: Commanding Officer

text: Prussian

text: Iron Cross

text: Löwenberg

text: Silesia

text: Breslau

text: Silesia

text: Löwenberg

text: Silesia

text: Löwenberg

text: Silesia

text: Oels

text: Silesia

text: Oels

text: Silesia

text: Oels

text: Silesia

text: Oels

text: Silesia

text: Friedrich Wilhelm von Forcade de Biaix

text: Prussian

text: colonel

text: Rittmeister

text: 34th Prussian Infantry Regiment

text: 1 July

text: Regimentschef

text: 24th Prussian Infantry Regiment

text: Frankfurt/Oder

text: Kingdom of Prussia

text: order of merit

text: Knight

text: Pour le Mérite

text: Prussian

text: Major

text: Hussar

text: Regiment

text: Lord

text: Seneschal

text: governor

text: Bailiff

text: Castellan

text: (in German and English)

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categories: 18th century in Austria,Recipients of the Pour le Mérite (military class),Prussian nobility,Kingdom of Prussia,Military history of Prussia,1808 deaths,1747 births,People from Berlin,18th century in Prussia,People from Prussian Silesia

paragraph: Friedrich Heinrich Ferdinand Leopold von Forcade de Biaix, aka "Heinrich Friedrich Ferdinand Leopold von Forcade de Biaix", aka "Friedrich Heinrich Ferdinand Leopold Marquis de Forcade de Biaix" (* 19 December 1747, Berlin; † 12 October 1808, "Schleibitz Manor", Oels, Silesia), was a Royal Prussian lieutenant colonel. He served in the Prussian Army from 1761-1793. His last command was as Commanding Officer of the 10th Prussian Fusilier Battalion, with which he served in the Rhine Campaigns of 1791, where he was awarded the Kingdom of Prussia's highest military order of merit for heroism, Knight of the Order of "Pour le Mérite (1791)." He left the Prussian Army after 32 years of service in 1793 as the result of invalidity. At the time of his death, he was the owner of "Schleibitz Manor", near Oels, Silesia.

paragraph: He was the third son, of Royal Prussian Lieutenant General Friedrich Wilhelm Quirin von Forcade de Biaix, one of King Frederick the Great's most active and most treasured officers. His baptismal Godfather was none less than His Majesty Frederick the Great. As a gift, the King ordered his father to accept the hereditary title of "Drost zu Neuenrade" (""Castellan of Neuenrade"") in the County of Mark with the royal command that it be transferred to him upon his death. After his father's death in 1765, he became Castellan ("Drost") of Neuenrade.

paragraph: Section::::Military career.

paragraph: He followed the military tradition of his family, and:

paragraph: BULLET::::- entered Prussian military service in 1761 in his father's Regiment, the 23rd Prussian Infantry Regiment.

paragraph: BULLET::::- participated at the Siege of Schweidnitz ("4 August 1762 - 10 October 1762") during the Seven Years' War

paragraph: BULLET::::- fought in the Battle of Freiberg ("29 October 1762") during the Seven Years' War

paragraph: BULLET::::- 1774, transferred to the 28th Prussian Infantry Regiment, aka The Zaremba Regiment, in Brieg, Silesia.

paragraph: BULLET::::- 19 March 1788, as a major, appointed as Battalionschef of the 15th Füsilier Battalion in Löwenberg, Silesia.

paragraph: BULLET::::- September 1791, awarded the Kingdom of Prussia's highest military order of merit for heroism, Knight of the Order of "Pour le Mérite".

paragraph: BULLET::::- 13 November 1791, appointed as battalion commander of the 10th Füsilier Battalion in Neumarkt, Silesia, with which he fought during the Rhine Campaigns.

paragraph: BULLET::::- 1793, retired from active military service for reason of invalidity.

paragraph: BULLET::::- 1798, promoted to the rank of lieutenant colonel by His Majesty, Frederick William III of Prussia.

paragraph: Section::::Family.

paragraph: Section::::Family.:Coat of arms.

paragraph: The family motto of the Prussian branch is ""In Virtute Pertinax"".

paragraph: Coat of Arms: An escutcheon with the field divided into four parts. Left half: argent tincture, a gules lion holding a sinople eradicated oak tree between its paws; azure tincture charged with three or mullets; Right half: a gules castle with three towers on an argent tincture; sinople tincture charged with three argent roses below it. A "Grafenkrone" (Count's coronet) as helmut on top of the escutcheon, crested with a or fleur-de-lis. Two or lions supporting the escutcheon. Motto: ""In Virtute Pertinax"".

paragraph: Heraldic Symbolism: The lion symbolizes courage; the eradicated oak tree symbolizes strength and endurance; the towers are symbols of defense and of individual fortitude; the mullets (5-star) symbolizes divine quality bestowed by god; the rose is a symbol of hope and joy; the fleur-de-lis is the floral emblem of France; the coronet is a symbol of victory, sovereignty and empire. A Count's coronet to demonstrate rank and because the family originally served the counts of Foix and Béarn during the English Wars in the Middle Ages.

paragraph: Section::::Family.:Parents.

paragraph: His father was Friedrich Wilhelm Quirin von Forcade de Biaix (1699-1729), one of King Frederick the Great's most active and most treasured officers. Twice wounded and left for dead on the battlefield, he was Regimentschef of the 23rd Prussian Infantry Regiment, recipient of the Kingdom of Prussia's highest military order of merit for heroism, Knight of the Order of "Pour le Mérite", Knight of the Order of the Black Eagle, "Canon of Havelberg", "Castellan of Neuenrade" in the County of Mark, "Lord Seneschal of Zinna", President of the "Ober-Collegium Sanitatis" in Berlin and Lieutenant governor of Breslau. He married in 1727 at the French Cathedral in Berlin with "Marie de Montolieu, Baronne de St.-Hippolyte" aka "Maria von Montaulieu, Freiin von St.-Hippolyte" (1709-1767), daughter of Sardinian and Prussian Major General "Louis de Montolieu, Baron de St.-Hippolyte" († 1738, Berlin), also a Huguenot exile.

paragraph: Section::::Family.:Marriage.

paragraph: "Friedrich Heinrich Ferdinand Leopold von Forcade de Biaix" married on 15 April 1782 at "Ossen Manor" in Oels, Silesia, to "Wilhelmine von Koshembahr und Skorkau" from the house of Ossen, (* 13 January 1761, "Ossen Manor", Oels; † 9 July 1816, Breslau), the daughter of "Christian Leopold von Koschembahr und Skorkau", Herr of Ober- and Nieder-Ossen, Pühlau, Dörndorf and Jacobsdorf, and his second wife "Charlotte Wilhelmine Wutge von Wutgenau".

paragraph: Section::::Family.:Children.

paragraph: The couple had at least seven children from their marriage; known are five sons and two daughters. Three sons survived into adulthood.

paragraph: BULLET::::- Friedrich Wilhelm Leopold Konstantin Quirin von Forcade de Biaix, Herr of Schleibitz, Hamm, Groß-Naedlitz and Loslau, (* 12 May 1784, Berlin; † 22 October 1840, Breslau Silesia), Royal Prussian Major, Knight of the Iron Cross 2nd Class, Knight of the Cross of the Royal Prussian Order of St. John Bailiwick of Brandenburg, Royal Prussian Chamberlain, and Castellan of Neuenrade in the County of Mark.

paragraph: BULLET::::- Wilhelm Friedrich Erdmann Ferdinand von Forcade de Biaix (26 February 1786, Brieg, Silesia; † 1816), Imperial Russian Army lieutenant colonel, adjutant to Imperial Russian Army Infantry General Loggin Osipovitch Roth (""von Roth""), recipient of the Kingdom of Prussia's highest military order of merit, Knight of the Order of "Pour le Mérite" (26 May 1814).

paragraph: BULLET::::- Friedrich Wilhelm Ferdinand Ernst Heinrich von Forcade de Biaix (* 7 October 1787, Brieg, Silesia; † 14 November 1835, in Rawicz, Posen), Royal Prussian Major, Commanding Officer of the 10th Prussian Division's Garrison Company and Knight of the Iron Cross 2nd Class.

