• Images
• Videos
• Documents
• Books
• Articles

Related Image Collections Add Image

Profiles

1 Image

We don't have any YouTube videos related to Pythagoras yet.

You can add one yourself here.

We don't have any PDF documents related to Pythagoras yet.

You can add one yourself here.

We don't have any Books related to Pythagoras yet.

You can add one yourself here.

Archived Web Articles Add Article

Early Greek Writings on Pythagoras

web.archive.org

Life

No authentic writings of Pythagoras have survived,⁴⁵ and almost nothing is known for certain about his life.⁶⁷ The earliest sources on Pythagoras's life, from Xenophanes, Heraclitus, Empedocles, Ion of Chios, and Herodotus⁸ are brief, ambiguous, and often satirical.⁹¹⁰ The major sources on Pythagoras's life are three biographies from late antiquity written by Diogenes Laërtius, Porphyry, and Iamblichus, all of which are filled primarily with myths and legends¹¹¹²¹³ and which become longer and more fantastic in their descriptions of Pythagoras's achievements the more removed they are from Pythagoras's times.¹⁴¹⁵ However, Porphyry and Iamblichus also used some material taken from earlier writings in the 4th century BC by Aristotle's students Dicaearchus, Aristoxenus, and Heraclides Ponticus,¹⁶ which, when it can be identified, is generally considered to be the most reliable.¹⁷

Early life

There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account.

— Walter Burkert, 1972¹⁸

Herodotus¹⁹ and Isocrates agree that Pythagoras was the son of Mnesarchus,²⁰²¹ and that he was born on the Greek island of Samos in the eastern Aegean.²²²³²⁴ He is said to have been a gem-engraver or a wealthy merchant²⁵²⁶²⁷ but his ancestry is disputed and unclear.²⁸ Apollonius of Tyana, gives her name as Pythaïs.²⁹³⁰ 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.³¹ 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.³² Pythagoras's name led him to be associated with Pythian Apollo (Pūthíā); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke [ἀγορεύω, agoreúō] the truth no less than did the Pythian [πυθικός puthikós]".³³

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.³⁴ It was a major center of trade in the Aegean where traders brought goods from the Near East.³⁵ According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions.³⁶ Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy.³⁷³⁸ He was a contemporary of the philosophers Anaximander, Anaximenes, and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos.³⁹

Reputed travels

Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures, which appears to have been recognized by authors later in the Classical and Hellenistic periods, who attributed many of Pythagoras' unusual and unconventional beliefs to invented travels to far off lands, where he learned from those people himself.⁴⁰ The doctrine of metempsychosis, or reincarnation of the soul after death, which Herodotus had mistakenly attributed to the Egyptians, led to an elaborate tale⁴¹ where Pythagoras learned the Egyptian language from the Pharaoh Amasis II himself, and then traveled to study with the Egyptian priests at Diospolis (Thebes), where he was the only foreigner ever to be granted the privilege of taking part in their worship.⁴² Other ancient writers, however, claimed that Pythagoras had learned these teachings from the Magi in Persia or even from Zoroaster himself.⁴³⁴⁴ The Phoenicians are also reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy.⁴⁵ By the third century BC, Pythagoras was already reported to have studied under the Jews as well.⁴⁶ By the third century AD, Pythagoras was also reported by Philostratus to have studied under sages or gymnosophists in India, and, according to Iamblichus, also with the Celts and Iberians.⁴⁷

Alleged Greek teachers

Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers.⁴⁸ Diogenes Laërtius asserts that Pythagoras later visited Crete, where he went to the Cave of Ida with Epimenides.⁴⁹ Some identify Hermodamas of Samos as a possible tutor.⁵⁰⁵¹ Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer.⁵² Others credit Bias of Priene, Thales,⁵³ or Anaximander (a pupil of Thales).⁵⁴⁵⁵⁵⁶ Other traditions claim the mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries.⁵⁷ 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.⁵⁸ Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship.⁵⁹ 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.⁶⁰ 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.⁶¹ Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent.⁶²

Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros is mentioned most often.⁶³⁶⁴ 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.⁶⁵ 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.⁶⁶ 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.⁶⁷ 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.⁶⁸ 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.⁶⁹ Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis.⁷⁰

In Croton

Porphyry repeats an account from Antiphon, who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle".⁷¹⁷² Here, Samians debated matters of public concern.⁷³⁷⁴ Supposedly, the school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach.⁷⁵ Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends.⁷⁶⁷⁷ Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos,⁷⁸ 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.⁷⁹

Around 530 BC, when Pythagoras was about forty years old, he left Samos.^80818283 His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos;⁸⁴ 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.⁸⁵ 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.⁸⁶ He arrived in the Greek colony of Croton (today's Crotone, in Calabria) in what was then Magna Graecia.^8788899091 All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment.⁹²⁹³⁹⁴ He served as an advisor to the elites in Croton and gave them frequent advice.⁹⁵ 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.⁹⁶⁹⁷

Family and friends

Suda writes that Pythagoras had 4 children (Telauges, Mnesarchus, Myia and Arignote).⁹⁸ The wrestler Milo of Croton was said to have been a close associate of Pythagoras⁹⁹ and was credited with having saved the philosopher's life when a roof was about to collapse.¹⁰⁰ This association may have been the result of confusion with a different man named Pythagoras, who was an athletics trainer.¹⁰¹

Death

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.¹⁰² After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected.¹⁰³ 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.¹⁰⁴ 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.¹⁰⁵¹⁰⁶ Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC.¹⁰⁷¹⁰⁸ The building was apparently set on fire,¹⁰⁹ and many of the assembled members perished;¹¹⁰ only the younger and more active members managed to escape.¹¹¹

Sources disagree regarding whether Pythagoras was present when the attack occurred and, if he was, whether or not he managed to escape.¹¹²¹¹³ In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes.¹¹⁴ According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape,¹¹⁵ leading a small group of followers to the nearby city of Locris, where they pleaded for sanctuary, but were denied.¹¹⁶ 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.^117118119120 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.¹²¹ Pythagoras managed to escape, but was so despondent at the deaths of his beloved students that he committed suicide.¹²² A different legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape, but that he came to a fava bean field and refused to run through it, since doing so would violate his teachings, so he stopped instead and was killed.¹²³ This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself.¹²⁴

Teachings

Metempsychosis

Although the exact details of Pythagoras's teachings are uncertain,¹²⁵¹²⁶ it is possible to reconstruct a general outline of his main ideas.¹²⁷¹²⁸ Aristotle writes at length about the teachings of the Pythagoreans,¹²⁹¹³⁰ but without mentioning Pythagoras directly.¹³¹¹³² One of Pythagoras's main doctrines appears to have been metempsychosis,^{133134135136137} the belief that all souls are immortal and that, after death, a soul is transferred into a new body.¹³⁸¹³⁹ This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus.¹⁴⁰¹⁴¹ The earliest source on Pythagoras's metempsychosis is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon (c. 570 – c. 478 BC), who had been one of his contemporaries,¹⁴²¹⁴³ in which 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.^144145146147 Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur.¹⁴⁸

Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations.¹⁴⁹ 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.^150151152 The first of these lives was as Aethalides the son of Hermes, who granted him the ability to remember all his past incarnations.¹⁵³ Next, he was incarnated as Euphorbus, a minor hero from the Trojan War briefly mentioned in the Iliad.¹⁵⁴ He then became the philosopher Hermotimus,¹⁵⁵ who recognized the shield of Euphorbus in the temple of Apollo.¹⁵⁶ His final incarnation was as Pyrrhus, a fisherman from Delos.¹⁵⁷ One of his past lives, as reported by Dicaearchus, was as a beautiful courtesan.¹⁵⁸¹⁵⁹

Numerology

Another belief attributed to Pythagoras was that of the "harmony of the spheres",¹⁶⁰¹⁶¹ which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.¹⁶²¹⁶³ According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together.¹⁶⁴

The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything.

— Aristot. Met. 1, 985b

Modern scholars typically ascribe these discoveries to the later Pythagorean philosopher Philolaus of Croton (c. 470 – c. 385 BC), whose extant fragments are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras.¹⁶⁵ In his landmark study Lore and Science in Ancient Pythagoreanism, Walter Burkert argues that Pythagoras was a charismatic political and religious teacher,¹⁶⁶ but that the number philosophy attributed to him was really an innovation by Philolaus.¹⁶⁷ According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics.¹⁶⁸ Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic,¹⁶⁹ but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.¹⁷⁰ For the later Pythagoreans, Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the "perfect" number, ten.¹⁷¹¹⁷² The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance.¹⁷³ 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.¹⁷⁴¹⁷⁵

This shouldn't be confused with a simplified version known today as "Pythagorean numerology", involving a variant of an isopsephic technique known – among other names – as pythmenes 'roots'¹⁷⁶ or 'base numbers',¹⁷⁷ by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word.¹⁷⁸

Pythagoreanism

Communal lifestyle

Main article: Pythagoreanism

Both Plato and Isocrates state that, above all else, Pythagoras was known as the founder of a new way of life.^179180181 The organization Pythagoras founded at Croton was called a "school",¹⁸²¹⁸³ but, in many ways, resembled a monastery.¹⁸⁴ 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.¹⁸⁵ The members of the sect shared all their possessions in common¹⁸⁶ and were devoted to each other to the exclusion of outsiders.¹⁸⁷¹⁸⁸ Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans.¹⁸⁹¹⁹⁰ One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends").¹⁹¹ 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 mankind.¹⁹² Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time.¹⁹³ For Pythagoreans, the highest reward humans could attain was for their soul to join in the life of the gods and thus escape the cycle of reincarnation.¹⁹⁴ Two groups existed within early Pythagoreanism: the mathematikoi ("learners") and the akousmatikoi ("listeners").¹⁹⁵¹⁹⁶ The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings;¹⁹⁷ whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific.¹⁹⁸ Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed the two approaches were compatible.¹⁹⁹ The study of mathematics and music may have been connected to the worship of Apollo.²⁰⁰ The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body.²⁰¹ 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.²⁰² The Pythagoreans also placed particular emphasis on the importance of physical exercise;²⁰³ therapeutic dancing, daily morning walks along scenic routes, and athletics were major components of the Pythagorean lifestyle.²⁰⁴ Moments of contemplation at the beginning and end of each day were also advised.²⁰⁵

