Post Reply 
 
Thread Rating:
  • 1 Votes - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Pythagoreanism
06-08-2014, 11:18 AM
Post: #11
RE: Pythagoreanism
4.5 Pythagoreans as Relgious Experts, Magicians and Moral Exemplars: Pythagoreanism in Rome, The Golden Verses and Apollonius of Tyana

http://www.whiteheritage.org/newreply.php?tid=625&replyto=1709

A third strand in Neopythagoreanism emphasizes Pythagoras' practices rather than his supposed metaphysical system. This Pythagoras is an expert in religious and magical practices and/or a sage who lived the ideal moral life, upon whom we should model our lives. This strand is closely connected to the striking interest in and prominence of Pythagoreanism in Roman literature during the first century BCE and first century CE. Cicero (106–43 BCE) in particular refers to Pythagoras and other Pythagoreans with some frequency. In De Finibus (V 2), he presents himself as the excited tourist, who, upon his arrival in Metapontum in S. Italy and even before going to his lodgings, sought out the site where Pythagoras was supposed to have died. At the beginning of Book IV (1–2) of the Tusculan Disputations, Cicero notes that Pythagoras gained his fame in southern Italy at just the same time that L. Brutus freed Rome from the tyranny of the kings and founded the Republic; there is a clear implication that Pythagorean ideas, which reached Rome from southern Italy, had an influence on the early Roman Republic. Cicero goes on to assert explicitly that many Roman usages were derived from the Pythagoreans, although he does not give specifics. According to Cicero, it was admiration for Pythagoras that led Romans to suppose, without noticing the chronological impossibility, that the wisest of the early Roman kings, Numa, who was supposed to have ruled from 715–673 BCE, had been a pupil of Pythagoras.

In addition to references to Pythagoras himself, Cicero refers to the Pythagorean Archytas some eleven times, in particular emphasizing his high moral character, as revealed in his refusal to punish in anger and his suspicion of bodily pleasure (Rep. I 38. 59; Sen. XII 39–41; Huffman 2005, 21–24, 283 ff. and 323 ff.). Cicero's own philosophy is not much influenced by the Pythagoreans except in The Dream of Scipio (Rep. VI 9), which owes even more to Plato.

The interest in Pythagoras and Pythagoreans in the first century BCE is not limited to Cicero, however. Both a famous ode of Horace (I 28 – see Huffman 2005, 19–21) and a brief reference in Propertius (IV 1) present Archytas as a master astronomer. Most striking of all is the speech assigned to Pythagoras that constitutes half of Book XV of Ovid's Metamorphoses (early years of the first century CE) and that calls for strict vegetarianism in the context of the doctrine of transmigration of souls. These latter themes are true to the earliest evidence for Pythagoras, but the rest of Ovid's presentation assigns to Pythagoras a doctrine that is derived from a number of early Greek philosophers and in particular the doctrine of flux associated with Heraclitus (Kahn 2001, 146–149).

This flourishing of Pythagoreanism in Roman literature of the golden age has its roots in one of the earliest Roman literary figures, Ennius (239–169 BCE), who, in his poem Annales, adopts the Pythagorean doctrine of metempsychosis, in presenting himself as the reincarnation of Homer, although he does not mention Pythagoras by name in the surviving fragments. Roman nationalism also played a role in the emphasis on Pythagoreanism at Rome. Since Pythagoras did his work in Italy and Aristotle even referred to Pythagoreanism in some places as the philosophy of the Italians (e.g. Metaph. 987a10), it is not surprising that the Romans wanted to emphasize their connections to Pythagoras. This is particularly clear in Cicero's references to Pythagoreanism but once again finds its roots even earlier. In 343 BCE during the war with the Samnites, Apollo ordered the Romans to erect one statue of the wisest and another of the bravest of the Greeks; their choice for the former was Pythagoras and for the latter Alcibiades. Pliny, who reports the story (Nat. XXXIV 26), expresses surprise that Socrates was not chosen for the former, given that, according to Plato's Apology, Apollo himself had labeled Socrates the wisest; it is surely the Italian connection that explains the Romans' choice of Pythagoras. This attempt to forge a connection with Pythagoras can also be seen in the report of Plutarch (Aem. Paul. 1) that some writers traced the descent of the Aemelii, one of Rome's leading families, to Pythagoras, by claiming Pythagoras' son Mamercus as the founder of the house.

Although Rome's special connection to Pythagoras thus had earlier roots, those roots alone do not explain the efflorescence of Pythagoreanism in golden age Latin literature; some stimulus probably came from the rebirth of what were seen as Pythagorean practices in the way certain people lived. The two most learned figures in Rome of the first century BCE, Nigidius Figulus and Varro, both have connections to Pythagorean ritual practices. Thus we are told that Varro (116–27 BCE) was buried according to the Pythagorean fashion in myrtle, olive and black poplar leaves (Pliny, Nat. XXXV 160). Amongst Varro's voluminous works was the Hebdomadês (“Sevens”), a collection of 700 portraits of famous men, in the introduction to which Varro engaged in praise for the number 7, which is similar to the numerology of later Neopythagorean works such as Nicomachus' Theology of Arithmetic; in another work Varro presents a theory of gestation, which has Pythagorean connections, in that it is based on the whole number ratios that correspond to the concordant intervals in music (Rawson 1985, 161).

It is Nigidius Figulus, praetor in 58, who died in exile in 45, however, who is usually identified as the figure who was responsible for reviving Pythagorean practices. In the preface to his translation of Plato's Timaeus, which is often treated as virtually a Pythagorean treatise by the Neopythagoreans, Cicero asserts of Nigidius that “following on those noble Pythagoreans, whose school of philosophy had to a certain degree died out, … this man arose to revive it.” Some scholars are dubious about this claim of Cicero. They point to the evidence cited above for the importance of Pythagoreanism in Rome in the two centuries before Nigidius and suggest that Cicero may be illegitimately following Aristoxenus' claim that Pythagoreanism died out in the first half of the fourth century (Riedweg 2005, 123–124). While there may be some evidence that there were practicing Pythagoreans in the second half of the fourth century (see above section 3.4), it is hard to find anyone to whom to apply that label in the third and second centuries, so that, from the perspective of the evidence available to us at present, Cicero may well be right that Nigidius was the first person in several centuries to claim to follow Pythagorean practices.

It is difficult to be sure in what Nigidius' Pythagoreanism consisted. There is no mention of Pythagoras or Pythagoreans in the surviving fragments of his work nor do they show him engaging in Pythagorean style numerology as Varro did (Rawson 1985, 291 ff.). In Jerome's chronicle, Nigidius is labeled as Pythagorean and magus; the most likely suggestion, thus, is that his Pythagoreanism consisted in occult and magical practices. Nigidius' expertise as an astrologer (he is reported to have used astrology to predict Augustus' future greatness on the day of his birth [Suetonius, Aug. 94.5]) may be another Pythagorean connection; Propertius' reference (IV 1) to Archytas shows that Pythagorean work in astronomy was typically connected to astrology in first century Rome.