paragraph: BULLET::::- "Friedrike Wilhelmine Auguste Ulrike Karoline von Forcade de Biaix" (* 12 July 1789, Löwenberg, Silesia; † 19 February 1797, Breslau, Silesia)

paragraph: BULLET::::- "Henriette Eugenie Emilie Antoinette Sophie von Forcade de Biaix" (* 25 July 1791, Löwenberg, Silesia; † 12 September 1791, Löwenberg, Silesia)

paragraph: BULLET::::- "Friedrich Wilhelm Karl Ernst Heinrich von Forcade de Biaix" (* 5 November 1793, Schleibitz Manor, Oels, Silesia; † 3 January 1796, Schleibitz Manor, Oels, Silesia)

paragraph: BULLET::::- "Friedrich Wilhelm Albrecht Quirin Ludwig von Forcade de Biaix" (* 26 August 1797, Schleibitz Manor, Oels, Silesia; † 1 June 1805, Schleibitz Manor, Oels, Silesia)

paragraph: Section::::Family.:Other family.

paragraph: BULLET::::- Brother: Friedrich Wilhelm von Forcade de Biaix (1728-1778), the eldest son, Royal Prussian colonel, "Schwadronschef (Rittmeister)" of the 2nd Grenadier Company in the 34th Prussian Infantry Regiment (1761), and, after 1 July 1761, acting Regimentschef of the 24th Prussian Infantry Regiment garrisoned in Frankfurt/Oder, recipient of the Kingdom of Prussia's highest military order of merit for heroism, Knight of the Order of "Pour le Mérite" (1791).

paragraph: BULLET::::- Brother: Georg Friedrich Wilhelm von Forcade de Biaix (1746-1811), the second-born son, Royal Prussian Major in the 1st Hussar Regiment

paragraph: Section::::Titles and offices.

paragraph: Historical terms, in particular those related to offices, titles and awards, are often outdated in their usage to the point that modern dictionaries no longer contain them. To understand their meaning in the present day context it is necessary to look into dictionaries from the period. Historical terms in German used in the production of this article, and their English definitions, include:

paragraph: Section::::Titles and offices.:Drost zu Neuenrade.

paragraph: "Castellan of Neuenrade"

paragraph: BULLET::::- Drost (der): synonym with "Landdrost", "Landshauptmann" and "Landsvogt"; "a Lord Seneschal, a governor of a certain part of a country, an Upper Bailiff, a Castellan" See: Ebers, Johann, "The New And Complete Dictionary Of The German And English Languages: composed chiefly after the German Dictionaries of Mr. Adelung and of Mr. Schwan / 1: ... Containing the Letters A - G of the German Alphabet explained in English", Leipzig 1796, Page 618 (in German and English)

paragraph: Section::::References.

paragraph: BULLET::::- Blažek, Konrad: J. Siebmacher's grosses und allgemeines Wappenbuch in einer neuen, vollständig geordneten und reich vermehrten Auflage mit heraldischen und historisch- genealogischen Erläuterungen; Sechsten Bandes Achte Abtheilung. "Der abgestorbene Adel der Preussischen Provinz Schlesien. Dritter Theil", Nürnberg 1894, Page 131 & Page 267 Table 85. (in German)

paragraph: BULLET::::- Champeaux, Joseph de: "Devises, cris de guerre, légendes, dictons", Dijon 1890, Page 105. (in French)

paragraph: BULLET::::- Gieraths, Günther: "Die Kampfhandlungen der brandenburgisch-preussischen Armee, 1626-1807, Band 8", Berlin 1964, Page 189. (in German)

paragraph: BULLET::::- Heinsius, Johann Samuel (Verlag): "Fortgesetzte neue genealogisch-historische Nachrichten von den vornehmsten Begebenheiten, welche sich an den europäischen Höfen zutragen, worinn zugleich vieler Stands-Personen Lebens-Beschreibungen vorkommen. Der 49.-54. Theil (1764-1765)", Leipzig 1766, Page 241, Nr. V (in German)

paragraph: BULLET::::- Kneschke, Ernst Heinrich: "Neues allgemeines Deutsches Adels-Lexicon, Band 3", Leipzig 1861, Pages 293-294. (in German)

paragraph: BULLET::::- König, Anton Balthasar: "Biographisches Lexikon aller Helden und Militairpersonen, welche sich in Preußischen Diensten berühmt gemacht haben: A - F", Band 1, Pages 429-432. (in German)

paragraph: BULLET::::- Lehmann, Gustaf: "Die Ritter des Ordens pour le mérite. Auf Allerhöchsten Befehl Seiner Majestät des Kaisers und Königs, bearbeitet im Königlichen Kriegsministerium durch Gustav Lehmann, wirklichen geheimen Kriegsrat und vortragenden Rat im Kriegs-Ministerium, Erster Band: 1740-1811", Berlin 1913, Page 209, Nr. 145 (in German)

paragraph: BULLET::::- Zedlitz-Neukirch, Leopold von: "Neues preußisches Adelslexicon oder genealogische und diplomatische Nachrichten von den in der preussischen Monarchie ansässigen oder zu derselben in Beziehung stehenden fürstlichen, gräflichen, freiherrlichen und adeligen Häusern mit der Angabe ihrer Abstammung, ihres Besitzthums, ihres Wappens und der aus ihnen hervorgegangenen Civil- und Militärpersonen, Helden, Gelehrten und Künstler: E - H, Band 2," 1836, Pages 179-180. (in German)

paragraph: BULLET::::- Zedlitz-Neukirch, Leopold von: "Neues preußisches Adelslexicon oder genealogische und diplomatische Nachrichten von den in der preussischen Monarchie ansässigen oder zu derselben in Beziehung stehenden fürstlichen, gräflichen, freiherrlichen und adeligen Häusern mit der Angabe ihrer Abstammung, ihres Besitzthums, ihres Wappens und der aus ihnen hervorgegangenen Civil- und Militärpersonen, Helden, Gelehrten und Künstler: P - Z, Band 4," 1837, Pages 390-392. (in German)

paragraph: Section::::Literature.

paragraph: BULLET::::- Lehmann, Gustaf: "Die Ritter des Ordens pour le mérite. Auf Allerhöchsten Befehl Seiner Majestät des Kaisers und Königs, bearbeitet im Königlichen Kriegsministerium durch Gustav Lehmann, wirklichen geheimen Kriegsrat und vortragenden Rat im Kriegs-Ministerium, Erster Band: 1740-1811", Berlin 1913 (in German)

paragraph: BULLET::::- Lehmann, Gustaf: "Die Ritter des Ordens pour le mérite. Auf Allerhöchsten Befehl Seiner Majestät des Kaisers und Königs, bearbeitet im Königlichen Kriegsministerium durch Gustav Lehmann, wirklichen geheimen Kriegsrat und vortragenden Rat im Kriegs-Ministerium, Zweiter Band: 1812-1913", Berlin 1913, (in German)


text:
experimental
multimedia art
Hospital Productions
Wisconsin
Roman Catholic
death metal
tape trading
Deicide
Once Upon the Cross
New York City
Los Angeles
Hospital Productions
microphone
amplifier
Wolf Eyes
Macronympha
Philip Best
Whitehouse
Vegas Martyrs
Cold Cave
Hanson Records
RRRecords
Load Records
Troubleman Unlimited
Kitty Play Records
Hospital Productions
The New Yorker
Pitchfork Media
The Village Voice
AllMusic
Prurient discography
RateYourMusic
Prurient discography
Discogs

categories: Musicians from Wisconsin,Noise musicians,American electronic musicians,American industrial musicians,Living people

paragraph: Dominick Fernow

paragraph: Dominick Fernow is an American experimental musician, poet and multimedia artist. He is best known for extreme music released under the stage name Prurient, as well as numerous other aliases including Vatican Shadow and Rainforest Spiritual Enslavement. His first releases date back to 1998, the same year in which he founded the record label Hospital Productions.

paragraph: Section::::Biography.

paragraph: Fernow was born in Wisconsin into a Roman Catholic household. Fernow recounts his entrance into public school and his exposure to death metal and tape trading as early sources of musical interest. In particular, Fernow cites the death metal band Deicide's album "Once Upon the Cross" as, "frightening ... A huge record for me, still to this day."

paragraph: Fernow has resided in both New York City and Los Angeles, and runs the labels Hospital Productions and Bed Of Nails.

paragraph: Section::::Career.

paragraph: In his early work as Prurient, Fernow worked primarily with a microphone and amplifier, and sometimes drums. He eventually began utilizing more electronics, and currently works primarily with laptop and synthesizers. In the past, he collaborated with artists like John Wiese, Jeff Plummer (of Immaculate:Grotesque and Shallow Waters), Kris Lapke (of Alberich and MCMS), Wolf Eyes, Macronympha, and Philip Best (of Whitehouse and Consumer Electronics).