Prohibitions and regulations

Pythagorean teachings were known as "symbols" (symbola)²⁰⁶ and members took a vow of silence that they would not reveal these symbols to non-members.^207208209 Those who did not obey the laws of the community were expelled²¹⁰ and the remaining members would erect tombstones for them as though they had died.²¹¹ A number of "oral sayings" (akoúsmata) attributed to Pythagoras have survived,²¹²²¹³ 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.²¹⁴ Many of these sayings emphasize the importance of ritual purity and avoiding defilement.²¹⁵²¹⁶ Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs²¹⁷ and teach that a person should always put the right sandal on before the left.²¹⁸ The exact meanings of these sayings, however, are frequently obscure.²¹⁹ Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings,²²⁰ but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them:²²¹

New initiates were allegedly not permitted to meet Pythagoras until after they had completed a five-year initiation period,²³² during which they were required to remain silent.²³³ Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women²³⁴ and female members of Pythagoras's school appear to have played an active role in its operations.²³⁵²³⁶ Iamblichus provides a list of 235 famous Pythagoreans,²³⁷ seventeen of whom are women.²³⁸ In later times, many prominent female philosophers contributed to the development of Neopythagoreanism.²³⁹

Pythagoreanism also entailed a number of dietary prohibitions.^240241242 It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans²⁴³²⁴⁴ and the meat of non-sacrificial animals such as fish and poultry.²⁴⁵²⁴⁶ Both of these assumptions, however, have been contradicted.²⁴⁷²⁴⁸ Pythagorean dietary restrictions may have been motivated by belief in the doctrine of metempsychosis.^249250251252 Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet.^253254255 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."²⁵⁶²⁵⁷ Other authorities contradict this statement.²⁵⁸ According to Aristoxenus,²⁵⁹ Pythagoras allowed the use of all kinds of animal food except the flesh of oxen used for ploughing, and rams.²⁶⁰²⁶¹ According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices²⁶² and established a diet for athletes dependent on meat.²⁶³

Legends

Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends.²⁶⁴²⁶⁵ Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure.²⁶⁶²⁶⁷ In a fragment, Aristotle writes that Pythagoras had a golden thigh,^268269270 which he publicly exhibited at the Olympic Games²⁷¹ and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo".²⁷²²⁷³ Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications.²⁷⁴ He was supposedly once seen at both Metapontum and Croton at the same time.^275276277278 When Pythagoras crossed the river Kosas (the modern-day Basento), "several witnesses" reported that they heard it greet him by name.²⁷⁹²⁸⁰ In Roman times, a legend claimed that Pythagoras was the son of Apollo.²⁸¹

Pythagoras was said to have dressed all in white.²⁸²²⁸³ He is also said to have borne a golden wreath atop his head²⁸⁴ and to have worn trousers after the fashion of the Thracians.²⁸⁵ Pythagoras was said to have had extraordinary success in dealing with animals.²⁸⁶²⁸⁷ A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it.²⁸⁸²⁸⁹ Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans²⁹⁰²⁹¹ 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.²⁹²²⁹³ Riedweg suggests that Pythagoras may have personally encouraged these legends,²⁹⁴ but Gregory states that there is no direct evidence of this.²⁹⁵

Attributed discoveries

In mathematics

Although Pythagoras is most famous today for his alleged mathematical discoveries,²⁹⁶²⁹⁷ classical historians dispute whether he himself ever actually made any significant contributions to the field.²⁹⁸²⁹⁹ Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem,³⁰⁰ as well as discoveries in the fields of music,³⁰¹ astronomy,³⁰² and medicine.³⁰³ Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem,³⁰⁴³⁰⁵ 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"³⁰⁶—that is, a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb, to the gods.³⁰⁷³⁰⁸ Cicero rejected this story as spurious³⁰⁹ because of the much more widely held belief that Pythagoras forbade blood sacrifices.³¹⁰ Porphyry attempted to explain the story by asserting that the ox was actually made of dough.³¹¹

The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras,^312313314 and Burkert rejects the suggestion that Pythagoras had anything to do with it,³¹⁵ noting that Pythagoras was never credited with having proved any theorem in antiquity.³¹⁶ 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.³¹⁷

In music

See also: Pythagorean tuning and Pythagorean hammers

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.³¹⁸³¹⁹ Thinking that the sounds of the hammers were beautiful and harmonious, except for one,³²⁰ he rushed into the blacksmith shop and began testing the hammers.³²¹ 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.³²²³²³

In astronomy

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,³²⁴ the first to divide the globe into five climatic zones,³²⁵ and the first to identify the morning star and the evening star as the same celestial object (now known as Venus).³²⁶ Of the two philosophers, Parmenides has a much stronger claim to having been the first³²⁷ and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem.³²⁸ Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical.³²⁹ By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.³³⁰

Later influence in antiquity

On Greek philosophy

Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC.³³¹ Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia.³³² According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year.³³³ Archytas was also a renowned mathematician and musician.³³⁴ He was a close friend of Plato³³⁵ and he is quoted in Plato's Republic.³³⁶³³⁷ Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans.^338339340 Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean").³⁴¹ According to Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and The Republic, have a strong "Pythagorean coloring",³⁴² and his last few dialogues (particularly Philebus and Timaeus)³⁴³ are extremely Pythagorean in character.³⁴⁴

The poet Heraclitus of Ephesus (fl. c. 500 BC), who was born a few miles across the sea from Samos and may have lived within Pythagoras's lifetime,³⁴⁵ mocked Pythagoras as a clever charlatan,³⁴⁶³⁴⁷ 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."³⁴⁸³⁴⁹ Alcmaeon of Croton (fl. c. 450 BC), a doctor who lived in Croton at around the same time Pythagoras lived there,³⁵⁰ incorporates many Pythagorean teachings into his writings³⁵¹ and alludes to having possibly known Pythagoras personally.³⁵² The Greek poets Ion of Chios (c. 480 – c. 421 BC) and Empedocles of Acragas (c. 493 – c. 432 BC) both express admiration for Pythagoras in their poems.³⁵³

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.³⁵⁴ Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality.³⁵⁵ Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world"³⁵⁶ and both were probably influenced by Orphism.³⁵⁷ The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans.³⁵⁸

A revival of Pythagorean teachings occurred in the first century BC³⁵⁹ when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed the rise of a "new" Pythagoreanism in Alexandria.³⁶⁰ At around the same time, Neopythagoreanism became prominent.³⁶¹ The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings.³⁶² The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy³⁶³ and probably understood the soul as a "kind of mathematical harmony".³⁶⁴ The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory.³⁶⁵ Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines.³⁶⁶

On art and architecture

The oldest known building designed according to Pythagorean teachings is the Porta Maggiore Basilica,³⁶⁷ a subterranean basilica which was built during the reign of the Roman emperor Nero as a secret place of worship for Pythagoreans.³⁶⁸ The basilica was built underground because of the Pythagorean emphasis on secrecy³⁶⁹ and also because of the legend that Pythagoras had sequestered himself in a cave on Samos.³⁷⁰ The basilica's apse is in the east and its atrium in the west out of respect for the rising sun.³⁷¹ It has a narrow entrance leading to a small pool where the initiates could purify themselves.³⁷² The building is also designed according to Pythagorean numerology,³⁷³ with each table in the sanctuary providing seats for seven people.³⁷⁴ Three aisles lead to a single altar, symbolizing the three parts of the soul approaching the unity of Apollo.³⁷⁵ 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,³⁷⁶ symbolizing Pythagorean teachings about the immortality of the soul.³⁷⁷ The interior of the sanctuary is almost entirely white because the color white was regarded by Pythagoreans as sacred.³⁷⁸

The emperor Hadrian's Pantheon in Rome was also built based on Pythagorean numerology.³⁷⁹ 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.³⁸⁰ The single oculus at the top of the dome symbolizes the monad and the sun-god Apollo.³⁸¹ 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.³⁸² The five coffered rings beneath the ribs represent the marriage of the sun and moon.³⁸³

In early Christianity

Many early Christians had a deep respect for Pythagoras.³⁸⁴ Eusebius (c. 260 – c. 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.³⁸⁵ In another work, Eusebius compares Pythagoras to Moses.³⁸⁶ In one of his letters, the Church Father Jerome (c. 347 – c. 420 AD) praises Pythagoras for his wisdom³⁸⁷ and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.³⁸⁸ Augustine of Hippo (354–430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him.³⁸⁹ 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".³⁹⁰ In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.³⁹¹

Influence after antiquity

In the Middle Ages

During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts.³⁹² He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres.³⁹³ The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe,³⁹⁴ which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean.³⁹⁵ A large-scale translation movement emerged during the Abbasid Caliphate, translating many Greek texts into Arabic. Works ascribed to Pythagoras included the "Golden Verses" and snippets of his scientific and mathematical theories.³⁹⁶ By translating and disseminating Pythagorean texts, Islamic scholars ensured their survival and wider accessibility. This preserved knowledge that might have otherwise been lost through the decline of the Roman Empire and the neglect of classical learning in Europe.³⁹⁷ In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin³⁹⁸ and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well,³⁹⁹ thereby allowing them to be read and studied by western scholars.⁴⁰⁰ In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica,⁴⁰¹ thereby bringing them to a widespread audience.⁴⁰² In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.⁴⁰³

On modern science

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,⁴⁰⁴⁴⁰⁵ 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.⁴⁰⁶ Johannes Kepler considered himself to be a Pythagorean.⁴⁰⁷⁴⁰⁸ 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.⁴⁰⁹⁴¹⁰ He also called Pythagoras the "grandfather" of all Copernicans.⁴¹¹

