1

Pythagoras and Pythagoreanism

Pythagoras, the Greek philosopher and mathematician and founder of the Pythagorean school,

flourished about 530 B.C. Very little is known about the life and personality of Pythagoras. There

is an abundance of biographical material dating from the first centuries of the Christian era, from

the age of neo-Pythagoreanism, but, when we go back to the centuries nearer to Pythagoras's

time, our material becomes very scanty. It seems to be certain that Pythagoras was born at Samos

about the year 550 or 560 B.C., that he travelled to Magna Græcia in Southern Italy about the year

530, that he founded there a school of philosophy and that he died at Metapontum in Sicily. The

detailed accounts of how he invented the musical scale, performed miracles, pronounced

prophecies, and did many other wonderful things, belong to legend, and seem to have no

historical foundation. Similarly the story of his journey into Egypt, Asia Minor, and even to

Babylon is not attested by reliable historians. To the region of fable belongs also the description

of the learned works which he wrote and which were long kept secret in his school. It is certain,

however, that he founded a school, or, rather, a religious philosophical society, for which he

drew up a rule of life. In this rule are said to have been regulations imposing secrecy, a

protracted period of silence, celibacy, and various kinds of abstinence. The time-honoured

tradition that Pythagoras forbade his disciples to eat beans, for which various reasons, more or

less ingenious, were assigned by ancient and medieval writers, has been upset by some recent

writers, who understand the phrase, "Abstain from beans" (kyamon apechete), to refer to a

measure of practical prudence, and not to a gastronomic principle. Beans, black and white, were,

according to this interpretation, the means of voting in Magna Græcia, and "Abstain from beans"

would, therefore, mean merely "Avoid politics"—a warning which, we know, was warranted by

the troubles in which the school was involved on account of the active share which it took during

the founder's lifetime in the struggles of the popular with the aristocratic party in Southern Italy.

The school was instructed by its founder to devote itself to the cultivation of philosophy,

mathematics, music, and gymnastics, the aim of the organization being primarily ethical. The

theoretical doctrines taught by the master were strictly adhered to, so much so that the

Pythagoreans were known for their frequent citation of the ipse dixit of the founder. Naturally, as

soon as the legends began to grow up around the name of Pythagoras, many tenets were ascribed

him which were in fact introduced by later Pythagoreans, such as Philolaus and Archytas of

Tarentum.

It seems to be certain that, besides prescribing the rules that were to govern the society,

Pythagoras taught:

a doctrine of transmigration of souls which he probably borrowed from the Bacchic and

Orphic mysteries, the whole spirit of the doctrine being religious and ethical, intended to

show, by successive incarnations of the soul in the bodies of different animals a system

by which certain vices and virtues were to be punished and rewarded after death;

in a general way, the doctrine that mathematics contains the key to all philosophical

knowledge, a germ, so to speak, which was afterwards developed into an elaborate

number-theory by his followers; and

the notion that virtue is a harmony, and may be cultivated not only by contemplation and

meditation but also by the practice of gymnastics and music.

The subsequent elaboration of these three central doctrines into a complicated system is the work

of the followers of Pythagoras. The Pythagorean philosophy in its later elaboration is dominated

by the number-theory. Being the first, apparently, to observe that natural phenomena, especially

the phenomena of the astronomical world, may be expressed in mathematical formulas, the

Pythagoreans were carried on by the enthusiasm characteristic of discoverers to maintain that

numbers are not only the symbols of reality, but the very substance of real things. They held, for

example, that one is the point, two the line, three the surface, and four the solid. Seven they

2

considered to be the fate that dominates human life, because infancy ceases at seven, maturity

begins at fourteen, marriage takes place in the twenty-first year, and seventy years is the span of

life usually allotted to man. Ten is the perfect number, because it is the sum of one, two, three,

and four-the point, the line, the surface, and the solid. Having, naturally, observed that all

numbers may be ranged in parallel columns under "odd" and "even", they were led to attempt a

similar arrangement of the qualities of things. Under odd they placed light, straight, good, right,

masculine; under even, dark, crooked, evil, left, feminine. These opposites, they contended, are

found everywhere In nature, and the union of them constitutes the harmony of the real world.