paragraph: Fernow has also performed in various bands, such as Football Rabbit, Vegas Martyrs, Taylor Bow, Ash Pool (in which he also sings), and formerly as part of Cold Cave. Prurient has released material on numerous independent record labels, such as Hanson Records, RRRecords, Load Records, Troubleman Unlimited, Chrondritic Sound, Kitty Play Records, American Tapes, and his own label Hospital Productions. Fernow has also recorded music under a variety of aliases, including Vatican Shadow, Rainforest Spiritual Enslavement, Exploring Jezebel, River Magic, Winter Soldier, Window Cleaning By Ian, December Magic, and Tortured Hooker.

paragraph: Prurient has been covered in outlets such as The New Yorker, Pitchfork Media and The Village Voice.

paragraph: Section::::Partial discography.

paragraph: Section::::Partial discography.:As Rainforest Spiritual Enslavement.:Studio albums.

paragraph: BULLET::::- "Papua Land Where Spirits Still Rule" (2012)

paragraph: BULLET::::- "Folklore Venom" (2013)

paragraph: BULLET::::- "Green Graves" (2016)

paragraph: BULLET::::- "Ambient Black Magic" (2017)

paragraph: Section::::Partial discography.:As Rainforest Spiritual Enslavement.:EPs.

paragraph: BULLET::::- "The Plant With Many Faces" (2013)

paragraph: BULLET::::- "Black Magic Cannot Cross Water" (2013)

paragraph: BULLET::::- "Water Rose Above The Head" (2013)

paragraph: Section::::Partial discography.:As Rainforest Spiritual Enslavement.:Compilations.

paragraph: BULLET::::- "Water Witches" (2017)

paragraph: Section::::Partial discography.:As Christian Cosmos.:Studio Albums.

paragraph: BULLET::::- "Enthronement by God as the First-Born of the Dead" (2012)

paragraph: Section::::Partial discography.:As Christian Cosmos.:EPs.

paragraph: BULLET::::- "Cadence Upon The Threshold Of Judgement" (2012)

paragraph: BULLET::::- "The Sharp Lines That Delineate His Robes" (2012)

paragraph: BULLET::::- "Which Echo Again and Again" (2012)

paragraph: Section::::Partial discography.:As Exploring Jezebel.:Studio Albums.

paragraph: BULLET::::- "On a Business Trip to London" (2015)

paragraph: Section::::External links.

paragraph: BULLET::::- [ Prurient] on AllMusic

paragraph: BULLET::::- Prurient discography on RateYourMusic

paragraph: BULLET::::- Prurient discography on Discogs

alias:
Prurient
Vatican Shadow

description: musician

wikidata_label: Dominick Fernow

wikipedia_title: Dominick Fernow


text:
Rui Gonçalves da Câmara
Infanta Beatrice, Duchess of Viseu
Monastery of Alcobaça

categories: 15th-century Portuguese people,1460 births,Donatary-Captains of the Azores,1502 deaths

paragraph: João Rodrigues da Câmara

paragraph: João Rodrigues da Câmara (c.1460 – 1502), son of Rui Gonçalves da Câmara, who became the second Captain-Donatário of the island of São Miguel.

paragraph: Section::::Biography.

paragraph: Section::::Biography.:Early life.

paragraph: He was married to Inês da Câmara, lady-in-waiting to Infanta Beatrice, Duchess of Viseu, who had a good relation in the Portuguese Court. Firstborn son of Rui Gonçalves da Câmara, he was in Lisbon completing his education, while his brother was a novice at the Monastery of Alcobaça, indicating the importance of the family within the Portuguese Court at the time.

paragraph: Section::::Biography.:Donatário.

paragraph: João Rodrigues followed his father's policy of attracting settlers to the islands of the Azores. He invited many people from the kingdom, those with a spirit of adventure, that included many of the prominent families in the modern archipelago, including the Monizes, Baretos, Baldaias, Vaz, Sousas, Esteves, Rochas, Machados, Costas and Benevides.

paragraph: Section::::Biography.:Later life.

paragraph: João Rodrigues' tenure was short (1497–1502), when died suddenly in Lisbon, leaving behind his wife on the island of São Miguel, along with his four minor children. Following his death, the Captania of São Miguel was assumed (unofficially) by his brother Pedro Rodrigues da Câmara, until his son Rui Gonçalves da Câmara obtained age of majority. During Pedro's administration various Jewish families came to the Azores, after being expelled in 1497 from the continent (the document was only published four years later).

paragraph: Section::::References.

paragraph: BULLET::::- Notes

paragraph: BULLET::::- Sources

description: Portuguese noble

wikidata_label: João Rodrigues da Câmara

wikipedia_title: João Rodrigues da Câmara


text: Ionian

text: Greek philosopher

text: Pythagoreanism

text: Magna Graecia

text: Plato

text: Aristotle

text: Western philosophy

text: Samos

text: Croton

text: communal

text: ascetic

text: vegetarianism

text: metempsychosis

text: soul

text: immortal

text: enters into a new body

text: musica universalis

text: planets

text: mathematical

text: equation

text: symphony

text: numerological

text: Philolaus of Croton

text: Sybaris

text: democracy

text: Metapontum

text: Pythagorean theorem

text: Pythagorean tuning

text: five regular solids

text: Theory of Proportions

text: sphericity of the Earth

text: morning

text: evening stars

text: Venus

text: five climatic zones

text: natural philosophy

text: dialogues

text: Timaeus

text: ancient Greek art

text: Middle Platonists

text: Neopythagoreanism

text: Middle Ages

text: Nicolaus Copernicus

text: Johannes Kepler

text: Isaac Newton

text: European esotericism

text: Ovid

text: Metamorphoses

text: satirical

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text: Roman period

text: Walter Burkert

text: lives

text: Diogenes Laërtius

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text: natural philosophy

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text: Archaic Greece

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text: Diospolis

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text: Heliopolis

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text: Clement of Alexandria

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text: Homer

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text: Pherecydes of Syros

text: Messina

text: Apollonius Paradoxographus

text: thaumaturgic

text: Nicomachus

text: Delos

text: Duris

text: Thales of Miletus

text: special case

text: inscribed angle theorem

text: Samos

text: Aegean Sea

text: Miletus

text: Aristoxenus

text: moral

text: Delphic priestess

text: Themistoclea

text: ascetic

text: Orphic

text: Cretan mysteries

text: Delphic oracle

text: Antiphon

text: tyranny

text: Polycrates

text: Crotone

text: Calabria

text: Magna Graecia

text: Theano

text: Crete

text: Telauges

text: Arignote

text: Milo of Croton

text: pseudepigraphica

text: Sybaris

text: democratic constitution

text: Cylon

text: Ninon

text: Locris

text: Metapontum

text: Muses

text: metempsychosis

text: soul

text: Empedocles

text: Heraclides Ponticus

text: Aethalides

text: Hermes

text: Euphorbus

text: Trojan War

text: Iliad

text: Hermotimus

text: Delos

text: Dicaearchus

text: harmony of the spheres

text: Muse

text: seven planets

text: "Protrepticus"