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."⁴¹² 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".⁴¹³ By this measure, Whitehead declared that Einstein and other modern scientists like him are "following the pure Pythagorean tradition."⁴¹⁴⁴¹⁵

On vegetarianism

A fictionalized portrayal of Pythagoras appears in Book XV of Ovid's Metamorphoses,⁴¹⁶ in which he delivers a speech imploring his followers to adhere to a strictly vegetarian diet.⁴¹⁷ 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.⁴¹⁸ John Donne's Progress of the Soul discusses the implications of the doctrines expounded in the speech,⁴¹⁹ 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.⁴²⁰ John Dryden included a translation of the scene with Pythagoras in his 1700 work Fables, Ancient and Modern,⁴²¹ and John Gay's 1726 fable "Pythagoras and the Countryman" reiterates its major themes, linking carnivorism with tyranny.⁴²² Lord Chesterfield records that his conversion to vegetarianism had been motivated by reading Pythagoras's speech in Ovid's Metamorphoses.⁴²³ Until the word vegetarianism was coined in the 1840s, vegetarians were referred to in English as "Pythagoreans".⁴²⁴

On Western esotericism

Early modern European esotericism drew heavily on the teachings of Pythagoras.⁴²⁵ The German humanist scholar Johannes Reuchlin (1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah,⁴²⁶ arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic tradition⁴²⁷ and that Pythagoras was therefore a kabbalist.⁴²⁸ In his dialogue De verbo mirifico (1494), Reuchlin compared the Pythagorean tetractys to the ineffable divine name YHWH,⁴²⁹ ascribing each of the four letters of the tetragrammaton a symbolic meaning according to Pythagorean mystical teachings.⁴³⁰

Heinrich Cornelius Agrippa's popular and influential three-volume treatise De Occulta Philosophia cites Pythagoras as a "religious magi"⁴³¹ and advances the idea that Pythagoras's mystical numerology operates on a supercelestial level,⁴³² a religious term used to describe a high heavenly realm used during his time. The freemasons deliberately modeled their society on the community founded by Pythagoras at Croton.⁴³³ Rosicrucianism used Pythagorean symbolism,⁴³⁴ as did Robert Fludd (1574–1637),⁴³⁵ who believed his own musical writings to have been inspired by Pythagoras.⁴³⁶ John Dee was heavily influenced by Pythagorean ideology,⁴³⁷⁴³⁸ particularly the teaching that all things are made of numbers.⁴³⁹⁴⁴⁰

On literature

The Transcendentalists read the ancient Lives of Pythagoras as guides on how to live a model life.⁴⁴¹ Henry David Thoreau was impacted by Thomas Taylor's translations of Iamblichus's Life of Pythagoras and Stobaeus's Pythagoric Sayings⁴⁴² and his views on nature may have been influenced by the Pythagorean idea of images corresponding to archetypes.⁴⁴³ The Pythagorean teaching of musica universalis is a recurring theme throughout Thoreau's magnum opus, Walden.⁴⁴⁴

See also

• List of things named after Pythagoras
• Ex pede Herculem, "from his foot, [we can measure] Hercules" – a maxim based on the apocryphal story that Pythagoras estimated Hercules's stature based on the length of a racecourse at Pisae
• Pythagorean cup – a prank cup with a hidden siphon built in, attributed to Pythagoras
• Pythagorean means – the arithmetic mean, the geometric mean, and the harmonic mean, claimed to have been studied by Pythagoras

Notes

Citations

Classical sources

• Xenophanes (1960) [c. 525 BC]. "Xenophanes: Leben und Lehre (Life and Teachings)". In Walther, Kranz (ed.). Die Fragmente der Vorsokratiker. Vol. I. Translated by Hermann, Diels (9th ed.). Berlin: Weidmannsche Verlagsbuchhandlung. p. 130. OCLC 1072633182 – via Internet Archive.. [The original Greek fragments of Xenophanes are provided, which are primarily preserved through the work of Diogenes (Diog VIII). For English translation see Burnet (1920).]
• ——— (1920) [c. 525 BC]. "Science and Religion". Early Greek Philosophy. Translated by Burnet, John (3rd ed.). London: A. & C. Black, Ltd. p. 118. OCLC 3610194 – via Internet Archive.. [An English translation of DK 21B7.]
• Herodotus (1920) [c. 430 BC]. "Book II". The Persian Wars. Vol. I. Translated by Godley, A. D. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99130-9. OCLC 966656476 – via Perseus Digital Library (perseus.tufts.edu). {{citation}}: ISBN / Date incompatibility (help)
• ——— (1920) [c. 430 BC]. "Book IV". The Persian Wars. Vol. II. Translated by Godley, A. D. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99131-6. OCLC 966656315 – via Perseus Digital Library (perseus.tufts.edu). {{citation}}: ISBN / Date incompatibility (help)
• Plato (1969) [c. 380 BC]. "Republic". Plato in Twelve Volumes, Vols. 5 & 6. Translated by Shorey, Paul. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99304-4. OCLC 6947747 – via Perseus Digital Library (perseus.tufts.edu).
• Aristotle (2017) [c. 350 BC]. Johnson, Monte Ransome; Hutchinson, D. S (eds.). "Protrepticus". Archived from the original on 12 May 2024 – via PhilPapers.
• ——— (1931) [c. 350 BC]. "De Anima". In Ross, W.D. (ed.). The Works of Aristotle Translated into English. Vol. 3. Translated by Smith, J. A. Oxford: Oxford University Press. OCLC 237147799 – via The Internet Classics Archive (classics.mit.edu).
• ——— (1933) [c. 350 BC]. "Book I". Metaphysics Books I–IX. Vol. XVII. Translated by Tredennick, Hugh. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99299-3. OCLC 958278244 – via Perseus Digital Library (perseus.tufts.edu). {{cite book}}: ISBN / Date incompatibility (help)
• Cicero (1928) [c. 52 BC]. "De Re Publica". On the Republic. On the Laws (De Re Publica. De Legibus). Vol. XVI. Translated by Keyes, Clinton W. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99235-1. OCLC 298443420 – via Internet Archive. {{citation}}: ISBN / Date incompatibility (help)
• ——— (1928) [c. 52 BC]. "De Legibus". On the Republic. On the Laws (De Re Publica. De Legibus). Vol. XVI. Translated by Keyes, Clinton W. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99235-1. OCLC 298443420 – via Internet Archive. {{citation}}: ISBN / Date incompatibility (help)
• ——— (1914) [c. 45 BC]. On the Ends of Good and Evil (De Finibus Bonorum et Malorum). Vol. XVII. Translated by H., Rackham. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99044-9. OCLC 298443420 – via LacusCurtius. {{citation}}: ISBN / Date incompatibility (help)
• ——— (1923) [c. 45 BC]. Tusculan Disputations (Tusculanae Disputationes). Vol. XVIII. Translated by J.E., King. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99156-9. OCLC 298443420 – via Internet Archive. {{citation}}: ISBN / Date incompatibility (help)
• ——— (1927) [c. 44 BC]. "De Divinatione I". On Old Age. On Friendship. On Divination (De Senectute, De Amicitia, De Divinatione). Vol. XX. Translated by W. A., Falconer. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99170-5. OCLC 298443420 – via Internet Archive. {{citation}}: ISBN / Date incompatibility (help)
• ——— (1913) [c. 44 BC]. On Duties (De officiis). Vol. XXI. Translated by Miller, Walter. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99033-3. OCLC 298443420 – via Internet Archive. {{citation}}: ISBN / Date incompatibility (help)
• Plutarch (1962) [c. 100 AD]. "On Isis and Osiris (De Iside Et Osiride)". Plutarch's Moralia. Vol. V. Translated by Babbitt, Frank Cole. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC 13897903 – via Internet Archive.
• ——— (1968) [c. 100 AD]. "On the Signs of Socrates (De Genio Socratis)". Plutarch's Moralia. Vol. VII. Translated by De Lacy, Phillip H.; Einarson, Benedict. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC 938641243 – via Internet Archive.
• ——— (1957) [c. 100 AD]. "On the Eating of Flesh (Du Esu Carnium)". Plutarch's Moralia. Vol. XII. Translated by Helmbold, William C.; Cherniss, Harold. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd – via Internet Archive.
• ——— (1967) [c. 100 AD]. "That Epicurus Actually Makes a Pleasant Life Impossible (Non posse suaviter vivi secundum Epicurum)". Plutarch's Moralia. Vol. XIV. Translated by Einarson, Benedict; de Lacy, Phillip H. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd – via Internet Archive.
• Apuleius (1970) [c. 150 AD]. "Apologia". The Apologia and Florida of Apuleius of Madaura. Translated by Harold Edgeworth, Butler. Westport, Conn.: Greenwood Press. ISBN 978-0-8371-3066-8. OCLC 313541 – via Internet Archive.. [Which claims Zoroaster taught Pythagoras, also found in Strom, 1.15.]
• Diogenes Laërtius (1925) [c. 200 AD]. "Book I". Lives of the Eminent Philosophers. Vol. I. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99203-0. OCLC 908430780 – via Wikisource. {{cite book}}: ISBN / Date incompatibility (help)
• ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. {{cite book}}: ISBN / Date incompatibility (help)
• Clement of Alexandria (1991) [c. 200 AD]. "Book I, Chapter XV". Stromateis (Miscellanies). The Fathers of the Church. Vol. 86. Translated by John, Ferguson. Washington, D.C.: Catholic University of America Press. ISBN 978-0-8132-1185-5. OCLC 647919762 – via Internet Archive.
• Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive.
• Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive.
• Hierocles of Alexandria (1995) [c. 430 AD]. "Golden Verses of Pythagoras". The Pythagorean Golden Verses: With Introduction and Commentary. Religions in the Graeco-Roman World. Vol. 123. Translated by Thom, Johan C. Leiden: E.J. Brill. ISBN 978-90-04-10105-0. OCLC 31131998 – via Internet Archive.