The account given by the Pythagoreans of the "harmony of the spheres" is the best illustration of

their method. There are, they said, ten heavenly bodies, namely, the heaven of the fixed stars, the

five planets, the sun, the moon, the earth, and the counter-earth. The counter-earth is added

because it is necessary to make up the number ten, the perfect number. It is a body under the

earth, moving parallel with it, and, since it moves at the same rate of speed, it is invisible to us.

The five planets, the sun, the moon, and the earth with its counter-earth, moving from west to

east at rates of speed proportionate to the distance of each from the central fire, produce eight

tones which give an octave, and, therefore, a harmony. We are not conscious of the harmony,

either because it is too great to be perceptible by human ears, or because, like the blacksmith

who has grown accustomed to the noise of his hammer on the anvil, we have lived since our first

conscious moments in the sound of the heavenly music and can no longer perceive it. In their

psychology and their ethics the Pythagoreans used the idea of harmony and the notion of number

as the explanation of the mind and its states, and also of virtue and its various kinds. It was not

these particular doctrines of the school so much as the general notion which prevailed among the

Pythagoreans of the scope and aim of philosophy, that influenced the subsequent course of

speculation among the Greeks. Unlike the Ionians, who were scientists and related philosophy to

knowledge merely, the Pythagoreans were religiously and ethically inclined, and strove to bring

philosophy into relation with life as well as with knowledge. Aristotelianism, which reduced

philosophy to knowledge, never could compete, in the estimation of its advocates, with

Christianity, as neo-Pythagoreanism did, by setting up the claim that in the teachings of its

founder it had a "way of life" preferable to that taught by the Founder of Christianity.

Sources

IAMBLICHUS, Legendary Life of Pythagoras, in Latin (Leipzig, 1815), tr. TAYLOR (London,

1818); GROTE, Hist. of Greece, IV (London, 1885), 525 sqq.; ZELLER, Pre-Socratic Philos.,

tr. ALLEYNE, I (London, 1881), 306 sqq.; UEBERWEG, Hist. of Philos., tr. MORRIS, I (New

York, 1892), 42 sqq.; TANNERY, Pour l'hist. de la science hellène (Paris, 1887), 201 Sqq.;

TURNER, Hist. of Phil. (Boston, 1903), 38 Sqq.

About this page

APA citation. Turner, W. (1911). Pythagoras and Pythagoreanism. In The Catholic

Encyclopedia. New York: Robert Appleton Company. Retrieved October 11, 2015 from New

Advent: http://www.newadvent.org/cathen/12587b.htm

MLA citation. Turner, William. "Pythagoras and Pythagoreanism." The Catholic Encyclopedia.

Vol. 12. New York: Robert Appleton Company, 1911. 11 Oct. 2015

<http://www.newadvent.org/cathen/12587b.htm>.

Transcription. This article was transcribed for New Advent by Douglas J. Potter. Dedicated to

the Sacred Heart of Jesus Christ.

3

Ecclesiastical approbation. Nihil Obstat. June 1, 1911. Remy Lafort, S.T.D., Censor.

Imprimatur. +John Cardinal Farley, Archbishop of New York.

Contact information. The editor of New Advent is Kevin Knight. My email address is

webmaster at newadvent.org. Regrettably, I can't reply to every letter, but I greatly appreciate

your feedback — especially notifications about typographical errors and inappropriate ads.

Copyright © 2012 by Kevin Knight. Dedicated to the Immaculate Heart of Mary.

Fonte: http://www.newadvent.org/cathen/12587b.htm

4

Pythagoras

Mathematics

2002 | Atkins, William Arthur & Koth, Philip Edward

Pythagoras

Mathematician and Philosopher

c. 582 b.c.e.–c. 500 b.c.e.

