Pythagoreann.adj.

Brit.

/ˌpʌɪθaɡəˈriːən/,

/pʌɪˌθaɡəˈriːən/,

/pɪˌθaɡəˈriːən/, U.S.

/pᵻˌθæɡəˈriən/,

/paɪˌθæɡəˈriən/

Forms: 1500s Pithagorean, 1500s Pythagorien, 1500s 1900s– Pythagoran, 1500s–1600s Pithagorian, 1500s–1700s 1900s– Pythagorian, 1500s– Pythagorean, 1600s Phythagorean, 1600s Pithgorean, 1600s–1700s 1900s– Phythagorian.

Origin: A borrowing from Latin, combined with an English element. Partly also a borrowing from French. Etymons: Latin Pȳthagorēus , -an suffix; French Pythagorien.

Etymology: < classical Latin Pȳthagorēus, Pȳthagorīus of or relating to Pythagoras or his philosophy, (noun) follower of Pythagoras ( < ancient Greek Πυθαγόρειος of or relating to Pythagoras or his philosophy, (noun) follower of Pythagoras < Πυθαγόρας , the name of Pythagoras (see Pythagoras n.) + -ειος , suffix forming adjectives) + -an suffix (compare -ean suffix, -ian suffix). As adjective originally via Middle French, French Pythagorien (1559 in the passage translated in quot. 1579 at sense B. 1a); compare Middle French Pythagorien, noun (1546).According to Diogenes Laertius ( Lives of Philosophers 1. 12), ‘Pythagoras was the first person who invented the term philosophy, and called himself a philosopher’ (φιλοσοφίαν δὲ πρῶτος ὠνόμασε Πυθαγόρας καὶ ἑαυτὸν φιλόσοφον ). Pythagoras (of Samos) left no writings, but to him and his followers are ascribed traditions of thought both religious and scientific. Pythagoras is said to have introduced the doctrine of transmigration of souls into Greece, and his religious influence is reflected in the cult organization of the Pythagorean society, with periods of initiation, secret doctrines and passwords, special dietary restrictions, and burial rites. Aristotle reports that for the Pythagoreans all things are numbers or imitate numbers. One of the mathematical discoveries attributed to Pythagoras is the theorem of the right-angled triangle (see Pythagoras n.). In music Pythagoras is said to have discovered the ratios representing the length of strings corresponding to the octave and the basic harmonies (the fifth and the fourth). The same ratios are presumably reflected in the music of the spheres, which Pythagoras alone was said to hear. Pythagorean analysis of the courses of the sun, moon, and stars into circular motions was not set aside until the 17th cent. In early use (up to the 18th cent.) also stressed on the third syllable.

A. n.

1. An admirer or disciple of Pythagoras; a student or adherent of the philosophical ideas of Pythagoras or his followers. Chiefly in plural with the.

ΘΚΠ

the mind > mental capacity > philosophy > ancient Greek philosophy > pre-Socratic schools of philosophy > [noun] > Presocratic philosopher or adherent > of specific schools

Ionic1483

Pythagorean1531

Pythagorist1576

Italic1594

physiologer1598

Democritean1603

atomist1610

Pythagoric1652

physiologist1653

acousmatic1660

mathematic1660

Pythagorite1660

Anaxagorean1678

Anaximandrian1678

atomic1678

Heraclitic1678

Parmenidean1678

Pythagorician1678

hylopathian1809

atomician1850

neopythagorean1891

1531 T. Elyot Bk. named Gouernour ii. xi. sig. S5^v Two Pythagoriens, that is to say studentes of Pythagoras lerninge.

1550 W. Lynne tr. J. Carion Thre Bks. Cronicles ii. f. xxxvii The Pythagorians [L. Pythagorici] taughte their doctrines priuatly amonge themselues.

1598 J. Marston Certaine Satyres in Metamorph. Pigmalions Image 28 Giue him his fiddle once againe, Or he's more mute then a Pythagoran.

a1612 J. Harington Epigrams (1618) i. 68 An vse there was among some Pithagorians, If we giue credit to the best Historians: How they..Did keepe a wondrous strict and sparing dyet.

1678 R. Cudworth True Intellect. Syst. Universe i. iv. 225 Aristotle..was not occasioned to do that..because it was a Doctrine then Generally Received, but only because he had a mind, odiously to impute such a thing to the Pythagoreans.

1737 W. Whiston tr. Josephus Antiq. Jews xv. x, in tr. Josephus Genuine Wks. 501 These men [sc. Essens] live the same kind of life as do those whom the Greeks call Pythagoreans.