Modern secondary sources

• Afonasin, Eugene V. (2012). Afonasin, Eugene V.; Dillon, John M.; Finamore, John (eds.). Iamblichus and the Foundations of Late Platonism. Leiden and Boston: Brill. ISBN 978-90-04-23011-8.
• Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1.
• Bregman, Jay (2002). "Neoplatonism and American Aesthetics". In Alexandrakis, Aphrodite; Moulafakis, Nicholas J. (eds.). Neoplatonism and Western Aesthetics. Studies in Neoplatonism: Ancient and Modern. Vol. 12. Albany, New York: State University of New York Press. ISBN 978-0-7914-5280-6.
• Burkert, Walter (May 1960). "Platon oder Pythagoras? Zum Ursprung des Wortes "Philosophie"". Hermes (in German). 88 (2): 159–177. JSTOR 4475110.
• Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive.
• Burkert, Walter (1985). Greek Religion. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-36281-9.
• Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0.
• Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2.
• Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7.
• De Vogel, Cornelia J. (1966). Pythagoras and Early Pythagoreanism: An Interpretation of Neglected Evidence on the Philosopher Pythagoras. Assen: Van Gorcum. OCLC 513833.
• Dicks, D. R. (1970). Early Greek Astronomy to Aristotle. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-0561-7.
• Dillon, John; Hershbell, Jackson (1991). Betz, Hans Dieter; O'Neill, Edward N. (eds.). Iamblichus, On the Pythagorean way of life: Text, Translation and Notes. Text and Translations 29: Graeco Romain Religion Series. Vol. 11. Atlanta, Georgia: Scholars Press. ISBN 1-55540-522-3 – via Internet Archive.
• French, Peter J. (2002) [1972]. John Dee: The World of the Elizabethan Magus. New York City, New York and London, England: Routledge. ISBN 978-0-7448-0079-1.
• Grant, Michael (1989). The Classical Greeks. History of Civilization. New York City, New York: Charles Schribner's Sons. ISBN 978-0-684-19126-3.
• Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2.
• Guthrie, William Keith Chambers (1967) [1962]. A History of Greek Philosophy, Volume 1: The Earlier Presocratics and the Pythagoreans. Cambridge University Press. OCLC 973780248 – via Internet Archive.
• Hare, R. M. (1999) [1982]. "Plato". In Taylor, C. C. W.; Hare, R. M.; Barnes, Jonathan (eds.). Greek Philosophers: Socrates, Plato, and Aristotle. Past Masters. Oxford, England: Oxford University Press. pp. 103–189. ISBN 978-0-19-285422-3.
• Jacoby, Felix; Bollansée, Jan (1999). Schepens, Guido (ed.). Die Fragmente der griechischen Historiker. Vol. 4. Brill. ISBN 978-90-04-11303-9.
• James, Jamie (1993). The Music of the Spheres. New York, NY: Grove Press. ISBN 978-0-8021-1307-8 – via Internet Archive.
• Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5.
• Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive.
• Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8.
• Lindberg, David C. (1978). Science in the Middle Ages. University of Chicago Press. ISBN 978-0226482330.
• Lindberg, David C. (2013). The Cambridge History of Science: Volume 2, Medieval Science. Cambridge University Press. ISBN 978-0521594486.
• Lloyd, Geoffrey (24 April 2014). "Pythagoras". In Huffman, Carl A. (ed.). A History of Pythagoreanism. Cambridge University Press. pp. 24–45. ISBN 978-1-139-91598-4. Retrieved 18 May 2025.
• McKeown, J. C. (2013). A Cabinet of Greek Curiosities: Strange Tales and Surprising Facts from the Cradle of Western Civilization. Oxford, England: Oxford University Press. ISBN 978-0-19-998210-3.
• O'Meara, Dominic J. (1989). Pythagoras Revived. Oxford, England: Oxford University Press. ISBN 978-0-19-823913-0.
• Pomeroy, Sarah B. (2013). Pythagorean Women: The History and Writings. Baltimore, Maryland: The Johns Hopkins University Press. ISBN 978-1-4214-0956-6.
• Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1.
• Russo, Attilio (2004). "Costantino Lascaris tra fama e oblio nel Cinquecento messinese". Archivio Storico Messinese. LXXXIV–LXXXV: 5–87, especially 51–53. ISSN 0392-0240.
• Sherman, William Howard (1995). John Dee: The Politics of Reading and Writing in the English Renaissance. Amherst, Massachusetts: The University of Massachusetts Press. ISBN 978-1-55849-070-3.
• Taub, Liba (2017). Science Writing in Greco-Roman Antiquity. Cambridge University Press. ISBN 978-0-521-11370-0.
• Whitehead, Afred North (1953) [1926]. Science and the Modern World. Cambridge, England: Cambridge University Press. ISBN 978-0-521-23778-9. {{citation}}: ISBN / Date incompatibility (help)
• Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8.

Further reading

• Christensen, Thomas (2002). The Cambridge History of Western Music Theory. Cambridge, England: Cambridge University Press. ISBN 978-0-521-62371-1.
• Hermann, Arnold (2005). To Think Like God: Pythagoras and Parmenides—the Origins of Philosophy. Las Vegas, Nevada: Parmenides Publishing. ISBN 978-1-930972-00-1.
• Horky, Philip Sydney (2013). Plato and Pythagoreanism. Oxford, England: Oxford University Press. ISBN 978-0-19-989822-0.
• Kingsley, Peter (1995). Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition. Oxford, England: Oxford University Press.
• Scharinger, Stephan (2017). Die Wunder des Pythagoras: Überlieferungen im Vergleich [The miracles of Pythagoras: A comparison of traditions]. Philippika, vol. 107. Wiesbaden: Harrassowitz. ISBN 978-3-447-10787-7.
• Schofield, Malcolm (2013). Aristotle, Plato and Pythagoreanism in the First Century BC: New Directions for Philosophy. Cambridge, England: Cambridge University Press. ISBN 978-1-107-02011-5.

External links

• Pythagoras on In Our Time at the BBC
• Huffman, Carl. "Pythagoras". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.{{cite encyclopedia}}: CS1 maint: overridden setting (link)
• "Pythagoras and the Pythagoreans, Fragments and Commentary", Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
• "Pythagoras and the Pythagoreans" Archived 2009-03-09 at the Wayback Machine, Department of Mathematics, Texas A&M University
• "Pythagoras and Pythagoreanism", The Catholic Encyclopedia
• Works by or about Pythagoras at the Internet Archive
• Works by Pythagoras at LibriVox (public domain audiobooks)

References

1. /paɪˈθæɡərəs/ py-THAG-ər-əs,[236] also US: /pɪˈθæɡərəs/ pih-.[237] Ancient Greek: Πυθαγόρας ὁ Σάμιος, romanized: Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or Πυθαγόρης, Pythagórēs in Ionian Greek. /wiki/Help:IPA/English ↩

2. "The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (Porphyry, Vit. Pyth, §9) that he left Samos to escape the tyranny of Polycrates at the age of forty, we may put his birth round about 570 BC, or a few years earlier. The length of his life was variously estimated in antiquity, but it is agreed that he lived to a fairly ripe old age, and most probably he died at about seventy-five or eighty." Guthrie (1967), p. 173 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

3. Cicero, Tusc. Qu, pp. 431–433, §5.3.8–§5.3.9 (citing Heraclides Ponticus fr. 88 Wehrli), Diog I, 1.12, Diog VIII, §8.8, Iamblichus, Vit. Pyth, §58. Burkert attempted to discredit this ancient tradition Burkert (1960) but it has been defended by De Vogel (1966), pp. 97–102 and Riedweg (2005), p. 92 - ——— (1923) [c. 45 BC]. Tusculan Disputations (Tusculanae Disputationes). Vol. XVIII. Translated by J.E., King. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99156-9. OCLC 298443420 – via Internet Archive. https://archive.org/details/cicerostusculand0000tran/mode/2up ↩

4. Joost-Gaugier (2006), p. 11. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

5. Celenza (2010), p. 796. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

6. Gregory (2015), pp. 21–23. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

7. Copleston (2003), p. 29. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

8. Lloyd 2014, p. 28. - Lloyd, Geoffrey (24 April 2014). "Pythagoras". In Huffman, Carl A. (ed.). A History of Pythagoreanism. Cambridge University Press. pp. 24–45. ISBN 978-1-139-91598-4. Retrieved 18 May 2025. https://books.google.com/books?id=xFdzAwAAQBAJ ↩

9. Kahn (2001), p. 2. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

10. Burkert (1985), p. 299. - Burkert, Walter (1985). Greek Religion. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-36281-9. https://archive.org/details/greekreligion0000burk ↩

11. Copleston (2003), p. 29. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

12. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

13. Zhmud (2012), p. 9. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

14. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

15. Zhmud (2012), p. 9. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

16. Burkert (1972), p. 109. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

17. Burkert (1972), p. 109. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

18. Burkert (1972), p. 106. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

19. Hdt. 4, p. 297, §95. - ——— (1920) [c. 430 BC]. "Book IV". The Persian Wars. Vol. II. Translated by Godley, A. D. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99131-6. OCLC 966656315 – via Perseus Digital Library (perseus.tufts.edu). https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0126%3Abook%3D4%3Achapter%3D95 ↩

20. Joost-Gaugier (2006), p. 16. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

21. Kahn (2001), p. 6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

22. Joost-Gaugier (2006), p. 11. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

23. Kahn (2001), p. 6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

24. Kenny (2004), p. 9. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

25. Porphyry, Vit. Pyth, §1, §10. - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

26. Strom, 1.62(2), cit. Afonasin (2012), p. 15 - Clement of Alexandria (1991) [c. 200 AD]. "Book I, Chapter XV". Stromateis (Miscellanies). The Fathers of the Church. Vol. 86. Translated by John, Ferguson. Washington, D.C.: Catholic University of America Press. ISBN 978-0-8132-1185-5. OCLC 647919762 – via Internet Archive. https://archive.org/details/stromateisbookso0085clem/page/72/mode/2up ↩