What led Nigidius and Varro to resurrect purported Pythagorean cult practices? One important influence may have been the Greek scholar Alexander Polyhistor, who was born in Miletus but was captured by the Romans during the Mithridatic wars and brought to Rome as a slave and freed by Sulla in 80 BCE. He taught in Rome in the 70s. It is an intriguing suggestion that Nigidius learned his Pythagoreanism from Alexander (Dillon 1977, 117). There is no evidence that Alexander himself followed Pythagorean practices, but he wrote a book On Pythagorean Symbols, which was presumably an account of the Pythagorean acusmata (or symbola), which set out the taboos that governed many aspects of the Pythagorean way of life. In addition, in his Successions of the Philosophers, he gave a summary of Pythagorean philosophy, which he supposedly found in “Pythagorean notebooks” and which has been preserved by Diogenes Laertius (VIII 25–35). The basic principles assigned to Pythagoras are those of the Neopythagorean tradition that begins in the early Academy, i.e., the monad and the indefinite dyad. Since Alexander also assigns to the Pythagoreans the doctrine that the elements change into one another, we might suppose that Ovid also used Alexander directly or indirectly, since he assigns a similar doctrine to Pythagoras in the Metamorphoses (XV 75 ff., Rawson 1985, 294).

It is necessary to look in a slightly different direction, in order to see how magical practices came to be particularly associated with Pythagoras and thus why Nigidius was called Pythagorean and magus. In the first century, it was widely believed that Pythagoras had studied with the Magi (Cicero, Fin. V 87), i.e. Persian priests/wise men. What Pythagoras was thought to have learned from the Magi most of all were the magical properties of plants. Pliny the elder (23–79 CE) identifies Pythagoras and Democritus as the experts on such magic and the Magi as their teachers (Nat. XXIV 156–160). Pliny goes on to give a number of specific examples from a book on plants ascribed to Pythagoras. This book is universally regarded as spurious by modern scholars, and even Pliny, who accepts its authenticity, reports that some people ascribe it to Cleemporus. We can date this treatise on plants to the first half of the second century or earlier, since Cato the elder (234–149 BCE) appears to make use of it in his On Agriculture (157), when he discusses the medicinal virtues of a kind of cabbage, which was named after Pythagoras (brassica Pythagorea).

A clearer understanding of this pseudo-Pythagorean treatise on plants and a further indication of its date can be obtained by looking at the work of Bolus of Mendes, an Egyptian educated in Greek (see Dickie 2001, 117–122, to whom the following treatment of Bolus is indebted). Bolus composed a work entitled Cheiromecta, which means “things worked by hand” and may thus refer to potions made by grinding plants and other substances (Dickie 2001, 119). Bolus discussed not just the magical properties of plants but also those of stones and animals. Pliny regarded the Cheiromecta as composed by Democritus on the basis of his studies with the Magi (Nat. 24. 160) and normally cites its contents as what Democritus or the Magi said. Columella, however, tells us what was really going on (On Agriculture VII 5.17). The work was in fact composed by Bolus, who published it under the name of Democritus. Bolus thus appears to have made a collection of magical recipes, some of which do seem to have connections to the Magi, since they are similar to recipes found in 8th century cuneiform texts (Dickie 2001, 121). In order to gain authority for this collection, he assigned it to the famous Democritus.

Since Democritus was sometimes regarded as the pupil of Pythagoreans (Diogenes Laertius IX 38), Bolus' choice of Democritus to give authority to his work may suggest that someone else (the Cleemporus mentioned by Pliny?) had already used Pythagoras for this purpose and that the pseudo-Pythagorean treatise on the magical properties of plants was thus already in existence when Bolus wrote, in the first half of the second century BCE. An example of the type of recipe involved is Pliny's ascription to Democritus of the idea that the tongue of a frog, cut out while the frog was still alive, if placed above the heart of a sleeping woman, will cause her to give true answers (Nat. XXXII 49). Thus, the picture of Pythagoras the magician, which may lie behind a number of the supposed Pythagorean practices of Nigidius Figulus, is based on little more than the tradition that Pythagoras had traveled to Egypt and the east, so that he became the authority figure, to whom the real collectors of magical recipes in the third and second century BCE ascribed their collections.

Nigidius' revival of supposed Pythagorean practices spread to other figures in first century Rome. Cicero attacked Vatinius, consul in 48 and a supporter of Caesar, for calling himself a Pythagorean and trying to shield his scandalous practices under the name of Pythagoras (Vat. 6). The scandalous practices involved necromancy, invoking the dead, by murdering young boys. Presumably this method of necromancy would not be ascribed to Pythagoras, but the suggestion is that some methods of consulting the dead were regarded as Pythagorean. Cicero later ended up defending this same Vatinius in a speech which has not survived but some of the contents of which we know from the ancient scholia on the speech against Vatinius. In this speech Cicero defended Vatinius' habit of wearing a black toga, which he attacked in the earlier speech (Vat. 12), as a harmless affectation of Pythagoreanism (Dickie 2001, 170). Thus, the title of Pythagorean in first century Rome carried with it associations with magical practices, not all of which would have been widely approved.

Another example of the connection between Pythagoreanism and magic and its possible negative connotations is Anaxilaus of Larissa (Rawson 1985, 293; Dickie 2001, 172–173). In his chronicle, Jerome describes him with the same words as he used for Nigidius, Pythagorean and magus, and reports that he was exiled from Rome in 28 BCE. We know that Anaxilaus wrote a work entitled Paignia (“tricks”), which seems to have consisted of some rather bizarre conjuring tricks for parties. Pliny reports one of Anaxilaus' tricks as calling for burning the discharge from a mare in heat in a flame, in order to cause the guests to see images of horses' heads (Nat. XXVIII 181). The passion for things Pythagorean can also be seen in the figure of king Juba of Mauretania (ca. 46 BCE – 23 CE), a learned and cultured man, educated at Rome and author of many books. Olympiodorus describes him as “a lover of Pythagorean compositions” and suggests that Pythagorean books were forged to satisfy the passion of collectors such as Juba (Commentaria in Aristotelem Graeca 12.1, p. 13).

The connection between Pythagoreanism and astrology visible in Nigidius can perhaps also be seen in Thrasyllus of Alexandria (d. 36 CE), the court astrologer and philosopher, whom the Roman emperor Tiberius met in Rhodes and brought to Rome. Thrasyllus is famous for his edition of Plato's dialogues arranged into tetralogies, but he was a Platonist with strong Pythagorean leanings. Porphyry in his Life of Plotinus (20) quotes Longinus as saying that Thrasyllus wrote on Platonic and Pythagorean first principles (Dillon 1977, 184–185). Most suggestive of all is the quotation from Thrasyllus preserved by Diogenes Laertius (Diogenes Laertius IX 38), in which Thrasyllus calls Democritus a zealous follower of the Pythagoreans and asserts that Democritus drew all his philosophy from Pythagoras and would have been thought to have been his pupil, if chronology did not prevent it. It is impossible to be sure what Thrasyllus had in mind here, but one very plausible suggestion is that he is thinking of Democritus as a sage, who practiced magic, the Democritus created by Bolus, who was the successor to the arch mage Pythagoras, the supposed author of the treatise on the magical uses of plants (Dickie 2001, 195).