Considered a mathematician, but foremost a philosopher,

Pythagoras was a very important figure in mathematics,

astronomy, musical theory, and in the world's history.

However, little in the way of reliable record is known

about his life and accomplishments. The accounts of

Pythagoras inventing the musical scale, performing

miracles, and announcing prophecies are probably only

legend, and appear to have little historical foundation.

Scholars generally agree only upon the main events in his

life, and usually combine together discoveries by

Pythagoras with those by his band of loyal followers.

Pythagoras established in what is now the southeastern

coast of Italy a philosophical, political, and religious

society whose members believed that the world could be

explained using mathematics as based upon whole

numbers and their ratios. Their motto was "All is number."

Even the words philosophy (or "love of wisdom") and

mathematics (or "that which is learned") is believed to

have been first used (and defined) by the Pythagoreans.

Many Pythagorean beliefs (such as secrecy, vegetarianism, periods of food abstinence and

silence, refusal to eat beans, refusal to wear animal skins, celibacy, self-examination,

immortality, and reincarnation) were directed as "rules of life." The main focus of Pythagorean

thought was ethics, developed primarily within philosophy, mathematics, music, and gymnastics.

The beliefs of the society were that reality is mathematical; philosophy is used for spiritual

purification; the soul is divine; and certain symbols possess mystical significance. Both men and

women were permitted to become members. In fact, several female Pythagoreans became noted

philosophers.*

*Aesara of Lucania was a Pythagorean philosopher known for her theory of the tripart

soul, which she believed consisted of the mind, spiritedness, and desire.

Pythagoras bust.

Musei Capitolini, Roma.

5

How Pythagoreans Conceptualized Numbers

Pythagoreans believed that all relationships could be reduced to numbers in order to account for

geometrical properties. This generalization originated from the observation that whenever the

ratios of lengths of strings were whole numbers, harmonious tones were produced when these

strings were vibrated.

The society studied properties of numbers that are familiar to modern mathematicians, such as

even and odd numbers, prime and square numbers. From this viewpoint, the Pythagoreans

developed the concept of number, which became their dominant principle of all proportion,

order, and harmony in the universe.

The society also believed in such numerical properties as masculine or feminine, perfect or

incomplete, and beautiful or ugly. These opposites, they believed, were found everywhere in

nature, and the combination of them brought about the harmony of the world.

The primary belief of Pythagoreans in the sole existence of whole numbers was later challenged

by their own findings, which proved the existence of "incommensurables," known today as

irrational numbers . What is commonly called the "first crisis in mathematics" caused a scandal

within the society, so serious that some members tried to suppress the knowledge of the

existence of incommensurables.

The Pythagorean philosophy was dominated by the ideal that numbers were not only symbols of

reality, but also were the final substance of real things, known as "number mysticism." They

held, for example, that one is the point, two the line, three the surface, and four the solid. Seven

was considered the destiny that dominates human life because infancy ends there, and also

because the number was associated with the seven wandering stars. Moreover, Pythagoreans

believed that maturity began at age 14, marriage occurred in the twenty-first year, and 70 years

was the normal life span. Ten was identified as the "perfect number" because it was the sum of

one, two, three, and four.

Pythagorean Contributions to Mathematics

The formalization of mathematics with the use of axiomatic systems was the most profound

contribution that the Pythagorean society made to mathematics. Pythagoreans developed this

significant concept by showing that arbitrary laws of empirical geometry could be proved as

logical conclusions from a small number of axioms, or postulates. Typical of the developed

axioms was "A straight line is the shortest distance between two points."

From these axioms, a number of theorems about the properties of points, lines, angles, curves,

and planes could be logically deduced. These theorems include the famous Pythagorean theorem,

which states that "the square of the hypotenuse of a right-angled triangle is equal to the sum of

the squares of the other two sides." Another theorem states that the sum of the interior angles of

any triangle is equal to the sum of two right angles.