27. Joost-Gaugier (2006), p. 21. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

28. Some writers call him a native Samian, a Tyrrhenian from Lemnos, or a Phliasian from Peloponnesus, and give Marmacus or Demaratus as his name (see Diog VIII, §1.1; Porphyry, Vit. Pyth, §1, §2; Justin, xx. 4; Pausanias, ii. 13; Iamblichus, Vit. Pyth, §2.4). Due to this obscurity, some modern scholars deem it safer to accept "that Pythagoras and his father were pure-blooded Greeks, of undiluted Samian stock". Jacoby & Bollansée (1999), pp. 256–257, n. 73 /wiki/Samos ↩

29. Taub (2017), p. 122. - Taub, Liba (2017). Science Writing in Greco-Roman Antiquity. Cambridge University Press. ISBN 978-0-521-11370-0. ↩

30. Apollonius of Tyana ap. Porphyry, Vit. Pyth, §2 /wiki/Apollonius_of_Tyana ↩

31. Riedweg (2005), p. 59. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

32. Porphyry, Vit. Pyth, §9. - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

33. Riedweg (2005), p. 59. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

34. Riedweg (2005), pp. 45–47. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

35. Joost-Gaugier (2006), p. 11. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

36. Joost-Gaugier (2006), p. 11. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

37. Kahn (2001), p. 6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

38. Riedweg (2005), pp. 44–45. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

39. Riedweg (2005), pp. 44–45. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

40. Riedweg (2005), pp. 7–8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

41. Porphyry, Vit. Pyth, §6. - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

42. Riedweg (2005), pp. 7–8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

43. Diog VIII, §1.1, §1.3. - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

44. Riedweg (2005), pp. 7–8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

45. Riedweg (2005), pp. 7–8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

46. Riedweg (2005), pp. 7–8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

47. Riedweg (2005), pp. 7–8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

48. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

49. Diog VIII, 1.1, 1.3. - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

50. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

51. Porphyry, Vit. Pyth, §2; Diog VIII, §1.2 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

52. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

53. Iamblichus, Vit. Pyth, §9. - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

54. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

55. Iamblichus, Vit. Pyth, §9. - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

56. Porphyry, Vit. Pyth, §2. - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

57. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

58. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

59. Riedweg (2005), pp. 8–9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

60. Riedweg (2005), pp. 8–9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

61. Riedweg (2005), p. 8. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

62. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

63. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

64. Diog I, 1.13, 1.15; Diog VIII, §1.2, §1.40; Cicero, de Div. I, p. 345, §49.122 - Diogenes Laërtius (1925) [c. 200 AD]. "Book I". Lives of the Eminent Philosophers. Vol. I. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99203-0. OCLC 908430780 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_I ↩

65. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

66. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

67. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

68. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

69. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

70. Riedweg (2005), p. 9. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

71. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

72. Cornelli & McKirahan (2013), p. 64. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

73. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

74. Cornelli & McKirahan (2013), p. 64. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

75. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

76. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

77. Cornelli & McKirahan (2013), p. 64. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

78. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

79. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

80. Joost-Gaugier (2006), p. 11. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

81. Kahn (2001), p. 6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

82. Riedweg (2005), p. 11. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

83. Gregory (2015), p. 22. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

84. Riedweg (2005), p. 11. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

85. Riedweg (2005), p. 11. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

86. Iamblichus, Vit. Pyth, §28; Porphyry, Vit. Pyth, §9 - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

87. Kahn (2001), p. 6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

88. Gregory (2015), p. 22. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

89. De Vogel (1966), pp. 21ff. - De Vogel, Cornelia J. (1966). Pythagoras and Early Pythagoreanism: An Interpretation of Neglected Evidence on the Philosopher Pythagoras. Assen: Van Gorcum. OCLC 513833. https://search.worldcat.org/oclc/513833 ↩

90. Cfr. Cicero, De Re Publica, pp. 137–139, §2.15.28–§2.15.30 - Cicero (1928) [c. 52 BC]. "De Re Publica". On the Republic. On the Laws (De Re Publica. De Legibus). Vol. XVI. Translated by Keyes, Clinton W. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99235-1. OCLC 298443420 – via Internet Archive. https://archive.org/details/ciceroderepublic0000clin/page/334/mode/2up ↩

91. Riedweg (2005), pp. 11–12. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

92. Kahn (2001), p. 6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

93. De Vogel (1966), pp. 148–150. - De Vogel, Cornelia J. (1966). Pythagoras and Early Pythagoreanism: An Interpretation of Neglected Evidence on the Philosopher Pythagoras. Assen: Van Gorcum. OCLC 513833. https://search.worldcat.org/oclc/513833 ↩

94. Riedweg (2005), pp. 12–13. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

95. Riedweg (2005), pp. 12–18. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

96. Porphyry, Vit. Pyth, §18; Iamblichus, Vit. Pyth, §37 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

97. Riedweg (2005), pp. 13–18. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

98. Suda Encyclopedia, th.84. https://www.cs.uky.edu/~raphael/sol/sol-entries/theta/84 ↩

99. Riedweg (2005), pp. 5–6, 59, 73. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

100. Riedweg (2005), pp. 5–6, 59, 73. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

101. Riedweg (2005), p. 10. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

102. Kahn (2001), pp. 6–7. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

103. Kahn (2001), pp. 6–7. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

104. Riedweg (2005), p. 19. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

105. Kahn (2001), p. 7. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

106. Riedweg (2005), pp. 19–20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

107. Riedweg (2005), p. 19. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

108. Plutarch, de Gen. Socr, p. 419, §583a. - ——— (1968) [c. 100 AD]. "On the Signs of Socrates (De Genio Socratis)". Plutarch's Moralia. Vol. VII. Translated by De Lacy, Phillip H.; Einarson, Benedict. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. OCLC 938641243 – via Internet Archive. https://archive.org/details/plutarchsmoralia07plut/page/360/mode/2up ↩

109. Kahn (2001), p. 7. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

110. Kahn (2001), p. 7. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

111. Iamblichus, Vit. Pyth, §255–§259; Porphyry, Vit. Pyth, §54–§57; Diog VIII, §1.39; comp. Plutarch, de Gen. Socr, p. 419, §583a - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

112. Burkert (1972), p. 106. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

113. Riedweg (2005), pp. 19–20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

114. Riedweg (2005), pp. 19–20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

115. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

116. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

117. Burkert (1972), p. 106. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

118. Kahn (2001), p. 7. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

119. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

120. Grant (1989), p. 278. - Grant, Michael (1989). The Classical Greeks. History of Civilization. New York City, New York: Charles Schribner's Sons. ISBN 978-0-684-19126-3. https://archive.org/details/classicalgreeks00gran_0 ↩

121. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

122. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

123. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

124. Riedweg (2005), p. 20. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

125. Burkert (1972), pp. 106–109. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

126. Kahn (2001), pp. 5–6. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

127. Burkert (1972), pp. 106–109. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

128. Kahn (2001), pp. 9–11. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

129. Copleston (2003), p. 31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

130. Burkert (1972), pp. 29–30. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

131. Copleston (2003), p. 31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

132. Burkert (1972), pp. 29–30. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

133. Kahn (2001), p. 11. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

134. Zhmud (2012), p. 232. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

135. Burkert (1985), pp. 300–301. - Burkert, Walter (1985). Greek Religion. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-36281-9. https://archive.org/details/greekreligion0000burk ↩

136. Gregory (2015), pp. 24–25. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

137. Copleston (2003), pp. 30–31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

138. Kahn (2001), p. 11. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

139. Gregory (2015), pp. 24–25. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

140. Kahn (2001), p. 11. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

141. Diog VIII, §1.36, comp. Aristot. De Anima, I. 2–3; Hdt. 2, p. 425, §123 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

142. Joost-Gaugier (2006), p. 12. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

143. Riedweg (2005), p. 62. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

144. Xenophanes' Poem (or Elegies) on Pythagorus is provided below, which was preserved in Diog VIII, §1.36: Greek: περὶ δὲ τοῦ ἄλλοτε ἄλλον γεγενῆσθαι (Pythagoras) Ζενοφάνης ἐν ἐλεγείαι προσμαρτυρεῖ, ἧς ἀρχή 'νῦν ... κέλενθον'. ὃ δὲ περὶ αὐτοῦ (Pythagoras) φησιν, οὕτως ἔχει καί ... αἰών'. νῦν αὖτ' ἄλλον ἔπειμι λόγον, δείξω δὲ κέλευθον. καί ποτέ μιν στυφελιζομένου σκύλακος παριόντα φασὶν ἐποικτῖραι καὶ τόδε φάσθαι ἔπος "παῦσαι μηδὲ ῥάπιζε, ἐπεὶ ἡ φίλου ἀνέρος ἐστὶν ψυχή, τὴν ἔγνων φθεγξαμένης αὐδῆς." DK 21B7, p. 130 English: "And now I will turn to another tale and point the way. ... Once they say that he (Pythagoras) was passing by when a dog was being beaten and spoke this word: "Stop! don't beat it! For it is the soul of a friend that I recognised when I heard its voice." Burnet (1920), p. 118 /wiki/Elegies ↩

145. Burkert (1985), p. 299. - Burkert, Walter (1985). Greek Religion. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-36281-9. https://archive.org/details/greekreligion0000burk ↩

146. Joost-Gaugier (2006), p. 12. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

147. Copleston (2003), p. 31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

148. Gregory (2015), p. 25. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

149. Kahn (2001), p. 12. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

150. Diog VIII, §1.3–§1.5. - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

151. Cornelli & McKirahan (2013), pp. 164–167. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

152. Porphyry, Vit. Pyth, §26; Pausanias, ii. 17; Horace, Od. i. 28,1. 10 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