We cannot be sure whether the Pythagoreanism of Nigidius, Varro and their successors was limited to such things as burial ritual, magical practices and black togas or whether it extended to less spectacular features of a “Pythagorean” life. Q. Sextius, however, founded a philosophical movement in the time of Augustus, which prescribed a vegetarian diet and taught the doctrine of transmigration of souls, although Sextius presented himself as using different arguments than Pythagoras for vegetarianism (Seneca, Ep. 108. 17 ff.) One of these Sextians, as they were known, was Sotion, the teacher of Seneca, and it is Seneca who gives us most of the information we have about them. It is also noteworthy that Sextius is also reported to have asked himself at the end of each day “What bad habit have you cured today? What vice have you resisted? In what way are you better” (Seneca, De Ira III 36). Cicero tells us that it was “the Pythagorean custom” to call to mind in the evening everything said, heard or done during the day (Sen. 38, cf. Iamblichus, VP 164). The practice described by Cicero is directed at training the memory in contrast to Sextius' questions, which call for moral self-examination.

Something similar to the Sextian version of the practice is found in lines 40–44 of the Golden Verses, a pseudepigraphical treatise consisting of 71 Greek hexameter verses, which were ascribed to Pythagoras or the Pythagoreans. The poem is a combination of materials from different dates, and it is uncertain when it took the form preserved in manuscripts and called the Golden Verses; dates ranging from 350 BCE to 400 CE have been suggested (see Thom 1995). The Golden Verses are frequently quoted in the first centuries CE and thus constitute one model of the Pythagorean life in Neopythagoreanism, one that is free from magical practices. Much of the advice is common to all of Greek ethical thought (e.g. honoring the gods and parents; mastering lust and anger; deliberating before acting, following measure in all things), but there are also mentions of dietary restrictions typical of early Pythagoreanism and the promise of leaving the body behind to join the aither as an immortal.

Our most detailed account of a Neopythagorean living a life inspired by Pythagoras is Philostratus' Life of Apollonius of Tyana. Apollonius was active in the second half of the first century CE and died in 97; Philostratus' life, which was written over a century later at the request of the empress Julia Domna and completed after her death in 217 CE, is more novel than sober biography. Some have even wondered if Apollonius' Pythagoreanism is largely the creation of Philostratus, but there is evidence that Apollonius wrote a life of Pythagoras used by Iamblichus (VP 254) and Porphyry (Burkert 1972, 100), and the fragment of his treatise On Sacrifices has clear connections to Neopythagorean philosophy (Kahn 2001, 143–145). According to Philostratus, Apollonius identified his wisdom as that of Pythagoras, who taught him the proper way to worship the gods, to wear linen rather than wool, to wear his hair long, and to eat no animal food (I 32).

Like Pythagoras, Apollonius journeys to consult the wise men of the east and learns from the Brahmins in India that the doctrine of transmigration, which Apollonius inherited from Pythagoras, originated in India and was handed on to the Egyptians from whom Pythagoras derived it (III 19). Philostratus (I 2) emphasizes that Apollonius was not a magician, thus trying to free him from the more disreputable connotations of Pythagorean practices associated with figures such as Anaxilaus and Vatinius (see above). Nonetheless, Philostratus' life does recount a number of Apollonius' miracles, such as the raising of a girl from the dead (IV 45).

These miracles made Apollonius into a pagan counterpart to Christ. The emperor Alexander Severus (222–235 CE) worshipped Apollonius alongside Christ, Abraham and Orpheus (Hist. Aug., Vita Alex. Sev. 29.2). Hierocles, the Roman governor of Bithynia, who was rigorous in his persecution of Christians, championed Apollonius at the expense of Christ, in The Lover of Truth, and drew as a response Eusebius' Against Hierocles. As mentioned above, there is some probability that Iamblichus intends to elevate Pythagoras himself as a pagan counterpart to Christ in his On the Pythagorean Life (Dillon and Hershbell 1991, 25–26).

The satirist Lucian (2nd CE) provides us with a hostile portrayal of another holy man with Pythagorean connections, Alexander of Abnoteichus in Paphlagonia, who was active in the middle of the second century CE. In Alexander the False Prophet, Lucian reports that Alexander compared himself to Pythagoras (4), could remember his previous incarnations (34) and had a golden thigh like Pythagoras (40). Lucian shows the not often seen negative side to both Pythagoras' and Alexander's reputations when he reports that, if one took even the worst things said about Pythagoras, Alexander would far outdo him in wickedness (4).

Despite these attacks on figures such as Apollonius and Alexander who modeled themselves on Pythagoras, the Pythagorean way of life was in general praised; the Neopythagorean tradition which portrays Pythagoras as living the ideal life on which we should model our own reaches its culmination in Iamblichus' On the Pythagorean Life and Porphyry's Life of Pythagoras.

http://www.whiteheritage.org/newreply.php?tid=625&replyto=1709
Find all posts by this user
Quote this message in a reply
06-08-2014, 11:59 AM
Post: #12
RE: Pythagoreanism
5. Pythagoreanism in the Middle Ages and Renaissance

http://www.whiteheritage.org/newreply.php?tid=625&replyto=1709

The influence of Pythagoreanism in the Middle Ages and Renaissance was extensive and was found in most disciplines, in literature and art as well as in philosophy and science. Here only the highlights of that influence can be given (see further Heninger 1974, Kahn 2001 and Riedweg 2005, to all of whom the following account is indebted). It is crucial to recognize from the beginning that the Pythagoras of the Middle Ages and Renaissance is the Pythagoras of the Neopythagorean tradition, in which he is regarded as either the most important or one of the most important philosophers in the Greek philosophical tradition. Thus, Ralph Cudworth, in The True Intellectual System of the Universe asserted that “Pythagoras was the most eminent of all the ancient Philosophers” (1845, II 4). This is a far cry from the Pythagoras that can be reconstructed by responsible scholarship. Riedweg has put it well: “Had Pythagoras and his teachings not been since the early Academy overwritten with Plato's philosophy, and had this ‘palimpsest' not in the course of the Roman empire achieved unchallenged authority among Platonists, it would be scarcely conceivable that scholars from the Middle Ages and modernity down to the present would have found the pre-Socratic charismatic from Samos so fascinating” (2005, 128).

5.1 Boethius/Nicomachus and the Middle Ages

Pythagoras was included in mediaeval encyclopedic works and was given particularly thorough treatment by Vincent of Beauvais (before 1200–1264), by Joannes Wallensis (fl. 1260–1283) in Anthology of the Life and Sayings of Illustrious Philosophers and in The Book of the Life and Character of Philosophers ascribed to, but probably not actually composed by, Walter Burley (1275–1344; see Riedweg 2005, 129 and Heninger 1974, 47). The most influential texts for the conception of Pythagoras in the Latin Middle Ages and early Renaissance were Boethius' (480–524 CE) De Institutione Arithmetica and De Institutione Musica, which are virtually translations of the Neopythagorean Nicomachus' (second century CE) Introduction to Arithmetic and Introduction to Music (this larger work is now lost, but a smaller Handbook of Harmonics survives).

