ARCHYTAS (c. 428-347 B.C.), of Tarentum, Greek philosopher and scientist of the Pythagorean school, famous as the intimate friend of Plato, was the son of Mnesagoras or Histiaeus.
The great Pythagorean oath was taken by the sacred tetractys.
The Pythagorean school of philosophers adopted the theory of a spherical earth, but from metaphysical rather than scientific reasons; their convincing argument was that a sphere being the most perfect solid figure was the only one worthy to circumscribe the dwellingplace of man.
He is described as the eighth leader of the Pythagorean school, and was a pupil (not the teacher, as some have maintained) of Philolaus.
The Pythagorean theory of numbers, Neoplatonic ideas of emanation, the Logos, the personified Wisdom, Gnosticism - these and many other features combine to show the antiquity of tendencies which, clad in other shapes, are already found in the old pre-Christian Oriental religions.
His dissatisfaction with Ptolemaic doctrines was of early date; and he returned from Italy, where so-called Pythagorean opinions were then freely discussed, in strong and irrevocable possession of the heliocentric theory.
He has, indeed, a system, but it is a singular medley of doctrines borrowed, not only from Saint-Simonian, but from Pythagorean and Buddhistic sources.
31 Discorso Intorno alle Opere di Messer Gioseffe Zarlino, and followed it up in his famous Dialogo, defending the Pythagorean system in very unmeasured language.
He produced in the end a synthesis of Plato and Aristotle with an admixture of Pythagorean or Oriental mysticism, and is closely allied to the Alexandrian school of thought.
Hippocrates, influenced as is thought by the Pythagorean doctrines of number, taught that they were to be expected on days fixed by certain numerical rules, in some cases on odd, in others on even numbers - the celebrated doctrine of "critical days."
The Pythagorean and Eleatic systems of philosophy had their chief seat in Magna Graecia.
ANAXILAUS, of Larissa, a physician and Pythagorean philosopher, who was banished from Rome by Augustus, B.C. 28, on the charge of practising the magic art.
The Pythagorean discovery of "squaring a square," i.e.
Constructing a square of twice the area of a given square (which follows as a corollary to the Pythagorean property of a right-angled triangle, viz.
As we have already intimated, Gnosticism had such a power 1 For the disciples of Valentinus, especially Marcus, after whom was named a separate sect, the Marcosians, with their Pythagorean theories of numbers and their strong tincture of the mystical, magic, and sacramental, see Valentinus And Valentinians.
His idea of the universe was essentially Pythagorean and Platonic. He started with the conviction that the arrangement of its parts must correspond with certain abstract conceptions of the beautiful and harmonious.
The Keplerian like the Pythagorean cosmos was threefold, consisting of the centre, or sun, the surface, represented by the sphere of the fixed stars, and the intermediate space, filled with ethereal matter.
HIPPASUS OF METAPONTUM, Pythagorean philosopher, was one of the earliest of the disciples of Pythagoras.
He seems to have regarded the soul as composed of igneous matter, and so approximates the orthodox Pythagorean doctrine of the central fire, or Hestia, to the more detailed theories of Heraclitus.
In order to explain the unity and variety of the world, the one universal form and the many individuals, and how the one good is the main cause of everything, he placed as it were at the back of his own doctrine of forms a Pythagorean mathematical philosophy.
Leibnitz, again, having become equally dissatisfied with Cartesianism, Spinozism and the Epicurean realism of Gassendi, in the latter part of his life came still nearer than Spinoza to metaphysical idealism in his monadology, or half-Pythagorean,half-Brunistic analysis of bodies into monads, or units, or simple substances, indivisible and unextended, but endowed with perception and appetite.
Granting then that some foreign influence was at work in Essenism, we have four theories offered to us - that this influence was Persian, Buddhist, Pythagorean, or lastly, as maintained by Lipsius, that of the surrounding Syrian heathenism.
He was also influenced by the Epicurean and the Academic and the revived Pythagorean schools.
C. 480), Greek philosopher of the Pythagorean school, was born at Tarentum or at Crotona 1 (so Diog.
He was the first who published a book on the Pythagorean doctrines, a treatise of which Plato made use in the composition of his Timaeus.