text: Aristotle

text: divination

text: prophecy

text: Delos

text: Sparta

text: Phlius

text: Crete

text: monad

text: dyad

text: Apollo

text: four seasons

text: four elements

text: odd numbers

text: masculine

text: feminine

text: tetractys

text: Philolaus of Croton

text: proofless

text: arithmetic

text: Plato

text: Isocrates

text: monastery

text: vow

text: religious

text: ascetic

text: philosophical

text: shared all their possessions in common

text: Sparta

text: maxim

text: gods

text: spondee

text: physical exercise

text: dancing

text: scenic route

text: athletics

text: tombstone

text: Neopythagoreanism

text: metempsychosis

text: vegetarian

text: Eudoxus of Cnidus

text: Aristoxenus

text: oxen

text: plough

text: rams

text: hagiographic

text: Olympic Games

text: Abaris the Hyperborean

text: at the same time

text: Basento

text: Muslim tradition

text: Hermes

text: Thoth

text: wreath

text: trousers

text: Thracians

text: self-control

text: his famous theorem

text: music

text: astronomy

text: medicine

text: Pythagorean theorem

text: hecatomb

text: dough

text: Babylonians

text: Indians

text: proof

text: cuneiform

text: five regular solids

text: Theory of Proportions

text: hammers

text: blacksmith

text: monochord

text: Parmenides of Elea

text: Earth was spherical

text: five climactic zones

text: morning star

text: evening star

text: Venus

text: pseudepigrapha

text: Phlius

text: Thebes

text: Archytas

text: Tarentum

text: strategos

text: Meno

text: Phaedo

text: The Republic

text: Philebus

text: Timaeus

text: R. M. Hare

text: Republic

text: soul

text: Orphism

text: Frederick Copleston

text: his tripartite theory of the soul

text: Bertrand Russell

text: A History of Western Philosophy

text: Middle Platonist

text: Eudorus

text: Philo of Alexandria

text: Alexandria

text: Neopythagoreanism

text: Apollonius of Tyana

text: Moderatus of Gades

text: Nicomachus

text: Numenius of Apamea

text: Archaic

text: Maurice Bowra

text: canon

text: Polykleitos

text: Rhys Carpenter

text: Doric order

text: Porta Maggiore Basilica

text: Nero

text: Sappho

text: Leucadian cliffs

text: Hadrian

text: Pantheon

text: Rome

text: dome

text: oculus

text: Eusebius

text: Caesarea

text: Moses

text: Church Father

text: Jerome

text: Augustine of Hippo

text: On the Trinity

text: Middle Ages

text: Seven Liberal Arts

text: Cathedral of Chartres

text: William of Conches

text: Ambrose Traversari

text: Marsilio Ficino

text: Constantine Lascaris

text: The Golden Verses of Pythagoras

text: Messina

text: On the Revolution of the Heavenly Spheres

text: Nicolaus Copernicus

text: heliocentric model

text: Aristarchus of Samos

text: Johannes Kepler

text: laws of planetary motion

text: Harmonices Mundi

text: Isaac Newton

text: Law of Universal Gravitation

text: Albert Einstein

text: Alfred North Whitehead

text: Ovid

text: Metamorphoses

text: Arthur Golding

text: John Donne

text: Michel de Montaigne

text: William Shakespeare

text: The Merchant of Venice

text: John Dryden

text: Fables, Ancient and Modern

text: John Gay

text: Lord Chesterfield

text: Percy Bysshe Shelley

text: Leo Tolstoy

text: European esotericism

text: humanist

text: Johannes Reuchlin

text: Christian theology

text: Kabbalah

text: Mosaic

text: ineffable

text: YHWH

text: Heinrich Cornelius Agrippa

text: De Occulta Philosophia

text: supercelestial

text: freemasons

text: Rosicrucianism

text: Robert Fludd

text: John Dee

text: Adam Weishaupt

text: Illuminati

text: Wolfgang Amadeus Mozart

text: The Magic Flute

text: Sylvain Maréchal

text: Dante Alighieri

text: Hell

text: Purgatory

text: Heaven

text: Paradiso

text: Divine Comedy

text: canto

text: Inferno

text: pi

text: God

text: squaring the circle

text: Beatrice

text: Transcendentalists

text: Henry David Thoreau

text: Thomas Taylor

text: Stobaeus

text: magnum opus

text: Walden

text: Isopsephy

text: Gematria

text: List of things named after Pythagoras

text: Lute of Pythagoras

text: Pythagoras tree (fractal)

text: Pythagorean comma

text: Pythagorean cup

text: Pythagorean triple

text: Pythagoras (sculptor)

text: Sacred geometry

text: Diogenes Laërtius

text: Vitae philosophorum VIII

text: lost work

text: Successions of Philosophers

text: Alexander Polyhistor

text: Porphyry

text: "Porphyry, Life of Pythagoras"

text: Kenneth Sylvan Guthrie

text: Iamblichus

text: "Iamblichus, Life of Pythagoras"

text: Kenneth Sylvan Guthrie

text: Apuleius

text: Aristoxenus

text: Zoroaster

text: Clement of Alexandria

text: Hierocles of Alexandria

text: "Pythagoras of Samos"

text: The MacTutor History of Mathematics archive

text: University of St Andrews

text: "Pythagoras and the Pythagoreans, Fragments and Commentary"

text: Arthur Fairbanks

text: Hanover College

text: "Pythagoras and the Pythagoreans"

text: Texas A&M University

text: "Pythagoras and Pythagoreanism"

text: The Catholic Encyclopedia

categories: History of ideas,Mystics,Presocratic philosophers,Ancient Greek mathematicians,Ancient Greek political refugees,Founders of religions,Metaphysicians,Epistemologists,Ancient Greek music theorists,Geometers,Numerologists,Philosophers of education,Philosophy of mathematics,Philosophy of music,Ontologists,History of philosophy,Ascetics,570s BC births,Founders of philosophical traditions,Ancient Greek shamans,5th-century BC Greek people,490s BC deaths,Esotericists,6th-century BC Greek people,Moral philosophers,Philosophers of ethics and morality,Philosophers of mind,6th-century BC philosophers,Ancient Greek metaphilosophers,Pythagoras,Philosophers of science,Ancient Samians,Ancient Greek metaphysicians,5th-century BC philosophers,Metaphilosophers

paragraph: Pythagoras

paragraph: Pythagoras of Samos () was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated for complete vegetarianism.

paragraph: The teaching most securely identified with Pythagoras is "metempsychosis", or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of "musica universalis", which holds that the planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or escaped to Metapontum, where he eventually died.

paragraph: In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones. Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy.

paragraph: Pythagoras influenced Plato, whose dialogues, especially his "Timaeus", exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art. His teachings underwent a major revival in the first century BC among Middle Platonists, coinciding with the rise of Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism and his teachings as portrayed in Ovid's "Metamorphoses" influenced the modern vegetarian movement.

paragraph: Section::::Biographical sources.

paragraph: No authentic writings of Pythagoras have survived, and almost nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical. The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by Xenophanes of Colophon, who had been one of his contemporaries. In the poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend. Alcmaeon of Croton, a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The poet Heraclitus of Ephesus, who was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, mocked Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery."

paragraph: The Greek poets Ion of Chios () and Empedocles of Acragas () both express admiration for Pythagoras in their poems. The first concise description of Pythagoras comes from the historian Herodotus of Halicarnassus (), who describes him as "not the most insignificant" of Greek sages and states that Pythagoras taught his followers how to attain immortality. The writings attributed to the Pythagorean philosopher Philolaus of Croton, who lived in the late fifth century BC, are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras. The Athenian rhetorician Isocrates (436–338 BC) was the first to describe Pythagoras as having visited Egypt. Aristotle wrote a treatise "On the Pythagoreans", which is no longer extant. Some of it may be preserved in the "Protrepticus". Aristotle's disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus also wrote on the same subject.

paragraph: Most of the major sources on Pythagoras's life are from the Roman period, by which point, according to the German classicist Walter Burkert, "the history of Pythagoreanism was already... the laborious reconstruction of something lost and gone." Three lives of Pythagoras have survived from late antiquity, all of which are filled primarily with myths and legends. The earliest and most respectable of these is the one from Diogenes Laërtius's "Lives and Opinions of Eminent Philosophers". The two later lives were written by the Neoplatonist philosophers Porphyry and Iamblichus and were partially intended as polemics against the rise of Christianity. The later sources are much lengthier than the earlier ones, and even more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus used material from the lost writings of Aristotle's disciples and material taken from these sources is generally considered to be the most reliable.

paragraph: Section::::Life.

paragraph: Section::::Life.:Early life.

paragraph: Herodotus, Isocrates, and other early writers agree that Pythagoras was the son of Mnesarchus and that he was born on the Greek island of Samos in the eastern Aegean. His father is said to have been a gem-engraver or a wealthy merchant, but his ancestry is disputed and unclear. Pythagoras's name led him to be associated with Pythian Apollo; Aristippus of Cyrene explained his name by saying, "He spoke (, ) the truth no less than did the (, )". A late source gives Pythagoras's mother's name as Pythaïs. Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful, wise, and beneficial to humankind. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates, at the age of 40, which would give a date of birth around 570 BC.

paragraph: During Pythagoras's formative years, Samos was a thriving cultural hub known for its feats of advanced architectural engineering, including the building of the Tunnel of Eupalinos, and for its riotous festival culture. It was a major center of trade in the Aegean where traders brought goods from the Near East. According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions. Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy. He was a contemporary of the philosophers Anaximander, Anaximenes, and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.

paragraph: Section::::Life.:Alleged travels.

paragraph: Pythagoras is traditionally thought to have received most of his education in the Near East. Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Near Eastern cultures. Like many other important Greek thinkers, Pythagoras was said to have studied in Egypt. By the time of Isocrates in the fourth century BC, Pythagoras's alleged studies in Egypt were already taken as fact. The writer Antiphon, who may have lived during the Hellenistic Era, claimed in his lost work "On Men of Outstanding Merit", used as a source by Porphyry, that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself, that he studied with the Egyptian priests at Diospolis (Thebes), and that he was the only foreigner ever to be granted the privilege of taking part in their worship. The Middle Platonist biographer Plutarch () writes in his treatise "On Isis and Osiris" that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile Solon received lectures from a Sonchis of Sais). According to the Christian theologian Clement of Alexandria (), "Pythagoras was a disciple of Soches, an Egyptian archprophet, as well as Plato of Sechnuphis of Heliopolis." Some ancient writers claimed, that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians.