These works present Pythagoras as the founder and master of the quadrivium (the four sciences of arithmetic, geometry, music and astronomy), which formed the basis of mediaeval education. He is also portrayed as the metaphysician who first made what is, in fact, the Platonic distinction between the sensible and intelligible world and argued that knowledge has to do with unchanging intelligible entities (Arith. I 1). In music, Boethius recounts the apocryphal story of Pythagoras' discovery in a blacksmith's shop of the ratios that govern the concordant intervals (Mus. I 10). Most important of all is the doctrine of the harmony of the spheres, which portrays the cosmos as a harmony, which is expressed in the music made by the revolutions of the planets (Mus. I 2). Later, in the Renaissance, Shakespeare refers to the doctrine memorably in The Merchant of Venice (V i. 54–65). Cicero's presentation of it in the Dream of Scipio was also influential in the Renaissance (Heninger 1974, 3).

Pythagorean influence also appeared at less elevated levels of mediaeval culture. A fourteenth-century manual for preachers, which contained lore about the natural world and is known as The Light of the Soul, ascribes a series of odd observations about nature to Archita Tharentinus, who is presumably intended to be the fourth century BCE Pythagorean, Archytas of Tarentum. These are mostly cited from a book, which was evidently forged in Archytas' name and known as On Events in Nature. Some of the observations are plausible enough, e.g., that a person at the bottom of a well sees stars in the middle of the day, others more puzzling, e.g., that a dying man emits fiery rays from his eyes at death, while still others may have connections to magic, e.g., “if someone looks at a mirror, before which a white flower has been placed, he cries.” Some magical lore ascribed to an Architas is also found in the thirteenth-century Marvels of the World (ps.-Albertus Magnus), e.g., “if the wax of the left ear of a dog be taken and hung on people with periodic fever, it is beneficial…” (see Huffman 2005, 610–615). These texts seem to continue the connection between Pythagoreanism and magic, which developed in the third and second centuries BCE, and is prominent in Rome during the first-century BCE (see above section 4.5).

5.2 The Renaissance: Ficino, Pico, Reuchlin, Copernicus and Kepler

In the Renaissance, Pythagoreanism played an important role in the thought of fifteenth-century Italian and German humanists. The Florentine Marsilio Ficino (1433–1499) is most properly described as a Neoplatonist. He made the philosophy of Plato available to the Latin-speaking west through his translation of all of Plato into Latin. In addition he translated important works of writers in the Neoplatonic and Neopythagorean tradition, such as Plotinus, Porphyry, Iamblichus and Proclus. From that tradition he accepted and developed the view that Plato was heir to an ancient theology/philosophy that was derived from earlier sages including Pythagoras. Ficino regarded works ascribed to the Chaldaean Zoroaster, the Egyptian Hermes Trismegistus, Orpheus and Pythagoras, which modern scholarship has shown to be forgeries of late antiquity, as genuine works on which Plato drew (Kristeller 1979, 131). Ficino provided a complete translation of the writings ascribed to Hermes Trismegistus into Latin as well as translations of 39 of the short Pythagorean sayings known as symbola, many of which are ancient, and Hierocles' commentary on the pseudo-Pythagorean Golden Verses (Heninger 1974, 63 and 66). The Golden Verses (see Thom 1995) were, in fact, one of the most popular Greek texts in the Renaissance and were commonly used in textbooks for learning Greek; other pseudo-Pythagorean texts, such as the treatises ascribed to Timaeus of Locri and Ocellus, were translated early and regarded as genuine texts on which Plato drew (Heninger 1974, 49, 55–56). Ficino thought, moreover, that this whole pagan tradition could be reconciled with Christian and Jewish religion and accepted the view that Pythagoras was born of a Jewish father (Heninger 1974, 201).

Ficino's friend and younger contemporary, Giovanni Pico della Mirandola (1463–1494), advanced an even more radical doctrine of universal truth, according to which all philosophies had a share of truth and could be reconciled in a comprehensive philosophy (Kristeller 1979, 205). His Oration on the Dignity of Man shows the variety of ways in which he was influenced by the Pythagorean tradition. He equates the friendship that the Pythagoreans saw as the goal of philosophy (see, e.g., Iamblichus, VP 229) with the peace that the angels announced to men of good will (1965, 11–12); the Pythagorean symbola forbidding urinating towards the sun or cutting the nails during sacrifice are interpreted allegorically as calling on us to relieve ourselves of excessive appetite for sensual pleasures and to trim the pricks of anger (1965, 15); the practice of philosophizing through numbers is assigned to Pythagoras along with Philolaus, Plato and the early Platonists (1965, 25–26); Pythagoras is said to have modeled his philosophy on the Orphic theology (1965, 33). Finally, on the basis of the pseudo-Pythagorean letter of Lysis to Hipparchus, Pythagoras is said to have kept silent about his doctrine and left just a few things in writing to his daughter at his death. In observing such silence, Pythagoras is portrayed as following an earlier practice symbolized by the sphinx in Egypt and most of all by Moses, who indeed published the law to men but supposedly kept the interpretation of that law a secret. Pico equates this secret interpretation of the law with the Cabala, an esoteric doctrine in which the words and numbers of Hebrew scripture are interpreted according to a mystical system (1965, 30; see also Heptaplus 1965, 68).

Pico's interest in reconciling the Cabala with Christianity and the pagan philosophical tradition, including Pythagoreanism, was further developed by the German humanist, Johannes Reuchlin (1445–1522). In the dedicatory letter for his Three Books On the Art of the Cabala (1517), which was addressed to Pope Leo X, Reuchlin says that as Ficino has restored Plato for Italy so he will “offer to the Germans Pythagoras reborn,” although he cannot “do this without the cabala of the Hebrews, because the philosophy of Pythagoras took its beginning from the precepts of the cabalists” (tr. Heninger 1974, 245). Thus, in an earlier work (De verbo mirifico) he had equated the four consonants in the Hebrew name for God, JHVH, with the Pythagorean tetraktys, and gave to each of the letters, which are equated with numbers as in Greek practice, a mystical meaning. The first H, which also stands for the number five that the Pythagoreans equated with marriage, is thus taken to symbolize the marriage of the trinity with material nature, which was equated with the dyad by the Neopythagoreans (Riedweg 2005, 130).