1759 A. Smith Theory Moral Sentiments vii. §ii. i. 422 In this consisted that compleat virtue, that perfect propriety of conduct, which Plato, after some of the antient Pythagoreans, denominated Justice.

1846 T. W. Jenkyn Baxter's Wks. Pref. 50 Those who understand..what Tetractysm was to the Pythagoreans will..comprehend what Triadism was to Baxter.

1876 G. Bancroft Hist. U.S. (rev. ed.) I. i. 5 Nearly three centuries before the Christian era, Aristotle, following the lessons of the Pythagoreans, had taught that the earth is a sphere.

1939 Fortune Nov. 115/1 The Pythagoreans..swore by the ‘holy tectractys’ illustrated above—which represents the number 10, and shows at a glance the 1+2+3+4=10.

1972 M. Kline Math. Thought iii. 28 There are no written works by the Pythagoreans; we know about them through the writings of others.

2003 S. Trépanier Empedocles iv. 118 Pythagoreans..were an actual community, founded on the authority of a genuine historical individual, but seemingly without any fixed text.

2. allusively. A person whose beliefs or practices (esp. as regards dietary restrictions) accord with or resemble those of Pythagoras or his followers.

ΘΚΠ

the world > food and drink > food > consumption of food or drink > eating > following specific diet > [noun] > vegetarianism or veganism > vegetarian or vegan

Pythagorean1819

Grahamite1834

vegetarian1842

pythagorizer1875

veg1884

fruitarian1893

nutarian1909

nut-fooder1917

lacto-ovo-vegetarian1940

vegan1944

veggie1955

1599 T. Nashe Lenten Stuffe 31 The Rhomish rotten Pithagoreans or Carthusian friers, that mumpe on nothing but fishe.

1683 R. Dixon Canidia 136 Beans and Bacon are no Meat, For a Pythagorean to eat.

1709–10 R. Steele Tatler No. 134. ⁋1 This ancient Pythagorean, who has as much Honesty as any Man living, but good Nature to an Excess.

1819 W. Cobbett Year's Resid. U.S.A. ii. xii. 256 Nor have even the Pythagoreans a much better battery against us. Sir Richard Phillips..does, indeed, eat neither flesh, fish, nor fowl... But..his shoes and breeches and gloves are made of the skins of animals.

1854 H. D. Thoreau Walden 175 Not that I wanted beans to eat, for I am by nature a Pythagorean.

1935 Times 4 Mar. 4/5 In food value, the result..does not equal the vegetables they [sc. trappers] could grow in the time: but they are not Pythagoreans, and look at it in quite another light.

2000 Amer. Scholar Autumn 87 Pythagoras's regimen, which, for obscure reasons, banned beans as well as meat, was so exemplary that for more than two thousand years those who abstained at least from flesh were called Pythagoreans.

B. adj.

a. Of, relating to, or characteristic of Pythagoras, his followers, or their philosophy.In early quots. often with reference to Pythagoras' belief in the transmigration of souls.

ΘΚΠ

the mind > mental capacity > philosophy > ancient Greek philosophy > pre-Socratic schools of philosophy > [adjective] > specific schools or philosophers

Pythagorical1570

Pythagorean1579

Anaxagorean1586

Pythagoric1589

Empedoclean1599

Democritean1603

Democritala1617

Democritical1650

atomical1653

Italic1662

Democritish1668

Anaximandrian1678

atomic1678

Democritic1678

Heraclitic1678

hylopathian1678

Parmenidean1678

Heracliticala1688

atomistic1695

Eleatic1695

atomistical1707

acousmatic1753

Pythagorico-Platonic1760

Zenonic1779

Heraclitean1791

neopythagorean1863

1579 T. North tr. Plutarch Liues 1036 Archytas the Pythagorian Philosopher [Fr. Archytas philosophe Pythagorien; Gk. τοὺς περὶ Αρχύταν Πυθαγορικούς].

1602 J. Marston Antonios Reuenge iii. ii. sig. F If Pythagorian Axiomes be true, Of spirits transmigration.

1649 J. Ogilby tr. Virgil Georgics (1684) iv. 116 (note) Upon this Pythagorean Opinion, ‘That Bees derive from a Celestial strain’.

1733 T. Ridgley Body of Divinity II. lxxxvii. 181/2 And then he represents them as speaking, according to the Pythagorean and Platonick way, concerning the body's being the prison of the soul, and its remaining when released from it.

1785 T. Reid Ess. Intellect. Powers iv. ii The Platonic system of ideas..was the invention of the Pythagorean school.

1839 Times 7 Dec. 7/5 The festivals of the goddess Fornax..took place at Rome on the same day as the Quirinalia, with offerings of barley and barley cakes, the former sprinkled with salt according to the Pythagorean rights of Numa.