paragraph: Other ancient writers, however, claimed that Pythagoras had learned these teachings from the Magi in Persia or even from Zoroaster himself. Diogenes Laërtius asserts that Pythagoras later visited Crete, where he went to the Cave of Ida with Epimenides. The Phoenicians are reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy. By the third century BC, Pythagoras was already reported to have studied under the Jews as well. Contradicting all these reports, the novelist Antonius Diogenes, writing in the second century BC, reports that Pythagoras discovered all his doctrines himself by interpreting dreams. The third-century AD Sophist Philostratus claims that, in addition to the Egyptians, Pythagoras also studied under Hindu sages in India. Iamblichus expands this list even further by claiming that Pythagoras also studied with the Celts and Iberians.

paragraph: Section::::Life.:Alleged Greek teachers.

paragraph: Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers. Some identify Hermodamas of Samos as a possible tutor. Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of rival of the poet Homer. Others credit Bias of Priene, Thales, or Anaximander (a pupil of Thales). Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries. The Neoplatonists wrote of a "sacred discourse" Pythagoras had written on the gods in the Doric Greek dialect, which they believed had been dictated to Pythagoras by the Orphic priest Aglaophamus upon his initiation to the orphic Mysteries at Leibethra. Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship. Iamblichus describes Pythagoreanism as a synthesis of everything Pythagoras had learned from Orpheus, from the Egyptian priests, from the Eleusinian Mysteries, and from other religious and philosophical traditions. Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent.

paragraph: Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often. Similar miracle stories were told about both Pythagoras and Pherecydes, including one in which the hero predicts a shipwreck, one in which he predicts the conquest of Messina, and one in which he drinks from a well and predicts an earthquake. Apollonius Paradoxographus, a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as a result of Pherecydes's influence. Another story, which may be traced to the Neopythagorean philosopher Nicomachus, tells that, when Pherecydes was old and dying on the island of Delos, Pythagoras returned to care for him and pay his respects. Duris, the historian and tyrant of Samos, is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras's wisdom exceeded his own. On the grounds of all these references connecting Pythagoras with Pherecydes, Riedweg concludes that there may well be some historical foundation to the tradition that Pherecydes was Pythagoras's teacher. Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis.

paragraph: Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras might have met Thales of Miletus, who would have been around fifty-four years older than him. Thales was a philosopher, scientist, mathematician, and engineer, also known for a special case of the inscribed angle theorem. Pythagoras's birthplace, the island of Samos, is situated in the Northeast Aegean Sea not far from Miletus. Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea. Porphyry agrees with this assertion, but calls the priestess Aristoclea ("Aristokleia"). Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries, or the Delphic oracle.

paragraph: Section::::Life.:In Croton.

paragraph: Porphyry repeats an account from Antiphon, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle". Here, Samians debated matters of public concern. Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach. Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends. Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos, but cautions that Antiphon's account, which makes reference to a specific building that was still in use during his own time, appears to be motivated by Samian patriotic interest.

paragraph: Around 530 BC, when Pythagoras was around forty years old, he left Samos. His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos, Riedweg notes that this explanation closely aligns with Nicomachus's emphasis on Pythagoras's purported love of freedom, but that Pythagoras's enemies portrayed him as having a proclivity towards tyranny. Other accounts claim that Pythagoras left Samos because he was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens. He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia. All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment. He served as an advisor to the elites in Croton and gave them frequent advice. Later biographers tell fantastical stories of the effects of his eloquent speeches in leading the people of Croton to abandon their luxurious and corrupt way of life and devote themselves to the purer system which he came to introduce.

paragraph: Section::::Life.:Family and friends.

paragraph: Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love" and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself". According to Porphyry, Pythagoras married Theano, a lady of Crete and the daughter of Pythenax and had several children with her. Porphyry writes that Pythagoras had two sons named Telauges and Arignote, and a daughter named Myia, who "took precedence among the maidens in Croton and, when a wife, among married women." Iamblichus mentions none of these children and instead only mentions a son named Mnesarchus after his grandfather. This son was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it.

paragraph: The wrestler Milo of Croton was said to have been a close associate of Pythagoras and was credited with having saved the philosopher's life when a roof was about to collapse. This association may been the result of confusion with a different man named Pythagoras, who was an athletics trainer. Diogenes Laërtius records Milo's wife's name as Myia. Iamblichus mentions Theano as the wife of Brontinus of Croton. Diogenes Laërtius states that the same Theano was Pythagoras's pupil and that Pythagoras's wife Theano was her daughter. Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime and quotes several opinions attributed to her. These writings are now known to be pseudepigraphical.

paragraph: Section::::Life.:Death.

paragraph: Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over the neighboring colony of Sybaris in 510 BC. After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected. The supporters of democracy, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. Followers of Cylon and Ninon attacked the Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place. Accounts of the attack are often contradictory and many probably confused it with later anti-Pythagorean rebellions. The building was apparently set on fire, and many of the assembled members perished; only the younger and more active members managed to escape.

paragraph: Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape. In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes. According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape, leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied. They reached the city of Metapontum, where they took shelter in the temple of the Muses and died there of starvation after forty days without food. Another tale recorded by Porphyry claims that, as Pythagoras's enemies were burning the house, his devoted students laid down on the ground to make a path for him to escape by walking over their bodies across the flames like a bridge. Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide. A different legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape, but that he came to a bean field and refused to run through it, since doing so would violate his teachings, so he stopped instead and was killed. This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.

paragraph: Section::::Teachings.

paragraph: Section::::Teachings.:Metempsychosis.

paragraph: Although the exact details of Pythagoras's teachings are uncertain, it is possible to reconstruct a general outline of his main ideas. Aristotle writes at length about the teachings of the Pythagoreans, but without mentioning Pythagoras directly. One of Pythagoras's main doctrines appears to have been "metempsychosis", the belief that all souls are immortal and that, after death, a soul is transferred into a new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus. Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.

paragraph: Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations. Diogenes Laërtius reports an account from Heraclides Ponticus that Pythagoras told people that he had lived four previous lives that he could remember in detail. The first of these lives was as Aethalides the son of Hermes, who granted him the ability to remember all his past incarnations. Next, he was incarnated as Euphorbus, a minor hero from the Trojan War briefly mentioned in the "Iliad". He then became the philosopher Hermotimus, who recognized the shield of Euphorbus in the temple of Apollo. His final incarnation was as Pyrrhus, a fisherman from Delos. One of his past lives, as reported by Dicaearchus, was as a beautiful courtesan.

paragraph: Section::::Teachings.:Mysticism.

paragraph: Another belief attributed to Pythagoras was that of the "harmony of the spheres", which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony. According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together. In his philosophical dialogue "Protrepticus", Aristotle has his literary double say:

paragraph: Pythagoras was said to have practiced divination and prophecy. In the visits to various places in Greece—Delos, Sparta, Phlius, Crete, etc.—which are ascribed to him, he usually appears either in his religious or priestly guise, or else as a lawgiver.

paragraph: Section::::Teachings.:Numerology.

paragraph: According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad) represented the origin of all things and the number two (the dyad) represented matter. The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo. The number four signified the four seasons and the four elements. The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage, because it was the sum of two and three.

paragraph: Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his "Life of Pythagoras", states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it. Andrew Gregory concludes that the tradition linking Pythagoras to the tetractys is probably genuine.

paragraph: Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton. In his landmark study "Lore and Science in Ancient Pythagoreanism", Walter Burkert argues that Pythagoras was a charismatic political and religious teacher, but that the number philosophy attributed to him was really an innovation by Philolaus. According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics. Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic, but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.

paragraph: Section::::Pythagoreanism.

paragraph: Section::::Pythagoreanism.:Communal lifestyle.

paragraph: Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life. The organization Pythagoras founded at Croton was called a "school", but, in many ways, resembled a monastery. The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other to the exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans. One Pythagorean maxim was ""koinà tà phílōn"" ("All things in common among friends"). Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as a divine figure, sent by the gods to benefit humankind. Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.

paragraph: Two groups existed within early Pythagoreanism: the "mathematikoi" ("learners") and the "akousmatikoi" ("listeners"). The "akousmatikoi" are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings; whereas the "mathematikoi" are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific. Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible. The study of mathematics and music may have been connected to the worship of Apollo. The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body. One anecdote of Pythagoras reports that when he encountered some drunken youths trying to break into the home of a virtuous woman, he sang a solemn tune with long spondees and the boys' "raging willfulness" was quelled. The Pythagoreans also placed particular emphasis on the importance of physical exercise; therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised.