At the level of popular culture, several fortune-telling devices were tied to Pythagoras, the most famous of which went under the name of the Wheel of Pythagoras (Heninger 1974, 237). Pythagoras was probably most widely known, however, through Ovid's presentation of him at the beginning of Book XV of the Metamorphoses, which was immensely popular in the Renaissance (Heninger 1974, 50). Ovid recounts the story, which had already been recognized as apocryphal by Cicero (Tusc. IV 1), that the second Roman king, Numa, studied with Pythagoras. Pythagoras is presented inaccurately by Ovid as a great natural philosopher, who discovered the secrets of the universe and who believed in a doctrine of the flux of four elements. On the other hand, Ovid's emphasis on the prohibition on eating animal flesh and on the immortality of the soul have some connection to the historical Pythagoras. In the Renaissance, Pythagoras was not primarily known for the “Pythagorean Theorem,” as he is today. Better known was the doubtful anecdote (Burkert 1960, Riedweg 2005, 90–97), going back ultimately to Heraclides of Pontus but known to the Renaissance mainly through Cicero (Tusc. V 3–4), that he was the first to coin the word “philosopher” (Heninger 1974, 29).

In the sixteenth century, Pythagorean influence was particularly important in the development of astronomy. The Polish astronomer Copernicus (1473–1543), in the Preface and Dedication to Pope Paul III attached to his epoch making work, On the Revolution of the Heavenly Spheres, reports that, in his dissatisfaction with the commonly accepted geocentric astronomical system of Ptolemy (2nd century CE), he laboriously reread the works of all the philosophers to see if any had ever proposed a different system. This labor led him to find inspiration not from Pythagoras himself but rather from later Pythagoreans and in particular from Philolaus. Copernicus found in Cicero (Ac. II 39. 123) that the Pythagorean Hicetas (4th century BCE — Copernicus mistakenly calls him Nicetas) had proposed that the earth revolved around its axis at the center of the universe and in pseudo-Plutarch (Diels 1958, 378) that another Pythagorean, Ecphantus, and Heraclides of Pontus (both 4th century BCE), whom Copernicus regarded as a Pythagorean, had proposed a similar view. More importantly, he also found in pseudo-Plutarch that the Pythagorean, Philolaus of Croton (5th century BCE), “held that the earth moved in a circle … and was one of the planets” (On the Revolutions of the Heavenly Spheres 1. 5, tr. Wallis).

Copernicus reports to the Pope that he was led by these earlier thinkers “to meditate on the mobility of the earth.” Pythagorean influence on Copernicus was not limited to the notion of a moving earth. In the same preface he explains his hesitation to publish his book in light of the pseudo-Pythagorean letter of Lysis to Hipparchus, which recounts the supposed reluctance of the Pythagoreans to divulge their views to the common run of people, who had not devoted themselves to study (for further Pythagorean influences on Copernicus see Kahn 2001, 159–161). A number of the followers of Copernicus saw him as primarily reviving the ancient Pythagorean system rather than presenting anything new (Heninger 1974, 130 and 144, n. 131); Edward Sherburne reflects the common view of the late 17th century in referring to the heliocentric system as “the system of Philolaus and Copernicus” (Heninger 1974, 129–130), although in the Philolaic system it is, in fact, a central fire and not the sun that is at the center of the universe.

The last great Pythagorean was Johannes Kepler (1571–1630 — see Kahn 2001, 161–172 for a good brief account of Kepler's Pythagoreanism). Kepler began by developing the Copernican system in light of the five regular solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron), to which Plato appealed in his construction of matter in the Timaeus (see especially 53B-55C). He followed the Renaissance practice illustrated above of regarding Greek philosophy as closely connected to the wisdom of the Near East, when he asserted that the Timaeus was a commentary on the first chapter of Genesis (Kahn 2001, 162). In the preface to his early work, Mysterium Cosmographicum (1596), Kepler says that his purpose is to show that God used the five regular bodies, “which have been most celebrated from the time of Pythagoras and Plato,” as his model in constructing the universe and that “he accommodated the number of heavenly spheres, their proportions, and the system of their motions” to these five regular solids (tr. Heninger 1974, 110–111).

In ascribing geometrical knowledge of the five regular solids to Pythagoras, Kepler is following an erroneous Neopythagorean tradition, although the dodecahedron may have served as an early Pythagorean symbol (see on Hippasus in section 3.3 above and Burkert 1972, 70–71, 404, 460). Thus, this aspect of Kepler's work is more Platonic than Pythagorean. The five solids were conceived of as circumscribing and inscribed in the spheres of the orbits of the planets, so that the five solids corresponded to the six planets known to Kepler (Saturn, Jupiter, Mars, Earth, Venus, Mercury). There were six planets, because there were precisely five regular bodies to be used in constructing the universe, corresponding to the five intervals between the planets. This view was overthrown by the later discovery of Uranus as a seventh planet. Kepler's cosmology was, however, far from a purely a priori exercise. Whereas his contemporary, Robert Fludd, developed a cosmology structured by musical numbers, which could in no way be confirmed by observation, Kepler strove to make his system consistent with precise observations. Kahn suggests that we here see again the split “between a rational and an obscurantist version of Pythagorean thought,” which is similar to the ancient split in the school between mathematici and acusmatici (2001, 163).

Close work with observational data collected by Tycho Brahe led Kepler to abandon the universal ancient view that the orbits of the planets were circular and to recognize their elliptical nature. More clearly Pythagorean is Kepler's consistent belief that the data show that the motions of the planets correspond in various ways to the ratios governing the musical concords (see Dreyer 1953, 405–410), so that there is a heavenly music, a doctrine attested for Philolaus and Archytas, which probably goes back to Pythagoras as well (Huffman 1993, 279 ff.; Huffman 2005, 137 ff.). For Kepler, however, the music produced by the heavenly motions was “perceived by reason, and not expressed in sound” (Harmonice Mundi V 7). In his attempt to make the numbers of the heavenly music work, he joked that he would appeal to the shade of Pythagoras for aid, “unless the soul of Pythagoras has migrated into mine” (Koestler 1959, 277).

Kepler has been described “as the last exponent of a form of mathematical cosmology that can be traced back to the shadowy figure of Pythagoras” (Field 1988, 170). It is true that Kepler's work led the way to Newton's mechanics, which cannot be described in terms of ancient geometry and number theory but relies on the calculus and which relies on a theory of physical forces that is alien to ancient thought. On the other hand, many modern scientists accept the basic tenet that knowledge of the natural world is to be expressed in mathematical formulae, which is rightly regarded as a central Pythagorean thesis, since it was first rigorously formulated by the Pythagoreans Philolaus ( Fr. 4 — see Huffman 1993) and Archytas (Huffman 2005, 65 ff.) and may, in a rudimentary form, go back to Pythagoras himself.

