PHYTAGORAS
if we talk about phytagoras , so you will automatically think about right triangle . but do you know where is term come from ,
Pythagoras (582?-500?bc), Greek philosopher and mathematician, whose doctrines strongly influenced Plato.
The School of Athens (1510-1511) by Italian Renaissance painter Raphael adorns a room in the Vatican Palace. The artist depicts several philosophers of classical antiquity and portrays each with a distinctive gesture, conveying complex ideas in simple images. In the center of the composition, Plato and Aristotle dominate the scene. Plato points upward to the world of ideas, where he believes knowledge lies, whereas Aristotle holds his forearm parallel to the earth, stressing observation of the world around us as the source of understanding. In addition, Raphael draws comparisons with his illustrious contemporaries, giving Plato the face of the Renaissance genius Leonardo da Vinci, and Heraclitus, who rests his elbow on a large marble block, the face of the Renaissance sculptor Michelangelo. Euclid, bending down at the right, resembles the Renaissance architect Bramante. Raphael paints his own portrait on the young man in a black beret at the far right. In accordance with Renaissance ideas, artists belong to the ranks of the learned and the fine arts have the stature and merit of the written word.
Born on the island of Sámos, Pythagoras was instructed in the teachings of the early Ionian philosophers Thales, Anaximander, and Anaximenes. Pythagoras is said to have been driven from Sámos by his disgust for the tyranny of Polycrates. About 530 bc Pythagoras settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism. The philosophy of Pythagoras is known only through the work of his disciples.
Pythagoras (582?-500?bc), Greek philosopher and mathematician, whose doctrines strongly influenced Plato.
The School of Athens (1510-1511) by Italian Renaissance painter Raphael adorns a room in the Vatican Palace. The artist depicts several philosophers of classical antiquity and portrays each with a distinctive gesture, conveying complex ideas in simple images. In the center of the composition, Plato and Aristotle dominate the scene. Plato points upward to the world of ideas, where he believes knowledge lies, whereas Aristotle holds his forearm parallel to the earth, stressing observation of the world around us as the source of understanding. In addition, Raphael draws comparisons with his illustrious contemporaries, giving Plato the face of the Renaissance genius Leonardo da Vinci, and Heraclitus, who rests his elbow on a large marble block, the face of the Renaissance sculptor Michelangelo. Euclid, bending down at the right, resembles the Renaissance architect Bramante. Raphael paints his own portrait on the young man in a black beret at the far right. In accordance with Renaissance ideas, artists belong to the ranks of the learned and the fine arts have the stature and merit of the written word.
Born on the island of Sámos, Pythagoras was instructed in the teachings of the early Ionian philosophers Thales, Anaximander, and Anaximenes. Pythagoras is said to have been driven from Sámos by his disgust for the tyranny of Polycrates. About 530 bc Pythagoras settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism. The philosophy of Pythagoras is known only through the work of his disciples.
DOCTRIN
Early Greek Writings on Pythagoras
Pythagoras
Some of the legends about Pythagoras were collected by Aristotle in his lost work On the Pythagoreans. Here is a representative sample: Pythagoras, the son of Mnesarchus, first studied mathematics and numbers but later also indulged in the miracle-mongering of Pherecydes. When at Metapontum a cargo ship was entering harbour and the onlookers were praying that it would dock safely because of its cargo, he stood up and said: ‘You will see that this ship is carrying a corpse.’ Again, in Caulonia, as Aristotle says, he foretold the appearance of the white shebear; and Aristotle in his writings about him tells many stories including the one about the poisonous snake in Tuscany which bit him and which he bit back and killed. And he foretold to the Pythagoreans the coming strife—which is why he left Metapontum without being observed by anybody. And while he was crossing the river Casas in company with others he heard a superhuman voice saying ‘Hail, Pythagoras’—and those who were there were terrified. And once he appeared both in Croton and in Metapontum on the same day and at the same hour. Once, when he was sitting in the theatre, he stood up, so Aristotle says, and revealed to the audience his own thigh, which was made of gold. Several other paradoxical stories are told of him; but since I do not want to be a mere transcriber, enough of Pythagoras.