This work of the Pythagorean, to which the mystical name BaKXac is sometimes given, seems to have consisted of three books: (I) IIEpi Kkuou, containing a general account of the origin and arrangement of the universe; (2) llepi ckaaes, an exposition of the nature of numbers; (3) IIEpc kxi)s, on the nature of the soul.
Very little is known about the members of this school, and there has been much discussion as to whether the Pythagorean literature which was widely published at the time in Alexandria was the original work of 1st-century writers or merely reproductions of and commentaries on the older Pythagorean writings.
45 B.C.) had made an attempt to revive Pythagorean doctrines, but he cannot be described as a member of the school.
They went back to the later period of Plato's thought, the period when Plato endeavoured to combine his doctrine of Ideas with the Pythagorean number-theory, and identified the Good with the One, the source of the duality of the Infinite and the Measured (rd .bretpov and 71-pas) with the resultant scale of realities from the One down to the objects of the material world.
But the most remarkable intellectual movement in Sicily at this time was the influence of the Pythagorean philosophy, which still lived on in southern Italy.
The Pythagorean philosophy, whose seat was in southern Italy, won adherents among the native chiefs (Cic. De senec. 12, cf.
Even these had been preceded by earlier Pythagorean constructions envisaging the divine life in divine triangles.
Thus in Italy the Pythagorean school was, in the fullest sense of the term, an educational institution; and in Sicily the rhetorical teaching of Corax and Tisias was presumably educational in the same sense as the teaching of Gorgias.
If Eleatic thought stands over against Pythagorean thought as what is valid or grounded against what is ungrounded or invalid, we are embarked upon dialectic, or the debate in which thought is countered by thought.
Hamilton was probably influenced by the recollection of its Greek equivalent, the Pythagorean Tetractys (TerpaKrt, the number four), the mystic source of all things.
Aristoxenus, who had formerly belonged to the Pythagorean school, maintained the position, already combated by Plato in the Phaedo, that the soul is to be regarded as nothing more than the harmony of the body.
The zodiac of Denderah; the Savoyards who carved their pine-forests into toys; the naked Derar, horsed on an idea, charging a troop of Roman cavalry; the long, austere Pythagorean lustrum of silence; Napoleon on the deck of the "Bellerophon," observing the drill of the English soldiers; the Egyptian doctrine that every man has two pairs of eyes; Empedocles and his shoe; the horizontal stratification of the earth; a soft mushroom pushing its way through the hard ground, - all these allusions and a thousand more are found in the same volume.
Of Speusippus's many philosophical writings nothing survives except a fragment of a treatise On Pythagorean Numbers.
Having accepted the Platonic metaphysical doctrine, he applied to it the Neo-Pythagorean principles and the Oriental doctrine of Emanation.
In the phenomenal world then, there are, it has been thought [and Parmenides accepts the theory, which appears to be of Pythagorean origin], two primary elements - namely, fire, which is gentle, thin, homogeneous, and night, which is dark, thick, heavy.
Hence, whatever influence the Pythagorean blending of ethical and mathematical notions may have had on Plato, and, through him, on later thought, we cannot regard the school as having really forestalled the Socratic inquiry after a completely reasoned theory of conduct.
Under the searchlights of the new learning, the dictatorship of Ptolemy appeared no more inevitable than that of Aristotle; advanced thinkers like Domenico Maria Novara (1454-1504) promulgated sub rosa what were called Pythagorean opinions; and they were eagerly and fully appropriated by Nicolaus Copernicus during his student-years (1496-1505) at Bologna and Padua.
Kepler's ineradicable belief in the existence of some such congruity was derived from the Pythagorean idea of an underlying harmony in nature; but his arduous efforts for its realization took a devious and fantastic course which seemed to give little promise of their surprising ultimate success.
MUSIC OF THE SPHERES, in Pythagorean philosophy, the harmony produced by the heavenly bodies in their orbits, inaudible to human ears.
Trans.) "there was nothing fanciful in the Pythagorean doctrine except only the belief that the differences of velocity in the movements of the stars were capable of producing a harmonious orchestration and not merely sounds of varying pitch."
For Pythagorean mathematics see further Pythagoras.