Bibliography
Aelian, 1997, Historical Miscellany, N. G. Wilson (ed.), Cambridge, Mass: Harvard University Press.
Aëtius — see Diels 1958.
Aristotle, 1933, Metaphysics, Hugh Tredennick (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1935, The Nicomachean Ethics, H. Rackham (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1957, Physics, 2 Vols., Philip H. Wicksteed and Francis M. Cornford (trs.), Cambridge, Mass.: Harvard University Press.
–––, 1984, Fragments, Jonathan Barnes and Gavin Lawrence (trs.), in The Complete Works of Aristotle, Vol. 2, Jonathan Barnes (ed.), Princeton: Princeton University Press, 2384–2462.
Arnott, W. Geoffrey, 1996, Alexis: The Fragments. A Commentary, Cambridge: Cambridge University Press.
Athenaeus, 1927, The Deipnosophists, 6 Vols., C. B. Gulick (tr.), Cambridge, Mass.: Harvard University Press.
Baltes, Matthias, 1972, Timaios Lokros: Über die Natur des Kosmos und der Seele, Leiden: Brill.
Barker, A. D., 1989, Greek Musical Writings, Vol. II: Harmonic and Acoustic Theory, Cambridge: Cambridge University Press.
–––, 2007, The Science of Harmonics in Classical Greece, Cambridge: Cambridge University Press.
Barnes, Jonathan, 1982, The Presocratic Philosophers, London: Routledge.
Boethius, 1867, De institutione arithmetica, Gottfried Friedlein (ed.), Leipzig: Teubner.
–––, 1867, De institutione musica, Gottfried Friedlein (ed.), Leipzig: Teubner.
–––, 1983, Boethian Number Theory: A translation of the De Institutione Arithemtica, Michael Masi (tr.), Amsterdam: Rodopi.
–––, 1989, Fundamentals of Music, Calvin M. Bower (tr.), New Haven: Yale University Press.
Burkert, W., 1960, ‘Platon oder Pythagoras? Zum Ursprung des Wortes “Philosophia”’, Hermes 88: 159–77.
–––. 1961, ‘Hellenistische Pseudopythagorica’, Philologus, 105: 16–43, 226–246.
–––, 1972a, Lore and Science in Ancient Pythagoreanism, E. Minar (tr.), Cambridge, Mass.: Harvard University Press; 1st German edn., 1962.
–––, 1972b, ‘Zur geistesgeschichtlichen Einordnung einiger Pseudopythagorica’, in Pseudepigrapha I, Fondation Hardt Entretiens XVIII, Vandoeuvres-Genève, 25–55.
–––, 1998, ‘Pythagoreische Retraktationen: Von den Grenzen einer möglichen Edition’, in Aporemata 3: Fragmentsammlungen philosphischer Texte der Antike, Walter Burkert, Laura Gemelli Marciano, Elisabetta Matelli, Lucia Orelli (eds.), Göttingen: Vandenhoeck and Ruprecht, 303–319.
CAG = Commentaria in Aristotelem Graeca
Cambiano, Giuseppe, 1998, ‘Archimede Meccanico et La Meccanica di Archita’, Elenchos, 19.2: 291–324.
Cato, 1935, On Agriculture, William Davis Hooper (tr.), Cambridge, Mass.: Harvard University Press.
Centrone, Bruno, 1990, Pseudopythagorica Ethica, Naples: Bibliopolis.
–––, 1994, ‘Pseudo-Archytas’, in Dictionnaire des Philosophes Antiques, Vol. 1, Richard Goulet (ed.), Paris: CNRS Editions, 342–345.
Cicero, 1923, De Senectute, De Amicitia, De Divinatione, W. A. Falconer (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1928, De Republica, De Legibus, Clinton Walker Keyes (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1931, De Finibus, H. Rackham (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1945, Tusculan Disputations, J. E. King (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1967, De Natura Deorum, Academica, H. Rackham (tr.), Cambridge, Mass.: Harvard University Press.
Columella, 1941, On Agriculture, H. B. Ash (tr.), Cambridge, Mass.: Harvard University Press.
Commentaria in Aristotelem Graeca, 1882–1909, Berlin: G. Reimeri.
Copernicus, Nicolaus, 1939, On the Revolutions of the Heavenly Spheres, Charles Glenn Wallis (tr.), Chicago: Encyclopedia Britannica.
Cornford, F. M., 1922–1923, ‘Mysticism and Science in the Pythagorean Tradition’, CQ 16: 137–150; 17: 1–12.
Cudworth, Ralph, 1845, The True Intellectual System of the Universe, 3 Vols., London: Thomas Tegg.
Delatte, A., 1915, Études sur la littérature pythagoricienne, Paris: Champion.
–––, 1922, La vie de Pythagore de Diogène Laërce, Brussels: M. Lamertin.
Dickie, Matthew W., 2001, Magic and Magicians in the Greco-Roman World, London: Routledge.
Diels, H., 1958, Doxographi Graeci, Berlin: De Gruyter.
–––, 1965, Antike Technik, 3rd edn., Osnabrück: Zeller.
Dillon, John, 1977, The Middle Platonists, Ithaca: Cornell University Press.
–––, 2003, The Heirs of Plato, Oxford: Clarendon Press.
Dillon and Hershbell, see Iamblichus, On the Pythagorean Life.
Diodorus Siculus, 1933–1967, Library of History, C. H. Oldfather et al. (trs.), 12 Vols., Cambridge, Mass.: Harvard University Press.
Diogenes Laertius, 1925, Lives of Eminent Philosophers, R. D. Hicks (tr.), Cambridge, Mass.: Harvard University Press.
DK = Diels, H. and W. Kranz, 1952, Die Fragmente der Vorsokratiker, 6th edition, 3 Vols., Dublin and Zürich: Weidmann.
Dreyer, J. L. E., 1953, A History of Astronomy from Thales to Kepler, New York: Dover.
Festugière, A.-J., 1945, ‘Les Mémoires Pythagoriques cités par Alexandre Polyhistor’, REG 58: 1–65.
Field, J. V., 1988, Kepler's Geometrical Cosmology, London: The Athlone Press.
Fritz, Kurt von, 1940, Pythagorean Politics in Southern Italy, New York: Columbia University Press.
–––, 1945, ‘The Discovery of Incommensurability by Hippasos of Metapontum’, Annals of Mathematics 46: 242–264.
Gellius, Aulus, 1927, The Attic Nights, John C. Rolfe (tr.), Cambridge, Mass: Harvard University Press.
Gottschalk, H. B., 1980, Heraclides of Pontus, Oxford: Clarendon Press.
Guthrie, W. K. C., 1962, A History of Greek Philosophy, Vol. 1, Cambridge: Cambridge University Press.
Harder, Richard, 1966, Ocellus Lucanus, Dublin and Zürich: Weidmann.
Heath, T. L., 1921, A History of Greek Mathematics, 2 vols., Oxford: Clarendon Press.