The Pythagorean Theorem

The Pythagoreans knew that any triangle whose sides were in the ratio 3:4:5 was a right-angled

triangle. Their desire to find the mathematical harmonies of all things led them to prove the

geometric theorem, today named for Pythagoras. The earlier Egyptians stated this theorem as an

empirical relationship and, as far as is known today, the Pythagoreans were the first to prove it.

6

The Pythagorean (hypotenuse) theorem states that the square of the hypotenuse of a right-angle

triangle (c ) is equal to the sum of the squares of the other two sides (a and b ), shown as c 2 = a

2

+ b 2. The numbers 3, 4, and 5 are called Pythagorean numbers (5

2 = 3

2 + 4

2, or 25 = 9 + 16).

However, the Pythagoreans did not consider the square on the hypotenuse to be that number (c )

multiplied by itself (c 2). Instead, it was conceptualized as a geometrical square (C ) constructed

on the side of the hypotenuse, and that the sum of the areas of the two squares (A and B ) is equal

to the area of the third square (C ), as shown below.

Astronomy and the Pythagoreans

In astronomy, the Pythagoreans produced important advances in ancient scientific thought. They

were the first to consider the Earth as a sphere revolving with the other planets and the Sun

around a universal "central fire." Ten planets were believed to exist in order to produce the

"magical" number of 10. This arrangement was explained as the harmonious arrangement of

bodies in a complete sphere of reality based on a numerical pattern, calling it a "harmony of

sphere." The Pythagoreans also recognized that the orbit of the Moon was inclined to the equator

of the Earth, and were one of the first to accept that Venus was both the evening star and the

morning star.

Even though much of the Pythagorean doctrine consisted of numerology and number mysticism,

their influence in developing the idea that nature could be understood through mathematics and

science was extremely important for studying and understanding the world in which we live.

see also Numbers: Abundant, Deficient, Perfect, and Amicable; Numbers, Forbidden and

Superstitious; Numbers, Irrational; Numbers, Rational; Numbers, Whole; Triangle.

William Arthur Atkins with

Philip Edward Koth

Bibliography

Boyer, Carl B. A History of Mathematics, 2nd

ed., New York: John Wiley & Sons, 1991.

O'Meara, Dominic J. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity. New

York: Clarendon Press, 1990.

Philip, James A. Pythagoras and Early Pythagoreanism. Toronto: University of Toronto Press,

1966.

MAGIC OVER MATHEMATICS

During the time of Pythagoras, most people either believed that the world could only be

explained by magic or that it could not be explained at all. Thus, many people did not attempt to

understand mathematics.

COPYRIGHT 2002 The Gale Group Inc.

7

Pythagoras

Encyclopedia of World Biography 2004

Pythagoras

The Greek philosopher, scientist, and religious teacher Pythagoras (ca. 575-ca. 495 B.C.)

evolved a school of thought that accepted the transmigration of souls and established

number as the principle in the universe.

Born on the island of Samos, Pythagoras was the son of Mnesarchus. He fled to southern Italy to

escape the tyranny of Polycrates, who came to power about 538, and he is said to have traveled

to Egypt and Babylon. He and his followers became politically powerful in Croton in southern

Italy, where Pythagoras had established a school for his newly formed sect. It is probable that the

Pythagoreans took positions in the local government in order to lead men to the pure life which

their teachings set forth. Eventually, however, a rival faction launched an attack on the

Pythagoreans at a gathering of the sect, and the group was almost completely annihilated.

Pythagoras either had been banished from Croton or had left voluntarily shortly before this

attack. He died in Metapontum early in the 5th century.

Religious Teachings

Pythagoras and his followers were important for their contributions to both religion and science.

His religious teachings were based on the doctrine of metempsychosis, which held that the soul

was immortal and was destined to a cycle of rebirths until it could liberate itself from the cycle

through the purity of its life. A number of precepts were drawn up as inviolable rules by which

initiates must live.