paragraph: Section::::Pythagoreanism.:Prohibitions and regulations.

paragraph: Pythagorean teachings were known as "symbols" ("symbola") and members took a vow of silence that they would not reveal these symbols to non-members. Those who did not obey the laws of the community were expelled and the remaining members would erect tombstones for them as though they had died. A number of "oral sayings" ("akoúsmata") attributed to Pythagoras have survived, dealing with how members of the Pythagorean community should perform sacrifices, how they should honor the gods, how they should "move from here", and how they should be buried. Many of these sayings emphasize the importance of ritual purity and avoiding defilement. For instance, a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments. Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs and teach that a person should always put the right sandal on before the left. The exact meanings of these sayings, however, are frequently obscure. Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings, but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them:

paragraph: New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period, during which they were required to remain silent. Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations. Iamblichus provides a list of 235 famous Pythagoreans, seventeen of whom are women. In later times, many prominent female philosophers contributed to the development of Neopythagoreanism.

paragraph: Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of beans and the meat of non-sacrificial animals such as fish and poultry. Both of these assumptions, however, have been contradicted. Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis. Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet. Eudoxus of Cnidus, a student of Archytas, writes, "Pythagoras was distinguished by such purity and so avoided killing and killers that he not only abstained from animal foods, but even kept his distance from cooks and hunters." Other authorities contradict this statement. According to Aristoxenus, Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams. According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat.

paragraph: Section::::Legends.

paragraph: Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In a fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo". Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was supposedly once seen at both Metapontum and Croton at the same time. When Pythagoras crossed the river Kosas (the modern-day Basento), "several witnesses" reported that they heard it greet him by name. In Roman times, a legend claimed that Pythagoras was the son of Apollo. According to Muslim tradition, Pythagoras was said to have been initiated by Hermes (Egyptian Thoth).

paragraph: Pythagoras was said to have dressed all in white. He is also said to have borne a golden wreath atop his head and to have worn trousers after the fashion of the Thracians. Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control; he was always cheerful, but "abstained wholly from laughter, and from all such indulgences as jests and idle stories". Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word.

paragraph: Riedweg suggests that Pythagoras may have personally encouraged these legends, but Gregory states that there is no direct evidence of this. Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives.

paragraph: Section::::Attributed discoveries.

paragraph: Section::::Attributed discoveries.:In mathematics.

paragraph: Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem, as well as discoveries in the fields of music, astronomy, and medicine. Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"—that is, formula_1. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole "hecatomb", to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough.

paragraph: The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, but it is possible that he may have been the first one to introduce it to the Greeks. Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof. Burkert rejects this suggestion as implausible, noting that Pythagoras was never credited with having proved any theorem in antiquity. Furthermore, the manner in which the Babylonians employed Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources. Pythagoras's biographers state that he also was the first to identify the five regular solids and that he was the first to discover the Theory of Proportions.

paragraph: Section::::Attributed discoveries.:In music.

paragraph: According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard the sound of their hammers clanging against the anvils. Thinking that the sounds of the hammers were beautiful and harmonious, except for one, he rushed into the blacksmith shop and began testing the hammers. He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical. However, this legend is demonstrably false, as these ratios are only relevant to string length (such as the string of a monochord), and not to hammer weight.

paragraph: Section::::Attributed discoveries.:In astronomy.

paragraph: In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been the first to teach that the Earth was spherical, the first to divide the globe into five climactic zones, and the first to identify the morning star and the evening star as the same celestial object (now known as Venus). Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem. Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.

paragraph: Section::::Later influence in antiquity.

paragraph: Section::::Later influence in antiquity.:On Greek philosophy.

paragraph: Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC. Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia. According to later tradition, Archytas was elected as "strategos" ("general") seven times, even though others were prohibited from serving more than a year. Archytas was also a renowned mathematician and musician. He was a close friend of Plato and he is quoted in Plato's "Republic". Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that "Platonem ferunt didicisse Pythagorea omnia" ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn, Plato's middle dialogues, including "Meno", "Phaedo", and "The Republic", have a strong "Pythagorean coloring", and his last few dialogues (particularly "Philebus" and "Timaeus") are extremely Pythagorean in character.

paragraph: According to R. M. Hare, Plato's "Republic" may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton. Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality. Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and it is probable that both were influenced by Orphism. The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans. Bertrand Russell, in his "A History of Western Philosophy", contends that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought."

paragraph: A revival of Pythagorean teachings occurred in the first century BC when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria. At around the same time, Neopythagoreanism became prominent. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy and probably understood the soul as a "kind of mathematical harmony." The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory. Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.

paragraph: Section::::Later influence in antiquity.:On art and architecture.

paragraph: Greek sculpture sought to represent the permanent reality behind superficial appearances. Early Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies. The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type (), which was mathematically calculated. When dimensions changed, architects sought to relay permanence through mathematics. Maurice Bowra believes that these ideas influenced the theory of Pythagoras and his students, who believed that "all things are numbers".

paragraph: During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture. Greek sculptors and architects attempted to find the mathematical relation (canon) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor Polykleitos writes in his "Canon" that beauty consists in the proportion, not of the elements (materials), but of the interrelation of parts with one another and with the whole. In the Greek architectural orders, every element was calculated and constructed by mathematical relations. Rhys Carpenter states that the ratio 2:1 was "the generative ratio of the Doric order, and in Hellenistic times an ordinary Doric colonnade, beats out a rhythm of notes."

paragraph: The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica, a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans. The basilica was built underground because of the Pythagorean emphasis on secrecy and also because of the legend that Pythagoras had sequestered himself in a cave on Samos. The basilica's apse is in the east and its atrium in the west out of respect for the rising sun. It has a narrow entrance leading to a small pool where the initiates could purify themselves. The building is also designed according to Pythagorean numerology, with each table in the sanctuary providing seats for seven people. Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo. The apse depicts a scene of the poet Sappho leaping off the Leucadian cliffs, clutching her lyre to her breast, while Apollo stands beneath her, extending his right hand in a gesture of protection, symbolizing Pythagorean teachings about the immortality of the soul. The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred.

paragraph: The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology. The temple's circular plan, central axis, hemispherical dome, and alignment with the four cardinal directions symbolize Pythagorean views on the order of the universe. The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo. The twenty-eight ribs extending from the oculus symbolize the moon, because twenty-eight was the same number of months on the Pythagorean lunar calendar. The five coffered rings beneath the ribs represent the marriage of the sun and moon.

paragraph: Section::::Later influence in antiquity.:In early Christianity.

paragraph: Many early Christians had a deep respect for Pythagoras. Eusebius ( 260 – 340 AD), bishop of Caesarea, praises Pythagoras in his "Against Hierokles" for his rule of silence, his frugality, his "extraordinary" morality, and his wise teachings. In another work, Eusebius compares Pythagoras to Moses. In one of his letter, the Church Father Jerome ( 347 – 420 AD) praises Pythagoras for his wisdom and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him. Augustine of Hippo (354 – 430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him. In "On the Trinity", Augustine lauds the fact that Pythagoras was humble enough to call himself a "philosophos" or "lover of wisdom" rather than a "sage". In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.

paragraph: Section::::After antiquity.

paragraph: Section::::After antiquity.:In the Middle Ages.

paragraph: During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts. He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres. The "Timaeus" was the only dialogue of Plato to survive in Latin translation in western Europe, which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean. In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's "Lives and Opinions of Eminent Philosophers" from Greek into Latin and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's "Lives of Pythagoras" into Latin as well, thereby allowing them to be read and studied by western scholars. In 1494, the Greek Neopythagorean scholar Constantine Lascaris published "The Golden Verses of Pythagoras", translated into Latin, with a printed edition of his "Grammatica", thereby bringing them to a widespread audience. In 1499, he published the first Renaissance biography of Pythagoras in his work "Vitae illustrium philosophorum siculorum et calabrorum", issued in Messina.

paragraph: Section::::After antiquity.:On modern science.

paragraph: In his preface to his book "On the Revolution of the Heavenly Spheres" (1543), Nicolaus Copernicus cites various Pythagoreans as the most important influences on the development of his heliocentric model of the universe, deliberately omitting mention of Aristarchus of Samos, a non-Pythagorean astronomer who had developed a fully heliocentric model in the fourth century BC, in effort to portray his model as fundamentally Pythagorean. Johannes Kepler considered himself to be a Pythagorean. He believed in the Pythagorean doctrine of "musica universalis" and it was his search for the mathematical equations behind this doctrine that led to his discovery of the laws of planetary motion. Kepler titled his book on the subject "Harmonices Mundi" ("Harmonics of the World"), after the Pythagorean teaching that had inspired him. Near the conclusion of the book, Kepler describes himself falling asleep to the sound of the heavenly music, "warmed by having drunk a generous draught... from the cup of Pythagoras."