–––, 1956, Euclid: The Thirteen Books of the Elements, Vol. 1, New York: Dover.
Heinze, R., 1892, Xenokrates, Leipzig: Teubner.
Heninger, S. K., Jr., 1974, Touches of Sweet Harmony: Pythagorean Cosmology and Renaissance Poetics, San Marino, California: The Huntington Library.
Herodotus, 1920–1925, The Persian Wars, 4 Vols., A. D. Godley (tr.), Cambridge, Mass.: Harvard University Press.
Hippolytus, 1986, Refutatio Omnium Haeresium, M. Marcovich (ed.), Berlin: Walter de Gruyter.
–––, 1994, The Refutation of all Heresies, J. H. MacMahon (tr.), in The Ante-Nicene Fathers, vol. 5 (repr.), Peabody, MA: Hendrickson.
Historia Augusta, 1922–1932, D. Magie (tr.), Cambridge, Mass.: Harvard University Press.
Horace, 1927, The Odes and Epodes, C. E. Bennett (tr.), Cambridge, Mass.: Harvard University Press.
Huffman, C. A., 1993, Philolaus of Croton: Pythagorean and Presocratic, Cambridge: Cambridge University Press.
–––, 1999a, ‘Limite et illimité chez les premiers philosophes grecs’, in La Fêlure du Plaisir : Études sur le Philèbe de Platon, Vol. II: Contextes, M. Dixsaut (ed.), Paris: Vrin, 11–31.
–––, 1999b, ‘The Pythagorean Tradition’, in The Cambridge Companion to Early Greek Philosophy, A. A. Long (ed.), Cambridge: Cambridge University Press, 66–87.
–––, 2001, ‘The Philolaic Method: The Pythagoreanism behind the Philebus’, in Essays in Ancient Greek Philosophy VI: Before Plato, A. Preus (ed.), Albany: State University of New York Press, 67–85.
–––, 2002, ‘Polyclète et les Présocratiques’, in Qu’ est-ce que La Philosophie Présocratique?, A. Laks and C. Louguet (eds.), Lille: Septentrion, 303–327.
–––, 2005, Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King, Cambridge: Cambridge University Press.
–––, 2006, ‘Aristoxenus' Pythagorean Precepts: A Rational Pythagorean Ethics’, in The Construction of Philosophical Discourse in the Age of the Presocratics, M. M. Sassi (ed.), Pisa: Edizioni Della Normale, 103–121.
–––, 2008a, ‘Two Problems in Pythagoreanism’, in The Oxford Handbook of Presocratic Philosophy, P. Curd and D. Graham (eds.), New York: Oxford University Press, 284–304.
–––, 2008b, ‘The Pythagorean Precepts of Aristoxenus: Crucial Evidence for Pythagorean Moral Philosophy’, Classical Quarterly 58.1: 104–119.
–––, 2008c, ‘Another Incarnation of Pythagoras’, review of C. Riedweg, Pythagoras: His Life, Teaching and Influence, Ancient Philosophy 28: 201–225.
–––, 2009, ‘The Pythagorean Conception of the Soul from Pythagoras to Philolaus’, in Body and Soul in Ancient Philosophy, D. Frede and B. Reis (eds.), Berlin: Walter de Gruyter, 21–43.
[Iamblichus], 1922, Theologoumena Arithmeticae, Victorius De Falco (ed.), Leipzig: Teubner.
–––, 1988, The Theology of Arithmetic, Robin Waterfield (tr.), Grand Rapids: Phanes Press.
Iamblichus, 1888, Protrepticus, H. Pistelli (ed.), Stuttgart and Leipzig: Teubner.
–––, 1975a, De Communi Mathematica Scientia, N. Festa (ed.), Stuttgart: Teubner.
–––, 1975b, In Nicomachi Arithmeticae Introductionem Liber, H. Pistelli (ed.), Stuttgart: Teubner.
–––, 1991, On the Pythagorean Way of Life, John Dillon and Jackson Hershbell (trs.), Atlanta: Scholars Press (Referred to as VP).
Isocrates, 1945, ‘Busiris’, in Isocrates, Vol. 3, Larue van Hook (tr.), Cambridge, Mass.: Harvard University Press.
Jacoby, F., 1923–1958, Die Fragmente der griechischen Historiker, Berlin: Weidmann, Leiden: Brill.
Junge, G., and Thomson, W. (eds.), 1930, The Commentary of Pappus on Book X of Euclid's Elements, Cambridge, Mass.: Harvard University Press.
Kahn, C., 2001, Pythagoras and the Pythagoreans, Indianapolis: Hackett.
Kalligas, Paul, 2004, ‘Platonism in Athens During the First Two Centuries AD: An Overview’, Rhizai 1.2: 37–56.
Karamanolis, George E., 2006, Plato and Aristotle in Agreement?, Oxford: Oxford University Press.
Kassel, R. and C. Austin (eds.), 1983-, Poetae Comici Graeci, Berlin: Walter de Gruyter.
Kepler, J., 1940–5, Gesammelte Werke, W. von Dyck and M. Caspar (eds.), Munich: C. H. Beck.
–––, 1997, The Harmony of the World, E. J. Anton, A. M. Duncan and J. V. Field (trs.), Philadelphia: American Philosophical Society.
Kirk, G. S. and J. E. Raven, 1957, The Presocratic Philosophers, Cambridge: Cambridge University Press.
Kirk, G. S., J. E. Raven, and M. Schofield, 1983, The Presocratic Philosophers, 2nd ed., Cambridge: Cambridge University Press.
Kingsley, Peter, 1995, Ancient Philosophy, Mystery and Magic, Oxford: Clarendon Press.
Koestler, A., 1959, The Sleepwalkers: A History of Man's Changing Vision of the Universe, New York: Macmillan.
Kristeller, Paul Oskar, 1979, Renaissance Thought and Its Sources, New York: Columbia University Press.
Lucian, 1913, Lucian, 7 Vols., A. M. Harmon (tr.), Cambridge, Mass.: Harvard University Press.
Majercik, Ruth, 1989, The Chaldaean Oracles: Text, Translation and Commentary, Leiden: Brill.
Mansfeld, Jaap, 1992, Heresiography in Context: Hippolytus' Elenchos as a Source for Greek Philosophy, Leiden: Brill.
Marg, Walter, 1972, Timaeus Locrus: De Natura Mundi et Animae, Leiden: Brill.
Marinus, 1985, Marino di Neapoli. Vita di Proclo, R. Masullo (ed.), Naples: d’Auria.
–––, 1986, The Life of Proclus or Concerning Happiness, Kenneth Sylvan Guthrie (tr.), Grand Rapids, Phanes Press.
Marsden, E. W., 1969, Greek and Roman Artillery: Historical Development, Oxford: Clarendon Press.
–––, 1971, Greek and Roman Artillery: Technical Treatises, Oxford: Clarendon Press.
Mills, Michael J., 1982, ‘TUXH in Aristoxenus, Fr. 41, and Eudemian Ethics Θ.2’, AJP 103.2: 204–8.
Minar, Edwin L., 1942, Early Pythagorean Politics in Practice and Theory, Baltimore: Waverly Press.
Montepaone, C., 1993, ‘Teano, la pitagorica’, in Grecia al femminile, N. Loraux (ed.), Rome: Laterza, 73–105.