Pythagoreanism differed from the other philosophical systems of its time in being not merely an

intellectual search for truth but a whole way of life which would lead to salvation. In this respect

it had more in common with the mystery religions than with philosophy. Several taboos and

mystical beliefs were taught which sprang from a variety of primitive sources such as folk taboo,

ritual, and sympathetic magic and were examples of the traditional beliefs that the Greeks

continued to hold while developing highly imaginative and rational scientific systems.

An important underlying tenet of Pythagoreanism was the kinship of all life. A universal life

spirit was thought to be present in animal and vegetable life, although there is no evidence to

show that Pythagoras believed that the soul could be born in the form of a plant. It could be born,

however, in the body of an animal, and Pythagoras claimed to have heard the voice of a dead

friend in the howl of a dog being beaten.

The number of lives which the soul had to live before being liberated from the cycle is uncertain.

Its liberation came through an ascetic life of high moral and ethical standards and strict

adherence to the teachings and practices of the sect. Pythagoras himself claimed to remember

four different lives. Followers of the sect were enjoined to secrecy, although the discussions of

Pythagoras's teachings in other writers proved that the injunction was not faithfully observed.

Mathematical Teachings

The Pythagoreans posited the dualism between Limited and Unlimited. It was probably

Pythagoras himself who declared that number was the principle in the universe, limiting and

8

giving shape to matter. His study of musical intervals, leading to the discovery that the chief

intervals can be expressed in numerical ratios between the first four integers, also led to the

theory that the number 10, the sum of the first four integers, embraced the whole nature of

number.

So great was the Pythagoreans' veneration for the "Tetractys of the Decad" (the sum of 1 + 2 + 3

+ 4) that they swore their oaths by it rather than by the gods, as was conventional. Pythagoras

may have discovered the theorem which still bears his name (in right triangles, the square on the

hypotenuse equals the sum of the squares on the other sides), although this proposition has been

discovered on a tablet dating from the time of the Babylonian king Hammurabi. Regardless of

their sources, the Pythagoreans did important work in systematizing and extending the body of

mathematical knowledge.

As a more general scheme, the Pythagoreans posited the two contraries, Limited and Unlimited,

as ultimate principles. Numerical oddness and evenness are equated with Limited and Unlimited,

as are one and plurality, right and left, male and female, motionlessness and movement, straight

and crooked, light and darkness, good and bad, and square and oblong. It is not clear whether an

ultimate One, or Monad, was posited as the cause of the two categories.

Cosmological Views

As a result of their religious beliefs and their careful study of mathematics, the Pythagoreans

developed a cosmology which differed in some important respects from the world views of their

contemporaries, the most important of which was their view of the earth as a sphere which

circled the center of the universe. The center of this system was fire, which was invisible to man

because his side of the earth was turned from it. The sun reflected that fire; there was a

counterearth closer to the center, and the other five planets were farther away and followed

longer courses around the center. It is not known how much of this theory was attributable to

Pythagoras himself. Later writers ascribe much of it to Philolaos (active 400 B.C.), although it

circulated as a view of the school as a whole.

The systematization of mathematical knowledge carried out by Pythagoras and his followers

would have sufficed to make him an important figure in the history of Western thought.

However, his religious sect and the asceticism which he taught, embracing as it did a vast

number of ancient beliefs, make him one of the great teachers of religion in the ancient Greek

world.

Further Reading

Pythagoras left no written works. A first-rate technical book, J. A. Philip, Pythagoras and Early

Pythagoreanism (1966), separates the valid from the spurious among the legends that surround

Pythagoras and his views. An excellent and thorough treatment of the evidence for his life and

teachings is in W. K. C. Guthrie, A History of Greek Philosophy (3 vols., 1962-1969). A good

account of Pythagoras and his followers is in Kathleen Freeman, The Pre-Socratic Philosophers

(1946; 3d ed. 1953), and G. S. Kirk and J. E. Raven, The Presocratic Philosophers (1962).