paragraph: Isaac Newton firmly believed in the Pythagorean teaching of the mathematical harmony and order of the universe. Though Newton was notorious for rarely giving others credit for their discoveries, he attributed the discovery of the Law of Universal Gravitation to Pythagoras. Albert Einstein believed that a scientist may also be "a Platonist or a Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research." The English philosopher Alfred North Whitehead argued that "In a sense, Plato and Pythagoras stand nearer to modern physical science than does Aristotle. The two former were mathematicians, whereas Aristotle was the son of a doctor". By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."

paragraph: Section::::After antiquity.:On vegetarianism.

paragraph: A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's "Metamorphoses", in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet. It was through Arthur Golding's 1567 English translation of Ovid's "Metamorphoses" that Pythagoras was best known to English-speakers throughout the early modern period. John Donne's "Progress of the Soul" discusses the implications of the doctrines expounded in the speech and Michel de Montaigne quoted the speech no less than three times in his treatise "Of Cruelty" to voice his moral objections against the mistreatment of animals. William Shakespeare references the speech in his play "The Merchant of Venice". John Dryden included a translation of the scene with Pythagoras in his 1700 work "Fables, Ancient and Modern" and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny. Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's "Metamorphoses". Until the word "vegetarianism" was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans". Percy Bysshe Shelley wrote an ode entitled "To the Pythagorean Diet" and Leo Tolstoy adopted the Pythagorean diet himself.

paragraph: Section::::After antiquity.:On Western esotericism.

paragraph: Early modern European esotericism drew heavily on the teachings of Pythagoras. The German humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah, arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition and that Pythagoras was therefore a kabbalist. In his dialogue "De verbo mirifico" (1494), Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH, ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.

paragraph: Heinrich Cornelius Agrippa's popular and influential three-volume treatise "De Occulta Philosophia" cites Pythagoras as a "religious magi" and indicates that Pythagoras's mystical numerology operates on a supercelestial level. The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton. Rosicrucianism used Pythagorean symbolism, as did Robert Fludd (1574–1637), who believed his own musical writings to have been inspired by Pythagoras. John Dee was heavily influenced by Pythagorean ideology, particularly the teaching that all things are made of numbers. Adam Weishaupt, the founder of the Illuminati, was a strong admirer of Pythagoras and, in his book "Pythagoras" (1787), he advocated that society should be reformed to be more like Pythagoras's commune at Croton. Wolfgang Amadeus Mozart incorporated Masonic and Pythagorean symbolism into his opera "The Magic Flute". Sylvain Maréchal, in his six-volume 1799 biography "The Voyages of Pythagoras", declared that all revolutionaries in all time periods are the "heirs of Pythagoras".

paragraph: Section::::After antiquity.:On literature.

paragraph: Dante Alighieri was fascinated by Pythagorean numerology and based his descriptions of Hell, Purgatory, and Heaven on Pythagorean numbers. Dante wrote that Pythagoras saw Unity as Good and Plurality as Evil and, in "Paradiso" XV, 56–57, he declares: "five and six, if understood, ray forth from unity." The number eleven and its multiples are found throughout the "Divine Comedy", each book of which has thirty-three cantos, except for the "Inferno", which has thirty-four, the first of which serves as a general introduction. Dante describes the ninth and tenth bolgias in the Eighth Circle of Hell as being twenty-two miles and eleven miles respectively, which correspond to the fraction , which was the Pythagorean approximation of pi. Hell, Purgatory, and Heaven are all described as circular and Dante compares the wonder of God's majesty to the mathematical puzzle of squaring the circle. The number three also features prominently: the "Divine Comedy" has three parts and Beatrice is associated with the number nine, which is equal to three times three.

paragraph: The Transcendentalists read the ancient "Lives of Pythagoras" as guides on how to live a model life. Henry David Thoreau was impacted by Thomas Taylor's translations of Iamblichus's "Life of Pythagoras" and Stobaeus's "Pythagoric Sayings" and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes. The Pythagorean teaching of "musica universalis" is a recurring theme throughout Thoreau's "magnum opus", "Walden".

paragraph: Section::::See also.

paragraph: BULLET::::- Isopsephy (Gematria)

paragraph: BULLET::::- List of things named after Pythagoras

paragraph: BULLET::::- Lute of Pythagoras

paragraph: BULLET::::- Pythagoras tree (fractal)

paragraph: BULLET::::- Pythagorean comma

paragraph: BULLET::::- Pythagorean cup

paragraph: BULLET::::- Pythagorean triple

paragraph: BULLET::::- Pythagoras (sculptor)

paragraph: BULLET::::- Sacred geometry

paragraph: Section::::References.

paragraph: Footnotes

paragraph: Citations

paragraph: Section::::References.:Works cited.

paragraph: Only a few relevant source texts deal with Pythagoras and the Pythagoreans; most are available in different translations. Later texts usually build solely upon information in these works.

paragraph: Classical sources

paragraph: BULLET::::- Diogenes Laërtius, "Vitae philosophorum VIII" ("Lives of Eminent Philosophers"), c. 200 AD, which in turn references the lost work "Successions of Philosophers" by Alexander Polyhistor —

paragraph: BULLET::::- Porphyry, "Vita Pythagorae" ("Life of Pythagoras"), c. 270 AD — "Porphyry, Life of Pythagoras", translated by Kenneth Sylvan Guthrie (1920)

paragraph: BULLET::::- Iamblichus, "De Vita Pythagorica" ("On the Pythagorean Life"), c. 300 AD — "Iamblichus, Life of Pythagoras", translated by Kenneth Sylvan Guthrie (1920)

paragraph: BULLET::::- Apuleius, following Aristoxenus, writes about Pythagoras in "Apologia", c. 150 AD, including a story of his being taught by Zoroaster—a story also found in Clement of Alexandria.

paragraph: BULLET::::- Hierocles of Alexandria, "Golden Verses of Pythagoras", c. 430 AD

paragraph: Modern secondary sources

paragraph: Section::::External links.

paragraph: BULLET::::- "Pythagoras of Samos", The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland

paragraph: BULLET::::- "Pythagoras and the Pythagoreans, Fragments and Commentary", Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History

paragraph: BULLET::::- "Pythagoras and the Pythagoreans", Department of Mathematics, Texas A&M University

paragraph: BULLET::::- "Pythagoras and Pythagoreanism", "The Catholic Encyclopedia"

alias:
Pythagoras of Samos
Pythagoras from Samos

description: ancient Greek mathematician and philosopher

enwikiquote_title: Pythagoras

wikidata_label: Pythagoras

wikipedia_title: Pythagoras


text:
racing cyclist
1976 Tour de France

categories: Italian male cyclists,People from the Province of Verona,1950 births,2016 deaths,Tour de France cyclists,Giro d'Italia cyclists

paragraph: Luciano Conati

paragraph: Luciano Conati (17 March 1950 – 6 February 2016) was an Italian professional racing cyclist. He rode in the 1976 Tour de France.

description: Italian bicycle racer (1950-2016)

wikidata_label: Luciano Conati

wikipedia_title: Luciano Conati


text:
Danish
actor
Royal Danish Theatre
silent film
Pas på pigerne
Huset på Christianshavn
Matador
Han, hun og Hamlet
5 raske piger
Ud i den kolde sne
Bag Københavns kulisser
Panserbasse
Incognito
Familien Olsen
My Son Peter
The Crime of Tove Andersen
Bussen
Crazy Paradise
Venus fra Vestø
The Girl and the Press Photographer
Miss April
Vi har det jo dejligt
It's Nifty in the Navy
Flagermusen
Onkel Joakims hemmelighed
The Olsen Gang
The Olsen Gang's Big Score
Girls at Sea
Fængslende feriedage

categories: Danish male film actors,1897 births,1981 deaths,Danish male silent film actors,Danish male stage actors,Male actors from Copenhagen,20th-century Danish male actors

paragraph: Arthur Jensen (actor)

paragraph: Arthur Jensen (9 November 1897 – 28 November 1981) was a Danish actor whose career lasted for almost 60 years. He made his début on stage at the Royal Danish Theatre in 1923, and he had his big screen début in the silent film "Pas på pigerne" in 1930.

paragraph: Today he is arguably best known for his roles as superintendent Meyer in the TV-series Huset på Christianshavn and as Hr. Schwann in the TV-series Matador in the 1970s.