(Apollonius, Marvellous Stories 6)
(Apollonius, Marvellous Stories 6)
A large body of teachings came to be ascribed to Pythagoras. They divide roughly into two categories, the mathematico-metaphysical and the moral—as the poet Callimachus put it, Pythagoras was the first to draw triangles and polygons and *to bisect* the circle—and to teach men to abstain from living things.
(Iambi fragment 191.60-62 Pfeiffer)
Most modern scholars are properly sceptical of these ascriptions, and their scepticism is nothing new. The best ancient commentary on Pythagoras’ doctrines is to be found in a passage of Porphyry: Pythagoras acquired a great reputation: he won many followers in the city of Croton itself (both men and women, one of whom, Theano, achieved some fame), and many from the nearby foreign territory, both kings and noblemen. What he said to his associates no-one can say with any certainty; for they preserved no ordinary silence. But it became very well known to everyone that he said, first, that the soul is immortal; then, that it changes into other kinds of animals; and further, that at certain periods whatever has happened happens again, there being nothing absolutely new; and that all living things should be considered as belonging to the same kind. Pythagoras seems to have been the first to introduce these doctrines into Greece.
(Porphyry, Life of Pythagoras 19)
(Iambi fragment 191.60-62 Pfeiffer)
Most modern scholars are properly sceptical of these ascriptions, and their scepticism is nothing new. The best ancient commentary on Pythagoras’ doctrines is to be found in a passage of Porphyry: Pythagoras acquired a great reputation: he won many followers in the city of Croton itself (both men and women, one of whom, Theano, achieved some fame), and many from the nearby foreign territory, both kings and noblemen. What he said to his associates no-one can say with any certainty; for they preserved no ordinary silence. But it became very well known to everyone that he said, first, that the soul is immortal; then, that it changes into other kinds of animals; and further, that at certain periods whatever has happened happens again, there being nothing absolutely new; and that all living things should be considered as belonging to the same kind. Pythagoras seems to have been the first to introduce these doctrines into Greece.
(Porphyry, Life of Pythagoras 19)
The theory of metempsychosis, or the transmigration of the soul, is implicitly ascribed to Pythagoras by Xenophanes in the text quoted above. Herodotus also mentions it: The Egyptians were the first to advance the idea that the soul is immortal and that when the body dies it enters into another animal which is then being born; when it has gone round all the creatures of the land, the sea and the air, it again enters into the body of a man which is then being born; and this cycle takes it three thousand years. Some of the Greeks—some earlier, some later—put forward this idea as though it were their own: I know their names but I do not transcribe them.
(Herodotus, Histories II 123)
The names Herodotus coyly refrains from transcribing will have included that of Pythagoras. Two later passages are worth quoting even though they belong to the legendary material. Heraclides of Pontus reports that [Pythagoras] tells the following story of himself: he was once born as Aethalides and was considered to be the son of Hermes. Hermes invited him to choose whatever he wanted, except immortality; so he asked that, alive and dead, he should remember what happened to him. Thus in his life he remembered everything, and when he died he retained the same memories. Some time later he became Euphorbus and was wounded by Menelaus. Euphorbus used to say that he had once been Aethalides and had acquired the gift from Hermes and learned of the circtilation of his soul—how it had circulated, into what plants and animals it had passed, what his soul had suffered in Hades and what other souls experienced. When Euphorbus died, his soul passed into Hermotimus, who himself wanted to give a proof and so went to Branchidae, entered the temple of Apollo and pointed to the shield which Menelaus had dedicated (he said that he had dedicated the shield to Apollo when he sailed back from Troy); it had by then decayed and all that was left was the ivory boss. When Hermotimus died, he became Pyrrhus, the Delian fisherman; and again he remembered everything—how he had been first Aethalides, then Euphorbus, then Hermotimus, then Pyrrhus. When Pyrrhus died, he became Pythagoras and remembered everything I have related.