Briefer treatments of the Pythagoreans and the intellectual currents of their time are in the

standard histories of Greek literature, such as Albin Lesky, A History of Greek Literature (trans.

1966), or in accounts of Greek philosophy, such as John Burnet, Greek Philosophy (1914). □

COPYRIGHT 2004 The Gale Group Inc.

9

Pythagoras

UXL Encyclopedia of World Biography 2003

Pythagoras

Born: c. 575 b.c.e.

Samos, Greece

Died: c. 495 b.c.e.

Metapontum Greek philosopher, scientist, and religious scholar

The Greek philosopher, scientist, and religious teacher Pythagoras developed a school of thought

that accepted the passage of the soul into another body and established many influential

mathematical and philosophical theories.

Early life

Born on the island of Samos, off Greece, in the Mediterranean Sea, Pythagoras was the son of

Mnesarchus. Little is known about his early life. After studying in Greece, he fled to southern

Italy to escape the harsh rule of Polycrates (died c. 522 b.c.e.), who came to power about 538

b.c.e. Pythagoras is said to have traveled to Egypt and Babylon during this time.

Pythagoras and his followers became politically powerful in Croton in southern Italy, where

Pythagoras had established a school for his newly formed sect, or group of followers. It is

probable that the Pythagoreans took positions in the local government in order to lead men to the

pure life that was directed by their teachings. Eventually, however, a rival group launched an

attack on the Pythagoreans at a gathering of the sect, and the group was almost completely

destroyed. Pythagoras either had been forced to leave Croton or had left voluntarily shortly

before this attack. He died in Metapontum early in the fifth century b.c.e.

Religious teachings

Pythagoras and his followers were important for their contributions to both religion and science.

His religious teachings were based on the doctrine (teaching) of metempsychosis, which teaches

that the soul never dies and is destined to a cycle of rebirths until it is able to free itself from the

cycle through the purity of its life.

Pythagoreanism differed from the other philosophical systems of its time in being not merely an

intellectual search for truth but a whole way of life which would lead to salvation, or to be

delivered from sin. An important part of Pythagoreanism was the relationship of all life. A

universal life spirit was thought to be present in animal and vegetable life, although there is no

evidence to show that Pythagoras believed that the soul could be born in the form of a plant. It

could be born, however, in the body of an animal, and Pythagoras claimed to have heard the

voice of a dead friend in the howl of a dog being beaten.

Mathematical teachings

The Pythagoreans presented as fact the dualism (that life is controlled by opposite forces)

between Limited and Unlimited. It was probably Pythagoras who declared that numbers could

uncover the secrets of the universe, limiting and giving shape to matter (anything that takes up

10

space). His study of musical intervals, leading to the discovery that the chief intervals can be

expressed in numerical ratios (relationships between numbers) between the first four integers

(positive whole numbers), also led to the theory that the number ten, the sum of the first four

integers, embraced the whole nature of number.

So great was the Pythagoreans' respect for the "Tetractys of the Decad" (the sum of 1 + 2 + 3 +

4) that they swore their oaths (promises) by it rather than by the gods, as was normal during his

day. Pythagoras may have discovered the theorem which still bears his name (in right triangles

[triangle with one angle equal to 90 degrees], the square on the hypotenuse equals the sum of the

squares on the other sides), although this proposal has been discovered on a writing stone dating

from the time of the Babylonian king Hammurabi (died c. 1750 b.c.e.). Regardless of their

sources, the Pythagoreans did important work in extending the body of mathematical knowledge.

As a more general outline, the Pythagoreans presented the two contraries (opposites), Limited

and Unlimited, as ultimate principles, or truths. Numerical oddness and evenness are equated

with Limited and Unlimited, as are one and plurality (many), right and left, male and female,

motionlessness and movement, straight and crooked, light and darkness, and good and bad. It is

not clear whether an ultimate One, or Monad, was presented as the cause of the two categories.