153. Cornelli & McKirahan (2013), pp. 164–165. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

154. Cornelli & McKirahan (2013), pp. 165–166. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

155. Cornelli & McKirahan (2013), p. 167. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

156. Cornelli & McKirahan (2013), p. 167. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

157. Cornelli & McKirahan (2013), p. 167. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

158. Zhmud (2012), p. 232. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

159. Aulus Gellius, iv. 11 ↩

160. Riedweg (2005), pp. 29–30. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

161. Gregory (2015), pp. 38–39. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

162. Riedweg (2005), pp. 29–30. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

163. Gregory (2015), pp. 38–39. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

164. Riedweg (2005), p. 30. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

165. Joost-Gaugier (2006), pp. 87–88. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

166. Kahn (2001), pp. 2–3. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

167. Kahn (2001), p. 3. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

168. Kahn (2001), pp. 2–3. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

169. Burkert (1972), pp. 428–433. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

170. Burkert (1972), p. 465. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

171. Gregory (2015), pp. 28–29. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

172. Burkert (1972), pp. 467–468. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

173. Riedweg (2005), p. 29. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

174. Riedweg (2005), p. 29. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

175. Iamblichus, Vit. Pyth, §29. - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

176. Gregory (2015), pp. 32–34 - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

177. Zhmud (2012), p. 277 - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

178. Gregory (2015), pp. 32–34 - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

179. Plato, Republic, X 600a–b; Isocrates, Busiris, 28 - Plato (1969) [c. 380 BC]. "Republic". Plato in Twelve Volumes, Vols. 5 & 6. Translated by Shorey, Paul. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99304-4. OCLC 6947747 – via Perseus Digital Library (perseus.tufts.edu). https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0168%3Abook%3D7%3Asection%3D530d#note-link3 ↩

180. Cornelli & McKirahan (2013), p. 168. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

181. Grant (1989), p. 277. - Grant, Michael (1989). The Classical Greeks. History of Civilization. New York City, New York: Charles Schribner's Sons. ISBN 978-0-684-19126-3. https://archive.org/details/classicalgreeks00gran_0 ↩

182. Porphyry, Vit. Pyth, §19. - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

183. Thirlwall, Hist. of Greece, vol. ii. p. 148 ↩

184. Riedweg (2005), p. 31. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

185. comp. Cicero, de Leg, p. 335, §1.12.34; Cicero, de Off, p. 59, §1.17.56; Diog VIII, §1.10 - ——— (1928) [c. 52 BC]. "De Legibus". On the Republic. On the Laws (De Re Publica. De Legibus). Vol. XVI. Translated by Keyes, Clinton W. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99235-1. OCLC 298443420 – via Internet Archive. https://archive.org/details/ciceroderepublic0000clin/page/334/mode/2up ↩

186. Cornelli & McKirahan (2013), p. 65. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

187. Aristonexus ap. Iamblichus, Vit. Pyth, §94, §101, 229, etc.; comp. the story of Damon and Phintias; Porphyry, Vit. Pyth, §60; Iamblichus, Vit. Pyth, §233 - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

188. Cornelli & McKirahan (2013), pp. 68–69. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

189. Iamblichus, Vit. Pyth, §98; Strabo, vi. - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

190. Kenny (2004), p. 10. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

191. Cornelli & McKirahan (2013), p. 65. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

192. Dillon & Hershbell (1991), p. 14; O'Meara (1989), pp. 35–40 - Dillon, John; Hershbell, Jackson (1991). Betz, Hans Dieter; O'Neill, Edward N. (eds.). Iamblichus, On the Pythagorean way of life: Text, Translation and Notes. Text and Translations 29: Graeco Romain Religion Series. Vol. 11. Atlanta, Georgia: Scholars Press. ISBN 1-55540-522-3 – via Internet Archive. https://archive.org/details/onpythagoreanway0000iamb/mode/2up ↩

193. Riedweg (2005), p. 31. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

194. Kahn (2001), p. 52. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

195. Zhmud (2012), pp. 2, 16. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

196. Gregory (2015), p. 31. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

197. Gregory (2015), p. 31. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

198. Gregory (2015), p. 31. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

199. Gregory (2015), p. 31. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

200. Aelian, Varia Historia, ii. 26; Diog VIII, §1.13; Iamblichus, Vit. Pyth, §8, §91, §141 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

201. Riedweg (2005), p. 30. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

202. Riedweg (2005), p. 30. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

203. Riedweg (2005), p. 31. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

204. Riedweg (2005), p. 31. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

205. Riedweg (2005), pp. 33–34. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

206. Kahn (2001), p. 8. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

207. Kahn (2001), p. 8. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

208. Cornelli & McKirahan (2013), p. 168. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

209. Scholion ad Aristophanes, Nub. 611; Iamblichus, Vit. Pyth, §237–§238 - Iamblichus (1987) [c. 300 AD]. "De Vita Pythagorica (On the Pythagorean Life)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/n49/mode/2up ↩

210. Cornelli & McKirahan (2013), p. 69. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

211. Cornelli & McKirahan (2013), p. 69. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

212. Copleston (2003), p. 31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

213. Riedweg (2005), pp. 64–67. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

214. Riedweg (2005), p. 64. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

215. Riedweg (2005), p. 65. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

216. Copleston (2003), pp. 30–31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

217. Kenny (2004), p. 10. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

218. Kenny (2004), p. 10. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

219. Riedweg (2005), pp. 65–67. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

220. Riedweg (2005), pp. 65–66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

221. Riedweg (2005), pp. 66–67. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

222. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

223. Copleston (2003), p. 31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

224. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

225. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

226. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

227. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

228. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

229. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

230. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

231. Riedweg (2005), p. 66. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

232. Cornelli & McKirahan (2013), p. 64. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

233. Cornelli & McKirahan (2013), p. 64. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

234. Pomeroy (2013), p. xvi. - Pomeroy, Sarah B. (2013). Pythagorean Women: The History and Writings. Baltimore, Maryland: The Johns Hopkins University Press. ISBN 978-1-4214-0956-6. https://books.google.com/books?id=jUMDAAAAQBAJ&q=women+and+Pythagoreanism ↩

235. Kahn (2001), p. 8. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

236. Pomeroy (2013), p. xvi. - Pomeroy, Sarah B. (2013). Pythagorean Women: The History and Writings. Baltimore, Maryland: The Johns Hopkins University Press. ISBN 978-1-4214-0956-6. https://books.google.com/books?id=jUMDAAAAQBAJ&q=women+and+Pythagoreanism ↩

237. Pomeroy (2013), p. 1. - Pomeroy, Sarah B. (2013). Pythagorean Women: The History and Writings. Baltimore, Maryland: The Johns Hopkins University Press. ISBN 978-1-4214-0956-6. https://books.google.com/books?id=jUMDAAAAQBAJ&q=women+and+Pythagoreanism ↩

238. Pomeroy (2013), p. 1. - Pomeroy, Sarah B. (2013). Pythagorean Women: The History and Writings. Baltimore, Maryland: The Johns Hopkins University Press. ISBN 978-1-4214-0956-6. https://books.google.com/books?id=jUMDAAAAQBAJ&q=women+and+Pythagoreanism ↩

239. Pomeroy (2013), pp. xvi–xvii. - Pomeroy, Sarah B. (2013). Pythagorean Women: The History and Writings. Baltimore, Maryland: The Johns Hopkins University Press. ISBN 978-1-4214-0956-6. https://books.google.com/books?id=jUMDAAAAQBAJ&q=women+and+Pythagoreanism ↩

240. Copleston (2003), pp. 30–31. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

241. Kenny (2004), p. 10. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

242. comp. Porphyry, Vit. Pyth, §32; Iamblichus, Vit. Pyth, §96 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

243. Zhmud (2012), pp. 137, 200. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

244. Kenny (2004), p. 10. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

245. Zhmud (2012), p. 200. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

246. Kenny (2004), p. 10. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

247. Copleston (2003), p. 30. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

248. Diog VIII, §1.19, §1.34; Aulus Gellius, iv. 11; Porphyry, Vit. Pyth, §34, de Abst. i. 26, Iamblichus, Vit. Pyth, §98 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

249. Cornelli & McKirahan (2013), p. 168. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

250. Plutarch, de Esu Carn, pp. 540–545, 557–571, §993, §996, §997. - ——— (1957) [c. 100 AD]. "On the Eating of Flesh (Du Esu Carnium)". Plutarch's Moralia. Vol. XII. Translated by Helmbold, William C.; Cherniss, Harold. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd – via Internet Archive. https://archive.org/details/plutarchsmoralia12plut/page/540/mode/2up ↩

251. Kahn (2001), p. 9. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

252. Kenny (2004), pp. 10–11. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

253. as Empedocles did afterwards, Aristotle, Rhet. i. 14. § 2; Sextus Empiricus, ix. 127. This was also one of the Orphic precepts, Aristoph. Ran. 1032 ↩

254. Cornelli & McKirahan (2013), p. 168. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

255. Kahn (2001), p. 9. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

256. Eudoxus, frg. 325 ↩

257. Zhmud (2012), p. 235. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

258. Aristoxenus ap. Diog VIII, §1.20; comp. Porphyry, Vit. Pyth, §7; Iamblichus, Vit. Pyth, §85, §108 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

259. Aristoxenus ap. Diog VIII, §1.20 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

260. Zhmud (2012), p. 235. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

261. comp. Porphyry, Vit. Pyth, §7; Iamblichus, Vit. Pyth, §85, §108 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

262. Zhmud (2012), p. 235. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

263. Zhmud (2012), p. 235. - Zhmud, Leonid (2012) [1994]. Pythagoras and the Early Pythagoreans. Translated by Windle, Kevin; Ireland, Rosh. Oxford University Press. ISBN 978-0-19-928931-8. https://books.google.com/books?id=of-ghBD9q1QC ↩

264. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

265. Riedweg (2005), p. 1. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

266. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

267. Gregory (2015), pp. 30–31. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

268. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

269. Gregory (2015), p. 30. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

270. Kenny (2004), p. 11. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

271. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

272. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

273. Porphyry, Vit. Pyth, §20; Iamblichus, Vit. Pyth, §31, §140; Aelian, Varia Historia, ii. 26; Diog VIII, §1.36 - Porphyry (1987) [c. 270 AD]. "Vita Pythagorae (Life of Pythagoras)". In Fideler, David R. (ed.). The Pythagorean Sourcebook And Library. Translated by Guthrie, Kenneth Sylvan. Michigan: Phanes Press. ISBN 978-0-933999-50-3. OCLC 16130530 – via Internet Archive. https://archive.org/details/guthrie-1987-the-pythagorean-sourcebook-and-library/page/122/mode/2up ↩

274. McKeown (2013), p. 155. - McKeown, J. C. (2013). A Cabinet of Greek Curiosities: Strange Tales and Surprising Facts from the Cradle of Western Civilization. Oxford, England: Oxford University Press. ISBN 978-0-19-998210-3. ↩

275. Comp. Herodian, iv. 94, etc. ↩

276. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

277. Gregory (2015), p. 30. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

278. Kenny (2004), p. 11. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

279. Burkert (1972), p. 144. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

280. Gregory (2015), p. 30. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

281. Kenny (2004), p. 11. - Kenny, Anthony (2004). Ancient Philosophy. A New History of Western Philosophy. Vol. 1. Oxford, England: Oxford University Press. ISBN 978-0-19-875273-8. https://books.google.com/books?id=cpYUDAAAQBAJ&q=Anthony+Kenny+Ancient+Philosophy ↩

282. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

283. Joost-Gaugier (2006), p. 47. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

284. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

285. Riedweg (2005), p. 2. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

286. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

287. Cornelli & McKirahan (2013), p. 160. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

288. McKeown (2013), p. 155. - McKeown, J. C. (2013). A Cabinet of Greek Curiosities: Strange Tales and Surprising Facts from the Cradle of Western Civilization. Oxford, England: Oxford University Press. ISBN 978-0-19-998210-3. ↩

289. Gregory (2015), p. 30. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

290. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

291. Cornelli & McKirahan (2013), p. 160. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

292. Kahn (2001), p. 5. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

293. Cornelli & McKirahan (2013), p. 160. - Cornelli, Gabriele; McKirahan, Richard (2013). In Search of Pythagoreanism: Pythagoreanism as an Historiographical Category. Berlin, Germany: Walter de Gruyter. ISBN 978-3-11-030650-7. https://books.google.com/books?id=p0ihjZufKncC&q=Pythagoreanism&pg=PA50 ↩

294. Riedweg (2005), p. 1. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

295. Gregory (2015), p. 31. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

296. Kahn (2001), pp. 1–2. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

297. Gregory (2015), pp. 21–22. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

298. Burkert (1972), pp. 428–433. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

299. Kahn (2001), pp. 2–3. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

300. Diog VIII, §1.12; Plutarch, Non posse suav. vivi sec. Ep., pp. 67–71, §1094 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

301. Porphyry, in Ptol. Harm. p. 213; Diog VIII, §1.12 - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

302. Diog VIII, §1.14; Pliny, Hist. Nat. ii. 8. - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

303. Diog VIII, §1.12, 14, 32. - ——— (1925) [c. 200 AD]. "Book VIII". Lives of the Eminent Philosophers. Vol. II. Translated by Hicks, Robert Drew. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99204-7. OCLC 758307224 – via Wikisource. https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII#Pythagoras ↩

304. Kahn (2001), pp. 32–33. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

305. Riedweg (2005), pp. 26–27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

306. Riedweg (2005), p. 27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

307. Riedweg (2005), p. 27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

308. Burkert (1972), p. 428. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

309. Riedweg (2005), p. 27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

310. Riedweg (2005), p. 27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

311. Riedweg (2005), p. 27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

312. Burkert (1972), pp. 429, 462. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

313. Riedweg (2005), p. 27. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

314. Kahn (2001), p. 32. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

315. Burkert (1972), p. 429. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

316. Burkert (1972), p. 429. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

317. There are about 100,000 unpublished cuneiform sources in the British Museum alone. Babylonian knowledge of proof of the Pythagorean theorem is discussed by J. Høyrup, 'The Pythagorean "Rule" and "Theorem" – Mirror of the Relation between Babylonian and Greek Mathematics,' in: J. Renger (red.): Babylon. Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne (1999). /wiki/British_Museum ↩

318. Riedweg (2005), pp. 27–28. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

319. Gregory (2015), p. 27. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

320. Riedweg (2005), p. 28. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

321. Riedweg (2005), p. 28. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

322. Gregory (2015), p. 27. - Gregory, Andrew (2015). "The Pythagoreans: number and numerology". In Lawrence, Snezana; McCartney, Mark (eds.). Mathematicians and their Gods: Interactions between mathematics and religious beliefs. Oxford University Press. pp. 21–50. ISBN 978-0-19-100755-2. https://books.google.com/books?id=5Zu9CQAAQBAJ ↩

323. Riedweg (2005), p. 28. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

324. Burkert (1972), p. 306. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

325. Burkert (1972), p. 306. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

326. Burkert (1972), pp. 307–308. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

327. Burkert (1972), pp. 306–308. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

328. Burkert (1972), pp. 307–308. - Burkert, Walter (1 June 1972). Lore and Science in Ancient Pythagoreanism. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-53918-1 – via Internet Archive. https://archive.org/details/lorescienceinanc0000burk/mode/2up ↩

329. Kahn (2001), p. 53. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

330. Dicks (1970), p. 68. - Dicks, D. R. (1970). Early Greek Astronomy to Aristotle. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-0561-7. https://archive.org/details/earlygreekastron0000dick ↩

331. Kahn (2001), pp. 48–49. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

332. Kahn (2001), p. 39. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

333. Kahn (2001), p. 39. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

334. Kahn (2001), pp. 39–43. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

335. Kahn (2001), pp. 39–40. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

336. Kahn (2001), pp. 40, 44–45. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

337. Plato, Republic, VII, 530d. - Plato (1969) [c. 380 BC]. "Republic". Plato in Twelve Volumes, Vols. 5 & 6. Translated by Shorey, Paul. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99304-4. OCLC 6947747 – via Perseus Digital Library (perseus.tufts.edu). https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0168%3Abook%3D7%3Asection%3D530d#note-link3 ↩

338. Aristot. Met. 1, 987a. - ——— (1933) [c. 350 BC]. "Book I". Metaphysics Books I–IX. Vol. XVII. Translated by Tredennick, Hugh. Loeb Classical Library. Cambridge, Massachusetts and London: Harvard University Press and William Heinemann Ltd. ISBN 978-0-674-99299-3. OCLC 958278244 – via Perseus Digital Library (perseus.tufts.edu). https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0052:book=1:section=986a ↩

339. Kahn (2001), p. 1. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

340. "Numbers, Ontologically Speaking: Plato on Numerosity". philpapers.org. Retrieved 2025-01-21. https://philpapers.org/versions/FLONOS ↩

341. Tusc. Disput. 1.17.39. ↩

342. Kahn (2001), p. 55. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

343. Kahn (2001), pp. 55–62. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

344. Kahn (2001), pp. 55–62. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

345. Joost-Gaugier (2006), p. 13. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

346. Kahn (2001), p. 2. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

347. Joost-Gaugier (2006), p. 13. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

348. Kahn (2001), p. 2. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

349. Joost-Gaugier (2006), p. 13. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

350. Joost-Gaugier (2006), p. 12. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

351. Joost-Gaugier (2006), pp. 12–13. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

352. Joost-Gaugier (2006), pp. 12–13. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

353. Joost-Gaugier (2006), pp. 14–15. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

354. Hare (1999), pp. 117–119. - Hare, R. M. (1999) [1982]. "Plato". In Taylor, C. C. W.; Hare, R. M.; Barnes, Jonathan (eds.). Greek Philosophers: Socrates, Plato, and Aristotle. Past Masters. Oxford, England: Oxford University Press. pp. 103–189. ISBN 978-0-19-285422-3. ↩

355. Hare (1999), pp. 117–119. - Hare, R. M. (1999) [1982]. "Plato". In Taylor, C. C. W.; Hare, R. M.; Barnes, Jonathan (eds.). Greek Philosophers: Socrates, Plato, and Aristotle. Past Masters. Oxford, England: Oxford University Press. pp. 103–189. ISBN 978-0-19-285422-3. ↩

356. Hare (1999), pp. 117–119. - Hare, R. M. (1999) [1982]. "Plato". In Taylor, C. C. W.; Hare, R. M.; Barnes, Jonathan (eds.). Greek Philosophers: Socrates, Plato, and Aristotle. Past Masters. Oxford, England: Oxford University Press. pp. 103–189. ISBN 978-0-19-285422-3. ↩

357. Hare (1999), pp. 117–119. - Hare, R. M. (1999) [1982]. "Plato". In Taylor, C. C. W.; Hare, R. M.; Barnes, Jonathan (eds.). Greek Philosophers: Socrates, Plato, and Aristotle. Past Masters. Oxford, England: Oxford University Press. pp. 103–189. ISBN 978-0-19-285422-3. ↩

358. Copleston (2003), p. 37. - Copleston, Frederick (2003) [1946]. "The Pythagorean Society". A History of Philosophy. Vol. 1 Greece and Rome. London, England and New York City, New York: Continuum. ISBN 978-0-8264-6947-2. ↩

