Vincenzo, through his tuning research, found the underlying truth at the heart of the misunderstood myth of ' Pythagoras ' hammers ' ( the square of the numbers concerned yielded those musical intervals, not the actual numbers, as believed ), and through this and other discoveries that demonstrated the fallibility of traditional authorities, a radically empirical attitude developed, passed on to Galileo, which regarded " experience and demonstration " as the sine qua non of valid rational enquiry.

He believed that Hesiod and Pythagoras lacked understanding though learned and that Homer and Archilochus deserved to be beaten.

The Christian historian Socrates Scholasticus was of the opinion that Julian believed himself to be Alexander the Great " in another body " via transmigration of souls, " in accordance with the teachings of Pythagoras and Plato ".

Pythagoras and other philosophers of the time believed that because mathematical concepts were more " practical " ( easier to regulate and classify ) than physical ones, they had greater actuality.

" Similar to Pythagoras, he too believed that everything had numerical relationships and it was up to the mind to seek and investigate the secrets of these relationships or have them revealed by divine grace.

However, Pythagoras believed that the mathematics of music should be based on the specific ratio of 3: 2 whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves.

Like Pythagoras, Plato believed that all things were composed of number, with the Empedocles ' elements taking the form of the Platonic solids.

Pythagoras, whom the Neo-Pythagoreans regarded as an exemplary sage, was believed to have travelled to India.

Pythagoras was a mathematician often described as the " father of numbers "; it is believed that he had the pioneering insight into the numerical ratios that determine the musical scale, and the Pythagorean theorem is commonly attributed to him.

Ancient Greek mathematician, astronomer and scientist Pythagoras, believed by some to be the originator of physiognomics, once rejected a prospective follower named Cylon simply because of his appearance, which Pythagoras deemed indicative of bad character

* Pherecydes of Syros, a pre-Socratic philosopher and author from the island of Syros, by some believed to have influenced Pythagoras

Some thought that mortal men, if sufficiently famous and virtuous, could do likewise ; there were myths about philosophers like Pythagoras and Empedocles calming storms at sea, chasing away pestilences, and being greeted as gods, and similarly some Jews believed that Elisha the Prophet had cured lepers and restored the dead.

Boyle then covers the history of counting in detail, starting with when numbers were considered to be divine and were the exclusive domain of the accountant-priests of the Assyrian Empire, then going on to Pythagoras and the Ancient Greeks who believed numbers represented the harmony of nature.

The term acousmatic dates back to Pythagoras ; the philosopher is believed to have tutored his students from behind a screen so as not to let his presence distract them from the content of his lectures.

The word acousmatic, from the French acousmatique, is derived from ἀκουσματικοί akousmatikoi, a term used to refer to probationary pupils of the philosopher Pythagoras who, so that they might better concentrate on his teachings, were required to sit in absolute silence while listening to their teacher deliver his lecture from behind a veil or screen.

It is said to be derived from akousmatikoi, the outer circle of Pythagoras ' disciples who only heard their teacher speaking from behind a veil.

Alexander takes on King Porus, who takes on his own appearance, then encounters Pythagoras at the end of the world.

Education is important for comprehending the scheme of things as presented by Aristotle, Plato and Pythagoras but also by the Chaldaean Oracles.

Education is important for comprehending the scheme of things as presented by Aristotle, Plato and Pythagoras but also by the Chaldaean Oracles.

Thinkers and teachers like the Buddha, Pythagoras, Heraclitus, Parmenides, and Anaxagoras contributed to such awakenings which Plato would later call anamnesis, or a remembering of things forgotten.

Of the customs of the Basilidians, we know no more than that Basilides enjoined on his followers, like Pythagoras, a silence of five years ; that they kept the anniversary of the day of the baptism of Jesus as a feast day and spent the eve of it in reading ; that their master told them not to scruple eating things offered to idols.

Aristotle mentions him as nearly contemporary with Pythagoras, but distinguishes between the stoicheia () of opposites, under which the Pythagoreans included all things ; and the double principle of Alcmaeon, according to Aristotle, less extended, although he does not explain the precise difference.

Likewise there is contrast between the practices of Pythagoras and Euclid.

In the area of cosmology there is less agreement about what Pythagoras himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul is too central to have been added by a later follower of Pythagoras.