Moraux, P., 1984, Der Aristotelismus bei den Griechen von Andronikos bis Alexander von Aphrodisias, ii: Der Aristotelismus im I. und II. Jh. n. Chr., Berlin: Walter de Gruyter.
Mueller, I., 1997, ‘Greek arithmetic, geometry and harmonics: Thales to Plato’, in Routledge History of Philosophy Vol. I: From the Beginning to Plato, C. C. W. Taylor (ed.), London: Routledge, 271–322.
Navia, L. E., 1990, Pythagoras: An Annotated Bibliography, New York: Garland.
Nicomachus, 1926, Introduction to Arithmetic, Martin Luther D’Ooge (tr.), Ann Arbor: University of Michigan Press.
–––, 1989, Enchiridion (Handbook), Andrew Barker (tr.), in Greek Musical Writings, Vol. II: Harmonic and Acoustic Theory, Andrew Barker (ed.), Cambridge: Cambridge University Press, 245–269.
Numenius, 1973, Fragments, Édouard Des Places (ed.), Paris: Les Belles Lettres.
O’Meara, D. J., 1989, Pythagoras Revived. Mathematics and Philosophy in Late Antiquity, Oxford: Clarendon Press.
Ovid, 1921, Metamorphoses, 2 Vols., Frank Justus Miller (tr.), Cambridge, Mass.: Harvard University Press.
Philip, J. A., 1966, Pythagoras and Early Pythagoreanism, Toronto: University of Toronto Press.
Philostratus, 1912, The Life of Apollonius of Tyana, 2 Vols., F. C. Conybeare (tr.), Cambridge, Mass.: Harvard University Press.
Pico della Mirandola, Giovanni, 1965, On the Dignity of Man, On Being and the One, Heptaplus, Paul W. Miller and Douglas Carmichael (trs.), Indianapolis: Bobbs-Merrill.
Plato, 1997, Complete Works, John M. Cooper (ed.), Indianapolis: Hackett.
Pliny, 1949–1962, Natural History, 10 Vols., H. Rackham, W. H. S. Jones, D. E. Eichholz (trs.), Cambridge, Mass.: Harvard University Press.
Plotinus, 1966–1988, Enneads, 7 Vols., A. H. Armstrong (tr.), Cambridge, Mass.: Harvard University Press.
Plutarch, 1914–1926, Lives, 11 Vols., Bernadotte Perrin (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1949, Moralia, 14 Vols., Cambridge, Mass.: Harvard University Press.
Porphyry, 1932, Porphyrios Kommentar zur Harmonielehre des Ptolemaios, I. Düring (ed.), Göteborg: Elanders Boktryckeri Aktiebolag.
–––, 1965, The Life of Pythagoras, in Heroes and Gods, Moses Hadas and Morton Smith (eds.), New York: Harper and Row, 105–128 (referred to as VP).
–––, 1999, On the Life of Plotinus and the Order of his Books, in Plotinus: Porphry on Plotinus, Ennead 1, A. H. Armstrong (tr.), Cambridge, Mass.: Harvard University Press.
–––, 2003, Vie de Pythagore, Lettre à Marcella, E. des Places (ed.), Paris: Les Belles Lettres.
Proclus, 1992, A Commentary on the First Book of Euclid's Elements, Glenn R. Morrow (tr.), Princeton: Princeton University Press.
Propertius, 1999, Elegies, G. P. Goold (tr.), Cambridge, Mass.: Harvard University Press.
Rawson, Elizabeth, 1985, Intellectual Life in the Late Roman Republic, Baltimore: Johns Hopkins.
Riedweg, Christoph, 2005, Pythagoras: His Life, Teaching, and Influence, Steven Rendall (tr.), Ithaca: Cornell University Press.
Rohde, E., 1871–1872, ‘Die Quellen des Iamblichus in seiner Biographie des Pythagoras’, Rheinische Museum 26: 554–576 and 27: 23–61.
Ryle, G., 1965, ‘The Timaeus Locrus’, Phronesis 10: 174–190.
Sachs, E., 1917, Die fünf Platonischen Körper, Berlin: Weidmann.
Seneca, 1917, Ad Lucilium Epistulae Morales, 3 Vols., Richard M. Gummere (tr.), Cambridge, Mass.: Harvard University Press.
–––, 1928, Moral Essays, 3 Vols., John W. Basore (tr.), Cambridge, Mass.: Harvard University Press.
Sextus Empiricus, 1933–1949, 4 Vols., Cambridge, Mass.: Harvard University Press.
Szlezak, T. A., 1972, Pseudo-Archytas über Die Kategorien, Berlin: Walter De Gruyter.
Suetonius, 1998, Lives of the Caesars, 2 Vols., J. C. Rolfe (tr.), Cambridge, Mass.: Harvard University Press.
Taran, Leonardo, 1981, Speusippus of Athens, Leiden: Brill.
Theophrastus, 1929, Metaphysics, W. D. Ross and F. H. Fobes (eds.), Oxford, Clarendon Press.
–––, 1976–1990, De Causis Plantarum, 3 Vols., Benedict Einarson and G. K. K. Link (trs.), Cambridge, Mass.: Harvard University Press.
Thesleff, H., 1961, An Introduction to the Pythagorean Writings of the Hellenistic Period, Åbo: Åbo Akademi.
–––, 1965, The Pythagorean Texts of the Hellenistic Period, Åbo: Åbo Akademi.
–––, 1972, ‘On the Problem of the Doric Pseudo-Pythagorica. An Alternative Theory of Date and Purpose’, in Pseudepigrapha I, Fondation Hardt Entretiens XVIII, Vandoeuvres-Genève, 59-87.
Thom, J. C., 1995, The Pythagorean ‘Golden Verses’, Leiden: Brill.
Timpanaro Cardini, Maria, 1958–1964, I Pitagorici: Testimonianze e Frammenti, 3 fascs., Florence: La Nuova Italia.
Waterhouse, William C., 1972, ‘The Discovery of the Regular Solids’, Archive for History of Exact Sciences, 9: 212–221.
Wehrli, Fritz, 1944, Dikaiarchos, Die Schule des Aristoteles, I, Basel: Schwabe.
–––, 1945, Aristoxenos, Die Schule des Aristoteles, II, Basel: Schwabe.
–––, 1953, Herakleides Pontikos, Die Schule des Aristoteles, VII, Basel: Schwabe.
West, M. L., 1983, The Orphic Poems, Oxford: Clarendon Press.
–––, 1992, Ancient Greek Music, Oxford: Clarendon Press.
Wilamowitz-Moellendorff, Ulrich von, 1962, Platon, 2 Vols., Berlin: Weidmann.
Zhmud, L., 1992, ‘Mathematici and Acusmatici in the Pythagorean School’, in Pythagorean Philosophy, K. Boudouris (ed.), Athens: International Association for Greek Philosophy, 240–249.
–––, 1997, Wissenschaft, Philosophie und Religion im frühen Pythagoreismus, Berlin: Akademie Verlag.
–––, 2003, Review of Riedweg (2002), Ancient Philosophy 23: 416–420.

http://www.whiteheritage.org/newreply.php?tid=625&replyto=1709
Find all posts by this user
Quote this message in a reply
Post Reply 


Forum Jump:


User(s) browsing this thread: 2 Guest(s)