1877 W. E. H. Lecky Hist. European Morals (ed. 3) I. 335 The Pythagorean and Neoplatonic schools revived the feeling of religious reverence, inculcated humility.

1912 G. Kapp Electr. viii. 210 The well-known Pythagorean axiom that the sum of the squares of the kathetes in a rectangular triangle is equal to the square of the hypotenuse.

1973 Sci. Amer. Apr. 103/2–3 As for intuitionists, they have in effect returned to the Pythagorean position that the natural numbers must be accepted without further analysis.

1994 J. North Fontana Hist. Astron. & Cosmol. vii. 167 Not only is the Indian doctrine reminiscent of Pythagorean and Stoic teaching, but the yugas themselves are almost all divisible by the third power of sixty, that is, 216 000.

b. That follows or accords with the lifestyle advocated by Pythagoras or his followers; spec. vegetarian.

ΘΚΠ

the world > food and drink > food > consumption of food or drink > eating > following specific diet > [adjective] > vegetarian or vegan

Pythagorical1570

Pythagorean1651

vegetable1812

vegetarian1847

vegetizing1857

vegetant1858

veg1884

lacto-ovo-vegetarian1940

veggie1942

vegan1944

1651 Bp. J. Taylor XXVIII Serm. x. 129 His little garden made for..the feasting of a few Pythagorean herbe-eaters.

1693 J. Dryden tr. Juvenal in J. Dryden et al. tr. Juvenal Satires iii. 47 There, love the Fork; thy Garden cultivate; And give thy frugal Friends a Pythagorean Treat [L. unde epulum possis centum dare Pythagoreis].

1700 T. Tryon Lett. xii. 67 If you can perswade your self to lead a Philosophical and Pythagorian Life, in Meats, Drinks, Exercises and Communications.

1739 M. Browne Poems 299 Herbs by culinary Art prepare, For thy plain Board, Pythagorean Fare.

1822 T. Taylor tr. Apuleius Metamorphosis i. 322 Desirous of imitating the Pythagorean abstinence and chastity.

1852 H. Melville Pierre xxii. 408 Nor shall all thy Pythagorean and Shellian dietings on appleparings, dried prunes, and crumbs of oat-meal cracker, ever fit thy body for heaven.

1931 Amer. Hist. Rev. 36 638 ‘He is a sick man,’ observed an acquaintance of this vegetarian, Pythagorean, ecstatic noble.

2000 Amer. Scholar 69 85 Airline food has probably done more..to persuade our neighbors to pass up meat. Is there sociological significance to the fact that the best-selling novel of the 1990s..tells the story of a livestock farmer's wife who falls in love with a Pythagorean stranger?

2. Music. Also with lower-case initial. Designating a system of pitch-relationships attributed to Pythagoras and based on simple arithmetical ratios, for example those for the octave (2:1), fifth (3:2), and others derived from them. Hence: of or relating to the diatonic scale based on these; relating to any interval derivable from the same calculations, as Pythagorean hemitone, Pythagorean third. See also Pythagorean comma n. at Compounds.

ΘΚΠ

society > leisure > the arts > music > musical sound > pitch > interval > [adjective] > others

Pythagorean1653

diazeuctic1698

redundant1753

direct1828

parallel1876

1653 H. Moseley in Ld. Brouncker tr. R. Descartes Excellent Compend. Musick To Rdr. sig. a4^v Please you, to understand Him to be such, as hath..swallowed the whole Theory of Musick; i. e. haveing profoundly speculated the Pythagorean Scheme of the various Sounds arising from various Hammers, beaten on an Anvill, respective to their different Weights.

1694 W. Holder Treat. Harmony vi. 152 The Pythagoreans, not using Tone Minor, but two Equal Tones Major, in a Fourth, were forced to take a lesser Interval for the Hemitone; which is call'd their Limma, or Pythagorean Hemitone.

1800 M. Young Anal. Princip. Nat. Philos. 291 This latter interval was anciently called the Pythagorean Hemitone, because the Pythagoreans did not use the minor tone.

1878 W. H. Stone Sci. Basis Music v. 52 The third of the Greek scale was made by four fifths taken upwards, and is still called a Pythagorean third.

1881 Musical Times Aug. 410/2 To the Greeks it [sc. the major third] was unpleasing, under most conditions, and in just or in pythagorean intonation.

1952 Galpin Soc. Jrnl. 5 37 A similar close correlation lies between the notes W and X..and the Pythagorean hemitone..which differ by only one-thirtieth of an equal-tempered semitone.