Cosmological views

The Pythagoreans, as a result of their religious beliefs and careful study of mathematics,

developed a cosmology (dealing with the structures of the universe) which differed in some

important respects from the world views at the time, the most important of which was their view

of the Earth as a sphere which circled the center of the universe. It is not known how much of

this theory was credited to Pythagoras himself.

The mathematical knowledge carried out by Pythagoras and his followers would have been

enough to make him an important figure in the history of Western thought. However, his

religious sect and the self-discipline and dedication which he taught, embracing as it did a vast

number of ancient beliefs, make him one of the great teachers of religion in the ancient Greek

world.

For More Information

Fey, James. Looking for Pythagoras: The Pythagorean Theorem. White Plains, NY: Dale

Seymour Publications, 1997.

Philip, J. A. Pythagoras and Early Pythagoreanism. Toronto: University of Toronto Press, 1966.

Strohmeyer, John, and Peter Westbrook. Divine Harmony: The Life and Teachings of

Pythagoras. Berkeley, CA: Berkeley Hills Books, 1999.

COPYRIGHT 2003 The Gale Group, Inc.

11

Pythagoras

Encyclopedia of Food and Culture

2003 | Saltveit, Mikal E.

PYTHAGORAS

PYTHAGORAS. Pythagoras (c. 580–c. 580 B.C.E.) was a Greek mathematician, philosopher,

and mystic. He wrote nothing himself, so his ideas survive through the writings of others,

including Aristotle. Many people are familiar with him as the mathematician who formulated the

Pythagorean theorem in geometry that relates the lengths of the sides in a right triangle. Others

know him as a mystic and the first person known to be motivated by moral and philosophical

concerns to adopt a vegetarian diet.

The schools and societies Pythagoras founded in the southern Italian area of Magna Graecia

flourished for a while, and they developed and spread many of his concepts, which were later

adopted and expanded by others. These concepts include bodily humors (evident in modern

descriptions of melancholic and phlegmatic personalities), a tripartite soul, reincarnation, and the

numerical ratios that determine the concordant intervals of the musical scales. Permeating all of

his thoughts was the idea that all things are numbers. Numbers (individuals, groups, and series)

were imbued with mystical properties that were carefully guarded and only shared among

initiates to the Pythagorean schools founded by him or his disciples.

Pythagoras and his followers practiced one of the first recorded diets known as vegetarianism.

He advocated a diet devoid of the flesh of slaughtered animals partially because he felt food

influenced the distribution of the bodily humors and thereby the health of the individual and

partially because it would prevent the killing of a reincarnated individual and its transmigrated

soul. Up until the late nineteenth century non–meat eaters were generally known as

"Pythagoreans."

Pythagoras is also alleged to have admonished his disciples to abstain from eating beans. Ancient

and medieval writers ingeniously ascribed this pronouncement to the belief that beans contained

or transmitted souls. The Greek phrase supporting this gastronomic recommendation, however,

could also be construed to imply that his followers should avoid politics. Black and white beans

were used as counters in voting in Magna Graecia. The school Pythagoras founded there became

actively involved in the populist political views that gained ascendancy in the town of Kroton,

where he lived for many years. Later an opposing aristocratic party gained control of the city and

banished him and his followers for their political views and activism. Pythagoras died in exile.

His supposed warning to "abstain from beans" is therefore thought to have meant "avoid

politics." Alternatively he may have realized that eating undercooked broad (fave) beans (Vica

faba vulgaris), a common food of the Mediterranean region, produced a severe hemolytic anemia

(favism) in some people. Interestingly the same mutant gene that makes people sensitive to

favism also increases their resistance to the malarial parasite, possibly accounting for the

widespread presence of the mutant gene in regions with endemic malaria.

See also Greece, Ancient ; Vegetarianism .

BIBLIOGRAPHY

Bamford, Christopher, ed. Homage to Pythagoras. Hudson, N.Y.: Lindisfarne Press, 1994.

12

Gorman, Peter. Pythagoras. London: Routledge and Kegan Paul, 1979.