359. Riedweg (2005), pp. 123–124. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

360. Riedweg (2005), p. 124. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

361. Riedweg (2005), pp. 125–126. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

362. Riedweg (2005), p. 125. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

363. Riedweg (2005), p. 125. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

364. Riedweg (2005), p. 125. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

365. Riedweg (2005), pp. 125–126. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

366. Riedweg (2005), pp. 126–127. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

367. Joost-Gaugier (2006), p. 154. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

368. Joost-Gaugier (2006), pp. 154–156. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

369. Joost-Gaugier (2006), pp. 157–158. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

370. Joost-Gaugier (2006), p. 158. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

371. Joost-Gaugier (2006), pp. 158–159. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

372. Joost-Gaugier (2006), p. 159. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

373. Joost-Gaugier (2006), pp. 159–161. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

374. Joost-Gaugier (2006), p. 161. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

375. Joost-Gaugier (2006), p. 161. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

376. Joost-Gaugier (2006), p. 162. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

377. Joost-Gaugier (2006), p. 162. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

378. Joost-Gaugier (2006), pp. 162–164. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

379. Joost-Gaugier (2006), pp. 166–181. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

380. Joost-Gaugier (2006), pp. 167–168. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

381. Joost-Gaugier (2006), p. 168. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

382. Joost-Gaugier (2006), pp. 169–170. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

383. Joost-Gaugier (2006), pp. 170–172. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

384. Joost-Gaugier (2006), pp. 57–65. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

385. Joost-Gaugier (2006), p. 57. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

386. Joost-Gaugier (2006), p. 57. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

387. Joost-Gaugier (2006), p. 57. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

388. Joost-Gaugier (2006), pp. 57–58. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

389. Joost-Gaugier (2006), pp. 58–59. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

390. Joost-Gaugier (2006), p. 59. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

391. Joost-Gaugier (2006), p. 59. - Joost-Gaugier, Christiane L. (2006). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7409-5. https://books.google.com/books?id=Cf9Rj_ADZU4C&q=Pythagoreanism&pg=PA116 ↩

392. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

393. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

394. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

395. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

396. Lindberg (1978). - Lindberg, David C. (1978). Science in the Middle Ages. University of Chicago Press. ISBN 978-0226482330. ↩

397. Lindberg (2013). - Lindberg, David C. (2013). The Cambridge History of Science: Volume 2, Medieval Science. Cambridge University Press. ISBN 978-0521594486. ↩

398. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

399. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

400. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

401. Russo (2004), pp. 5–87, especially 51–53. - Russo, Attilio (2004). "Costantino Lascaris tra fama e oblio nel Cinquecento messinese". Archivio Storico Messinese. LXXXIV–LXXXV: 5–87, especially 51–53. ISSN 0392-0240. https://search.worldcat.org/issn/0392-0240 ↩

402. Russo (2004), pp. 5–87, especially 51–53. - Russo, Attilio (2004). "Costantino Lascaris tra fama e oblio nel Cinquecento messinese". Archivio Storico Messinese. LXXXIV–LXXXV: 5–87, especially 51–53. ISSN 0392-0240. https://search.worldcat.org/issn/0392-0240 ↩

403. Russo (2004), pp. 5–87, especially 51–53. - Russo, Attilio (2004). "Costantino Lascaris tra fama e oblio nel Cinquecento messinese". Archivio Storico Messinese. LXXXIV–LXXXV: 5–87, especially 51–53. ISSN 0392-0240. https://search.worldcat.org/issn/0392-0240 ↩

404. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

405. Kahn (2001), p. 160. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

406. Kahn (2001), p. 160. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

407. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

408. Kahn (2001), pp. 161–171. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

409. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

410. Kahn (2001), p. 162. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

411. James (1993), p. 142. - James, Jamie (1993). The Music of the Spheres. New York, NY: Grove Press. ISBN 978-0-8021-1307-8 – via Internet Archive. https://archive.org/details/musicofspheresmu00jame/page/n7/mode/2up ↩

412. Kahn (2001), p. 172. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

413. Whitehead (1953), pp. 36–37. - Whitehead, Afred North (1953) [1926]. Science and the Modern World. Cambridge, England: Cambridge University Press. ISBN 978-0-521-23778-9. https://books.google.com/books?id=Npq_qnqwYOwC&q=Pythagoras+Whitehead+science&pg=PA36 ↩

414. Kahn (2001), p. 172. - Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, Indiana and Cambridge, England: Hackett Publishing Company. ISBN 978-0-87220-575-8. OCLC 46394974 – via Internet Archive. https://archive.org/details/pythagoraspythag0000kahn ↩

415. Whitehead (1953), p. 36. - Whitehead, Afred North (1953) [1926]. Science and the Modern World. Cambridge, England: Cambridge University Press. ISBN 978-0-521-23778-9. https://books.google.com/books?id=Npq_qnqwYOwC&q=Pythagoras+Whitehead+science&pg=PA36 ↩

416. Borlik (2011), p. 189. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

417. Borlik (2011), pp. 189–190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

418. Borlik (2011), pp. 189–190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

419. Borlik (2011), p. 190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

420. Borlik (2011), p. 190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

421. Borlik (2011), p. 190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

422. Borlik (2011), p. 190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

423. Borlik (2011), p. 190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

424. Borlik (2011), p. 190. - Borlik, Todd A. (2011). Ecocriticism and Early Modern English Literature: Green Pastures. Routledge Studies in Renaissance Literature and Culture. New York City, New York and London, England: Routledge. ISBN 978-0-203-81924-1. https://archive.org/details/ecocriticismearl0000borl/mode/2up ↩

425. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

426. Riedweg (2005), pp. 127–128. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

427. Riedweg (2005), p. 128. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

428. Riedweg (2005), p. 128. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

429. Riedweg (2005), pp. 127–128. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

430. Riedweg (2005), p. 128. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

431. French (2002), p. 30. - French, Peter J. (2002) [1972]. John Dee: The World of the Elizabethan Magus. New York City, New York and London, England: Routledge. ISBN 978-0-7448-0079-1. https://books.google.com/books?id=mcJYAQAAQBAJ&q=John+Dee+Pythagoras&pg=PA30 ↩

432. French (2002), p. 30. - French, Peter J. (2002) [1972]. John Dee: The World of the Elizabethan Magus. New York City, New York and London, England: Routledge. ISBN 978-0-7448-0079-1. https://books.google.com/books?id=mcJYAQAAQBAJ&q=John+Dee+Pythagoras&pg=PA30 ↩

433. Riedweg (2005), p. 133. - Riedweg, Christoph (2005) [2002]. Pythagoras: His Life, Teachings, and Influence. Ithaca, New York: Cornell University Press. ISBN 978-0-8014-7452-1. https://books.google.com/books?id=A8ixyQJA7_MC&q=Pythagoras ↩

434. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

435. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

436. Celenza (2010), p. 798. - Celenza, Christopher (2010). "Pythagoras and Pythagoreanism". In Grafton, Anthony; Most, Glenn W.; Settis, Salvatore (eds.). The Classical Tradition. Cambridge, Massachusetts and London, England: The Belknap Press of Harvard University Press. pp. 796–799. ISBN 978-0-674-03572-0. ↩

437. Sherman (1995), p. 15. - Sherman, William Howard (1995). John Dee: The Politics of Reading and Writing in the English Renaissance. Amherst, Massachusetts: The University of Massachusetts Press. ISBN 978-1-55849-070-3. https://books.google.com/books?id=0nmboW7qwvUC&q=John+Dee+Pythagoras&pg=PA15 ↩

438. French (2002), p. 30. - French, Peter J. (2002) [1972]. John Dee: The World of the Elizabethan Magus. New York City, New York and London, England: Routledge. ISBN 978-0-7448-0079-1. https://books.google.com/books?id=mcJYAQAAQBAJ&q=John+Dee+Pythagoras&pg=PA30 ↩

439. Sherman (1995), p. 15. - Sherman, William Howard (1995). John Dee: The Politics of Reading and Writing in the English Renaissance. Amherst, Massachusetts: The University of Massachusetts Press. ISBN 978-1-55849-070-3. https://books.google.com/books?id=0nmboW7qwvUC&q=John+Dee+Pythagoras&pg=PA15 ↩

440. French (2002), p. 30. - French, Peter J. (2002) [1972]. John Dee: The World of the Elizabethan Magus. New York City, New York and London, England: Routledge. ISBN 978-0-7448-0079-1. https://books.google.com/books?id=mcJYAQAAQBAJ&q=John+Dee+Pythagoras&pg=PA30 ↩

441. Bregman (2002), p. 186. - Bregman, Jay (2002). "Neoplatonism and American Aesthetics". In Alexandrakis, Aphrodite; Moulafakis, Nicholas J. (eds.). Neoplatonism and Western Aesthetics. Studies in Neoplatonism: Ancient and Modern. Vol. 12. Albany, New York: State University of New York Press. ISBN 978-0-7914-5280-6. https://books.google.com/books?id=wAKTvVIcwTgC&q=Pythagoras+and+the+Transcendentalists&pg=PA186 ↩

442. Bregman (2002), p. 186. - Bregman, Jay (2002). "Neoplatonism and American Aesthetics". In Alexandrakis, Aphrodite; Moulafakis, Nicholas J. (eds.). Neoplatonism and Western Aesthetics. Studies in Neoplatonism: Ancient and Modern. Vol. 12. Albany, New York: State University of New York Press. ISBN 978-0-7914-5280-6. https://books.google.com/books?id=wAKTvVIcwTgC&q=Pythagoras+and+the+Transcendentalists&pg=PA186 ↩

443. Bregman (2002), p. 186. - Bregman, Jay (2002). "Neoplatonism and American Aesthetics". In Alexandrakis, Aphrodite; Moulafakis, Nicholas J. (eds.). Neoplatonism and Western Aesthetics. Studies in Neoplatonism: Ancient and Modern. Vol. 12. Albany, New York: State University of New York Press. ISBN 978-0-7914-5280-6. https://books.google.com/books?id=wAKTvVIcwTgC&q=Pythagoras+and+the+Transcendentalists&pg=PA186 ↩

444. Bregman (2002), p. 186. - Bregman, Jay (2002). "Neoplatonism and American Aesthetics". In Alexandrakis, Aphrodite; Moulafakis, Nicholas J. (eds.). Neoplatonism and Western Aesthetics. Studies in Neoplatonism: Ancient and Modern. Vol. 12. Albany, New York: State University of New York Press. ISBN 978-0-7914-5280-6. https://books.google.com/books?id=wAKTvVIcwTgC&q=Pythagoras+and+the+Transcendentalists&pg=PA186 ↩