: Therefore for Spirits I am so farre from denying their existence, that I could easily believe, that not only whole Countries, but particular persons have their Tutelary, and Guardian Angels: It is not a new opinion of the Church of Rome, but an old one of Pythagoras and Plato ; there is no heresay in it, and if not manifestly defined in Scripiture, yet is it an opinion of a good and wholesome use in the course and actions of a man's life, and would serve as an Hypothesis to salve many doubts, whereof common philosophy affordeth no solution.

Iamblichus describes Pythagoras visiting the mountain on account of its reputation for sacredness, stating that it was the most holy of all mountains, and access was forbidden to many, while Tacitus states that there was an oracle situated there, which Vespasian visited for a consultation ; Tacitus states that there was an altar there, but without any image upon it, and without a temple around it.

Dr. Pythagoras, however, refuses to believe that, instead believing there should be a simple logical explanation.

The world is not uncreated nor is there spontaneous production of everything, as Pythagoras and the others have babbled ; instead the world is created and is providentially governed by the God who made everything.

The founders of the school sought to invest their doctrines with the halo of tradition by ascribing them to Pythagoras and Plato, and there is no reason to accuse them of insincerity.

His conviction was that there was one true original religion of mankind, followed by Moses, Pythagoras and the Indian Brahmins, but perverted by the majority of Christians.

Although Alcmaeon is often called a pupil of Pythagoras, there is great reason to doubt whether he was a Pythagorean at all ; his name seems to have crept into lists of Pythagoreans given us by later writers.

Pythagoras, for example, was against the act, though more on mathematical than moral grounds, believing that there was only a finite number of souls for use in the world, and that the sudden and unexpected departure of one upset a delicate balance.

Astraios tells how Mnesarchus, the father of Pythagoras, once on a journey in a white poplar was lying child that without blinking looked at the sun and of the poplar dripping, nourishing dew from a small tube called Mnesarchus this prodigy took with him, there was initially on Samos for a citizen named Androcles in nursing.

It seems that he was influenced by the theories of Pythagoras.

In the book " Pythagoras: Greek philosopher " it states ; " Nazaratus, the Assyrian, one of Pythagoras ' masters, was supposed to be the prophet Ezekiel, and Thomas Stanley's Life of Pythagoras says that Ezekiel and Pythagoras flourished together.

A more successful effort was the Standard Proof for Pythagoras ' Theorem, that replaced the more than 100 incompatible existing proofs.

The paradigm of a spherical Earth was developed in Greek astronomy, beginning with Pythagoras ( 6th century BC ), although most Pre-Socratics retained the flat Earth model.

In April 1800, through the introduction of Hungarian writer Ignaz Aurelius Fessler, he was initiated into Freemasonry in the Lodge Pythagoras of the Blazing Star where he was elected minor warden.

However, as time went by, Gardner became critical of many of the Rosicrucian Order's practices ; Sullivan's followers claimed that he was immortal, having formerly been the famous historical figures Pythagoras, Cornelius Agrippa and Francis Bacon.

Hippocrates was credited by the disciples of Pythagoras of allying philosophy and medicine.

Like Pythagoras, Julian was a vegetarian.

* Lambda was used by Pythagoras to denote the " Lambda number sequence " 1, 2, 3, 4, 9, 8, 27, ..., formed by the integers of the form 2 < sup > i </ sup > and 3 < sup > i </ sup >, for nonnegative integer i.

It is unknown if Plato's ideas of idealism have some earlier origin, but Plato held Pythagoras in high regard, and Pythagoras as well as his followers in the movement known as Pythagoreanism claimed the world was literally built up from numbers, an abstract, absolute form.

This is called Pythagorean tuning because it was first discovered by Pythagoras.

This doctrine is a central tenet of the Indian religions and is a belief that was held by such historic figures as Pythagoras, Plato and Socrates.

Authorities have not agreed on how the notion arose in Greece: sometimes Pythagoras is said to have been Pherecydes ' pupil, sometimes to have introduced it with the doctrine of Orphism, a Thracian religion that was to be important in the diffusion of reincarnation, or else to have brought the teaching from India.

It is, in its purely physical application, a theory that he fully accepts ; he holds that it was taught by Pythagoras, Empedocles, and in fact, nearly all the ancient philosophers, and was only perverted to atheism by Democritus.

The practical side of philosophy was introduced by Pythagoras of Samos ( 582-496 BCE ).

Thus it was Pythagoras who gave the word " theory " the specific meaning which leads to the classical and modern concept of a distinction between theory as uninvolved, neutral thinking, and practice.