(Diogenes Laertius, Lives of the Philosophers VIII 4-5)
Pythagoras believed in metempsychosis and thought that eating meat was an abominable thing, saying that the souls of all animals enter different animals after death. He himself used to say that he remembered being, in Trojan times, Euphorbus, Panthus’ son, who was killed by Menelaus. They say that once when he was staying at Argos he saw a shield from the spoils of Troy nailed up, and burst into tears. When the Argives asked him the reason for his emotion, he said that he himself had borne that shield at Troy when he was Euphorbus. They did not believe him and judged him to be mad, but he said he would provide a true sign that it was indeed the case: on the inside of the shield there had been inscribed in archaic lettering euphorbus. Because of the extraordinary nature of his claim they all urged that the shield be taken down—and it turned out that on the inside the inscription was found.
(Diodorus, Universal History X vi 1-3)…
(Herodotus, Histories II 123)
The names Herodotus coyly refrains from transcribing will have included that of Pythagoras. Two later passages are worth quoting even though they belong to the legendary material. Heraclides of Pontus reports that [Pythagoras] tells the following story of himself: he was once born as Aethalides and was considered to be the son of Hermes. Hermes invited him to choose whatever he wanted, except immortality; so he asked that, alive and dead, he should remember what happened to him. Thus in his life he remembered everything, and when he died he retained the same memories. Some time later he became Euphorbus and was wounded by Menelaus. Euphorbus used to say that he had once been Aethalides and had acquired the gift from Hermes and learned of the circtilation of his soul—how it had circulated, into what plants and animals it had passed, what his soul had suffered in Hades and what other souls experienced. When Euphorbus died, his soul passed into Hermotimus, who himself wanted to give a proof and so went to Branchidae, entered the temple of Apollo and pointed to the shield which Menelaus had dedicated (he said that he had dedicated the shield to Apollo when he sailed back from Troy); it had by then decayed and all that was left was the ivory boss. When Hermotimus died, he became Pyrrhus, the Delian fisherman; and again he remembered everything—how he had been first Aethalides, then Euphorbus, then Hermotimus, then Pyrrhus. When Pyrrhus died, he became Pythagoras and remembered everything I have related.
(Diogenes Laertius, Lives of the Philosophers VIII 4-5)
Pythagoras believed in metempsychosis and thought that eating meat was an abominable thing, saying that the souls of all animals enter different animals after death. He himself used to say that he remembered being, in Trojan times, Euphorbus, Panthus’ son, who was killed by Menelaus. They say that once when he was staying at Argos he saw a shield from the spoils of Troy nailed up, and burst into tears. When the Argives asked him the reason for his emotion, he said that he himself had borne that shield at Troy when he was Euphorbus. They did not believe him and judged him to be mad, but he said he would provide a true sign that it was indeed the case: on the inside of the shield there had been inscribed in archaic lettering euphorbus. Because of the extraordinary nature of his claim they all urged that the shield be taken down—and it turned out that on the inside the inscription was found.
(Diodorus, Universal History X vi 1-3)…
The idea of eternal recurrence had a wide currency in later Greek thought. It is ascribed to ‘the Pythagoreans’ in a passage from Simplicius: The Pythagoreans too used to say that numerically the same things occur again and again. It is worth setting down a passage from the third book of Eudemus’ Physics in which he paraphrases their views:
One might wonder whether or not the same time recurs as some say it does. Now we call things ‘the same’ in different ways: things the same in kind plainly recur—e.g. summer and winter and the other seasons and periods; again, motions recur the same in kind—for the sun completes the solstices and the equinoxes and the other movements. But if we are to believe the Pythagoreans and hold that things the same in number recur—that you will be sitting here and I shall talk to you, holding this stick, and so on for everything else—then it is plausible that the same time too recurs.
(Simplicius, Commentary on the Physics 732.23-33)
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One might wonder whether or not the same time recurs as some say it does. Now we call things ‘the same’ in different ways: things the same in kind plainly recur—e.g. summer and winter and the other seasons and periods; again, motions recur the same in kind—for the sun completes the solstices and the equinoxes and the other movements. But if we are to believe the Pythagoreans and hold that things the same in number recur—that you will be sitting here and I shall talk to you, holding this stick, and so on for everything else—then it is plausible that the same time too recurs.
(Simplicius, Commentary on the Physics 732.23-33)