paragraph: Section::::Selected filmography.

paragraph: BULLET::::- "Han, hun og Hamlet" (1932)

paragraph: BULLET::::- "5 raske piger" (1933)

paragraph: BULLET::::- "Ud i den kolde sne" (1934)

paragraph: BULLET::::- "Bag Københavns kulisser" (1935)

paragraph: BULLET::::- "Panserbasse" (1936)

paragraph: BULLET::::- "Incognito" (1937)

paragraph: BULLET::::- "Familien Olsen" (1940)

paragraph: BULLET::::- "My Son Peter" (1953)

paragraph: BULLET::::- "The Crime of Tove Andersen" (1953)

paragraph: BULLET::::- "Bussen" (1961)

paragraph: BULLET::::- "Crazy Paradise" (1962)

paragraph: BULLET::::- "Venus fra Vestø" (1962)

paragraph: BULLET::::- "The Girl and the Press Photographer" (1963)

paragraph: BULLET::::- "Miss April" (1963)

paragraph: BULLET::::- "Vi har det jo dejligt" (1963)

paragraph: BULLET::::- "It's Nifty in the Navy" (1965)

paragraph: BULLET::::- "Flagermusen" (1966)

paragraph: BULLET::::- "Onkel Joakims hemmelighed" (1967)

paragraph: BULLET::::- "The Olsen Gang" (1968)

paragraph: BULLET::::- "The Olsen Gang's Big Score" (1972)

paragraph: BULLET::::- "Girls at Sea" (1977)

paragraph: BULLET::::- "Fængslende feriedage" (1978)

description: Danish actor

wikidata_label: Arthur Jensen

wikipedia_title: Arthur Jensen (actor)


text:
14th century
Thomas III of Piedmont
Guyonne de Chalon
Dean
Salisbury Cathedral
canon
Archbishop of Lyon
Primate of Gaul
city walls
Philip the Fair
Louis, King of Navarre
Charles of Valois
Pope
John XXII
his city

paragraph: Peter of Savoy (Archbishop of Lyon)

paragraph: Peter of Savoy, died in November 1332, was a prelate of the 14th century.

paragraph: Peter was the son of Thomas III of Piedmont and Guyonne de Chalon. In 1304, he was Dean of Salisbury Cathedral and a canon.

paragraph: In December 1308, he was appointed Archbishop of Lyon and Primate of Gaul.

paragraph: Unlike his predecessor, Peter of Savoy does not accept the gradual takeover of the kingdom of France in Lyon. It therefore encourages residents to révolt, encourages them to strengthen the city walls, and he puts aside the historical dispute between the archbishop and cathédral chapter, providing a pretext for Philip the Fair to send his son Louis, King of Navarre and his brother Charles of Valois to lead an army besieging Lyon in 1310. The war ended with the intervention of the Archbishop's uncle, Amédée V of Savoie, who reluctantly agreed with the king's side not to be the next victim. A treaty was signed on 10 April 1312. But Peter losses control of Lyon to the King. The people of Lyon receive several franchises, such as the right to establish fees for the service of the city.

paragraph: These are the subject of two written papers, one by clerics Lyon between the opening of the Council of Vienna on 16 October 1311 and the Treaty of 10 April 1312, appointed Grauamina, the other by the prosecutor of the bailiff Macon, between this treaty and the end of 1312. The first seeks to demonstrate that the royal depredations were huge, considering the 150 000 pounds tournaments; the second minimizes the contrary, bringing the cost to 10 000 pounds tournaments only. Of this, the royal treasury will not give in that 2000 livres, which the king added, by "royal munificence" (sua munificentia regalis) 500 Other livres. These compensations are paid to the archbishop 27 December 1312.

paragraph: In 1316, he sees the election and coronation of Pope John XXII in his city.

wikidata_label: Pierre de Savoie

wikipedia_title: Peter of Savoy (Archbishop of Lyon)


text:
French
prelate
archbishop of Lyon
Louis de Villars, Archbishop of Lyon
chapter
Lyon
sacristan
Bishop of Viviers
Bishop of Valence and Die
Archbishop of Lyon
Dauphin
Humbert II
vicar
Dauphiné
France

categories: Archbishops of Lyon,Bishops of Viviers,1354 deaths,French bishops

paragraph: Henri de Villars (died 1354)

paragraph: Henri de Villars otherwise Henri de Thoire-Villars (died 1354) was a 14th-century French prelate, latterly archbishop of Lyon.

paragraph: Section::::Life.

paragraph: Henri was the son of Humbert V, sire of Thoire and Villars, and his wife Leonora de Beaujeu, and a nephew of Louis de Villars, Archbishop of Lyon.

paragraph: He was a canon of the chapter in Lyon, later sacristan and "chamarier" (the superintendent of the archbishop's finances). In 1333 he was appointed Bishop of Viviers and in 1336 Bishop of Valence and Die. In 1342 he was elected Archbishop of Lyon.

paragraph: On 28 April 1343, the Dauphin Humbert II appointed him vicar of the Dauphiné, of which he was the last governor before the sale of the principality to France in 1349.

wikidata_label: Henri II de Villars

wikipedia_title: Henri de Villars (died 1354)


text:
painter
Dublin
Hudson River school
National Academy of Design
Pennsylvania Academy of the Fine Arts
Amon Carter Museum
Honolulu Museum of Art
Hudson River Museum
Metropolitan Museum of Art
New-York Historical Society
ArtCyclopedia
A Hudson River Portfolio
Artwork by William Guy Wall

categories: 1864 deaths,1792 births,American people of Irish descent,American watercolorists,American male painters,People from Dublin (city),Landscape artists,19th-century American painters

paragraph: William Guy Wall

paragraph: William Guy Wall (1792 – 1864) was an American painter of Irish birth.

paragraph: Wall was born in Dublin in 1792 and arrived in New York in 1812. He was already a well trained artist and soon became well known for his sensitive watercolor views of the Hudson River Valley and surroundings. Some of these watercolors were published as engravings by John Hill and his son John William Hill in the Hudson River Portfolio (New York, 1821-1825), one of the first publications to make Americans aware of the beauty of their own country. Wall's landscapes (and a few seascapes) were straightforward representations of America's awe-inspiring vistas—neither romanticized nor idealized. He is classified as either a forerunner or an early member of the Hudson River school. Wall was a founding member of the National Academy of Design (New York) and exhibited frequently at such institutions as the Pennsylvania Academy of the Fine Arts (Philadelphia) and the Apollo Association (New York). He lived in America from 1812 to 1835 and again from 1856 to 1860. He returned to Ireland in 1860 and died in Dublin in 1864. William Guy Wall's son, William Archibald Wall (1820–1875), was also a landscape painter.

paragraph: The Amon Carter Museum (Fort Worth, Texas), the Honolulu Museum of Art, the Hudson River Museum (Yonkers, New York), the Metropolitan Museum of Art and the New-York Historical Society are among the public collections having paintings by William Guy Wall.

paragraph: Section::::References.

paragraph: BULLET::::- Howat, John K., "A Picturesque Site in the Catskills: The Kaaterskill Falls as Painted by William Guy Wall", "Honolulu Academy of Arts Journal", vol. I, 1974, 16.

paragraph: Section::::External links.

paragraph: BULLET::::- ArtCyclopedia

paragraph: BULLET::::- A Hudson River Portfolio

paragraph: BULLET::::- Artwork by William Guy Wall

alias:
william g. wall
W. Wall

description: American painter

wikidata_label: William Guy Wall

wikipedia_title: William Guy Wall


text: 5000 metres

categories: Sportspeople from Saxony,Medalists at the 1908 Summer Olympics,1984 deaths,People from Glashütte,German male cyclists,Olympic medalists in cycling,Olympic cyclists of Germany,Cyclists at the 1908 Summer Olympics,1887 births,Olympic bronze medalists for Germany,People from the Kingdom of Saxony,Olympic silver medalists for Germany,German track cyclists

paragraph: Karl Neumer

paragraph: Karl Neumer (23 February 1887 – 16 May 1984) was a German track cyclist. At the 1908 Olympics he won a bronze medal in the individual sprint and a silver in the team pursuit. He also competed in the 5000 metres race, but was eliminated in the first round.

paragraph: Neumer held the national sprint title in 1907–1910. In 1912 he raced professionally, but with little success. He then ran a vegetable shop in Dresden, which was destroyed by bombing in 1945. His 1908 bicycle was one of the first exhibits at the Leipzig Sports Museum. Before his death in 1984, Neumer was the oldest living German Olympic medalist.

description: German racing cyclist

wikidata_label: Karl Neumer

wikipedia_title: Karl Neumer