Spencer, Colin. The Heretic's Feast: A History of Vegetarianism. London: Fourth Estate, 1993.

Walters, Kerry S., and Lisa Portmess, eds. Ethical Vegetarianism: From Pythagoras to Peter

Singer. Albany: State University of New York Press, 1999.

Mikal E. Saltveit

COPYRIGHT 2003 The Gale Group Inc.

Pythagoras

The Columbia Encyclopedia, 6th ed. 2015

Pythagoras (pĬthăg´ərəs), c.582–c.507 BC, pre-Socratic Greek philosopher, founder of the

Pythagorean school. He migrated from his native Samos to Crotona and established a secret

religious society or order similar to, and possibly influenced by, the earlier Orphic cult. We

know little of his life and nothing of his writings. Since his disciples came to worship him as a

demigod and to attribute all the doctrines of their order to its founder, it is virtually impossible to

distinguish his teachings from those of his followers. The Pythagoreans are best known for two

teachings: the transmigration of souls and the theory that numbers constitute the true nature of

things. The believers performed purification rites and followed moral, ascetic, and dietary rules

to enable their souls to achieve a higher rank in their subsequent lives and thus eventually be

liberated from the "wheel of birth." This belief also led them to regard the sexes as equal, to treat

slaves humanely, and to respect animals. The highest purification was "philosophy," and

tradition credits Pythagoras with the first use of the term. Beginning with the discovery that the

relationship between musical notes could be expressed in numerical ratios (see Greek music), the

Pythagoreans elaborated a theory of numbers, the exact meaning of which is still disputed by

scholars. Briefly, they taught that all things were numbers, meaning that the essence of things

was number, and that all relationships—even abstract ethical concepts like justice—could be

expressed numerically. They held that numbers set a limit to the unlimited—thus foreshadowing

the distinction between form and matter that plays a key role in all later philosophy. The

Pythagoreans were influential mathematicians and geometricians, and the theorem that bears

their name is witness to their influence on the initial part of Euclidian geometry. They made

important contributions to medicine and astronomy and were among the first to teach that the

earth was a spherical planet, revolving about a fixed point. At the end of the 5th cent. BC the

Pythagoreans were forced to flee Magna Graecia when people grew enraged at their interference

with traditional religious customs; many were killed. A short-lived Neo-Pythagoreanism

developed at the beginning of the Christian era; it borrowed some elements from Jewish and

Hellenistic thought and greatly emphasized the mystical element in Pythagorean ideas.

See biographies by P. Gorman (1978) and T. Stanley (1988); D. J. O'Meara, Pythagoras

Revived: Mathematics and Philosophy in Late Antiquity (1989).

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Pythagoras

The Oxford Dictionary of Phrase and Fable

2006 | ELIZABETH KNOWLES

Pythagoras (c.580–500 bC), Greek philosopher; known as Pythagoras of Samos. Pythagoras

sought to interpret the entire physical world in terms of numbers, and founded their systematic

and mystical study; he is best known for the theorem of the right-angled triangle. His analysis of

the courses of the sun, moon, and stars into circular motions was not set aside until the 17th

century.

Pythagoras also founded a secret religious, political, and scientific sect in Italy: the Pythagoreans

held that the soul is condemned to a cycle of reincarnation, from which it may escape by

attaining a state of purity.

Pythagoras’theorem the theorem attributed to Pythagoras that the square on the hypotenuse of a

right-angled triangle is equal in area to the sum of the squares on the other two sides.

Pythagorean letter the Greek letter Y, used by Pythagoras as a symbol of the two divergent paths

of virtue and of vice.

Pythagorean system the system of astronomy proposed by Pythagoras, in which all celestial

bodies, including the earth, were held to revolve around a central fire (not the sun, but

presumably identified with the sun, resulting in the system being assumed identical with the

Copernican system).

© The Oxford Dictionary of Phrase and Fable 2006, originally published by Oxford University

Press 2006.

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