Feste: What is the opinion of Pythagoras concerning wild-fowl? Malvolio: That the soul of our grandam might haply inhabit a bird. Act V
Pythagoras conceived that the first attention that should be given to men should be addressed to the senses, as when one perceives beautiful figures and forms, or hears beautiful rhythms and melodies. Consequently he laid down that the first erudition was that which subsists through music's melodies and rhythms, and from these he obtained remedies of human manners and passions, and restored the pristine harmony of the faculties of the soul.iamblichus of chalcis
It seems probable that the early Greeks were largely indebted to the Phoenicians for their knowledge of practical arithmetic or the art of calculation, and perhaps also learnt from them a few properties of numbers. It may be worthy of note that Pythagoras was a Phoenician; and according to Herodotus , but this is more doubtful, Thales was also of that race.
Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.johannes kepler
What seems certain is that Pythagoras developed the idea of mathematical logic... He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute then any previous knowledge.simon singh
Pythagoras said that this world was like a stage, Whereon many play their parts; the lookers-on, the sage Philosophers are, saith he, whose part is to learn The manners of all nations, and the good from the bad to discern.richard edwardes
As soon as we venture on the paths of the physicist, we learn to weigh and measure , to deal with time and space and mass and their related concepts, and to find more and more our knowledge expressed and our needs satisfied through the concept of number , as in the dreams of Plato and Pythagoras .
Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables , which appeared to disprove his whole philosophy. So long as no adequate arithmetical theory on incommensurables existed, the method of Euclid was the best that was possible in geometry. When Descartes introduced co-ordinate geometry, thereby again making arithmetic supreme, he [Descartes] assumed the possibility of a solution of the problem of incommensurables, though in his day no such solution had been found.
The Eudemian Summary says that "Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom, and investigated its theorems in an immaterial and intellectual manner." His geometry was connected closely with his arithmetic. He was especially fond of those geometrical relations which admitted of arithmetical expression.
Of the theorems generally ascribed to the Italian school, some cannot be attributed to Pythagoras himself, nor to his earliest successors. The progress from empirical to reasoned solutions must, of necessity, have been slow. It is worth noticing that on the circle no theorem of any importance was discovered by this school.
As great Pythagoras of yore, Standing beside the blacksmith's door, And hearing the hammers, as they smote The anvils with a different note, Stole from the varying tones, that hung Vibrant on every iron tongue, The secret of the sounding wire, And formed the seven-chorded lyre.Henry Wadsworth Longfellow
It was Pythagoras who first called heaven kosmos , because it is perfect , and "adorned" with infinite beauty and living beings.
Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.
Pythagoras, when he was asked what time was, answered that it was the soul of this world.
The apparently ancient reports of the importance of Pythagoras and his pupils in laying the foundations of mathematics crumble on touch, and what we can get hold of is not authentic testimony by the efforts latecomers to paper over a crack, which they obviously found surprising, by the use of various kinds of reconstruction and reinterpretation. On the other hand, there are ancient and unassailable indications of a Greek mathematics antedating Pythagoras and quite outside his sphere of influence.
Pythagoras is the founder of European culture in the Western Mediterranean sphere.
Let us suppose that we have set the problem of finding a solution to the equation This is a problem for which the Babylonians around 1700 BC found the excellent approximation ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen the problem which caused the existentialist crisis in ancient Greek mathematics. The exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!
Pythagoras, the son of Mnesarchus, was the most learned of all men of history; and having selected from these writings, he thus formed his own wisdom and extensive learning, and mischievous art.
No one will deny that the soul of Pythagoras was sent to mankind from Apollo's domain, having either been one of his attendants, or more intimate associates, which may be inferred both from his birth, and his versatile wisdom.iamblichus of chalcis
Pythagoras was a teacher of the purest system of morals ever propounded to man.
It was Pythagoras who first called heaven kosmos , because it is perfect, and "adorned" with infinite beauty and living beings.
It was a maxim of Pythagoras that the two most excellent things for man were to speak the truth, and to render benefits to each other.
Pythagoras said that this world was like a stage, Whereon many play their parts; the lookers-on the sage Philosophers are, saith he, whose part is to learn The manners of all nations, and the good from the bad to discern.