2008 Nature 8 May 161/3 A scale defined by pythagorean proportions in C will be increasingly out of tune the farther the key moves away from C.

†3. Metamorphosed, transformed. Obsolete. rare.

ΘΚΠ

the world > time > change > change to something else, transformation > [adjective] > transformed

transformed1413

transmutate?a1475

leavened1587

trans-shaped1602

Pythagoreana1667

transfigured1678

metamorphosed1730

transmuted1749

transmogrifiedc1832

transnatural1907

metamorphosized1948

born-again1977

a1667 A. Cowley Verses Several Occasions 42 in Wks. (1668) This Pythagorean Ship (for it may claim Without presumption so deserv'd a Name, By knowledge once and transformation now).

Compounds

† Pythagorean bean n. Obsolete the sacred lotus, Nelumbo nucifera; (also) the fruit of this plant (cf. Egyptian bean n. at Egyptian adj. and n. Compounds 1).

ΚΠ

1846 Penny Cycl. Suppl. II. 352/1 N[elumbia] speciosum, Pythagorean Bean, has a polypetalous corolla and anthers drawn out beyond the cells into a club-shaped appendage.

1884 Jrnl. & Proc. Royal Soc. New South Wales 17 101 The flower is supposed to be the Lotus figured on Egyptian and Indian monuments, and the fruit is said to be the ‘Pythagorean Bean’.

Pythagorean comma n. Music the difference in pitch between twelve intervals of a perfect pitch above a given note and seven octaves above the same note; an interval of this size.The ratio of the two frequencies is 531441:524288, or 3¹²:2¹⁹.

ΚΠ

1784 J. Keeble Theory of Harmonics ii. 125 In the same manner we may proceed to discover by these tables all other intervals, however remote: as for instance, the Pythagorean comma..which is a comparison of a multiple of the first root, with the fifth of the twelfth power.

1875 London, Edinb., & Dublin Philos. Mag. 4th Ser. 50 169 In one of these, which is preferred, all the fifths except one are perfect, the remaining one erring of course by a Pythagorean comma.

1963 Jrnl. Aesthetics 22 189 Pythagoreans are usually credited with dividing the octave by a fourth and a fifth, constructing a scale using the whole-tone 8:9, and discovering the ‘pythagorean comma’ or difference between 12 fifths and 7 octaves.

Pythagorean letter n. the capital form of the Greek letter upsilon (Υ), esp. used as a symbol of the divergent paths of virtue and vice.

ΚΠ

1618 G. Chapman tr. Hesiod Georgicks i.14 And this paineful passage to Vertue Virgil imitated in his translation of the Pythagorean letter, Y.

1789 M. Madan tr. Persius Satires v, in New & Literal Transl. Juvenal & Persius II. 404 Compitum is a place where two or more ways meet.—The poet here alludes to the Pythagorean letter Y.

1851 Encycl. Americana (new ed.) XIII. 296/1 Y, in its Greek form (Υ), is also called the Pythagorean letter, because the Pythagoreans were said to signify by it the proceeding of the duad out of the monad, or the sacred triad..or the dividing road of life.

1929 S. Angus Relig. Quests Graeco-Roman World xvii. 308 The symbolic Pythagorean letter Upsilon divides the scene into two sections: on the right Virtue is seated as a woman with a little child.

1989 D. A. Carozza & H. J. Shey Petrarch's Secretum 146 The Pythagorean letter was ‘Y’, which by its form became in the Middle Ages a symbol for man's life. At a certain point every man makes a decisive step in the direction of virtue or pleasure.

Pythagorean lyre n. chiefly poetic a lyre with eight strings, said to have been invented by Pythagoras.

ΚΠ

1770 Musical Entertainment 5 How sweet with thee, blest Bard! When Spring descends..To listen to thy muse's varied song; Whether she paints the happy, golden age, Or touches light the Pythagorean lyre.

1851 Encycl. Americana (new ed.) X. 443/2 Tradition makes him the inventor of a musical [instrument] (Pythagorean lyre, octochordum Pythagoræ), which, after his death, was engraved in brass, and preserved in the temple of Juno at Samos.

1959 A. J. McVan tr. A. Machado in Antonio Machado 187 In the silence the Pythagorean lyre throbs, remote, rainbow in light, the light that fills my useless stereoscope.

2000 E. Loomis tr. A. Machado in tr. R. Dario & A. Machado El Nica & Don Antonio 124 And to the illusionist who sighs under the supreme order, and to the one who dreams the Pythagorean lyre in his hand.

Pythagorean number n. (a) a number as conceived in cosmic or mystical terms by Pythagoras or his followers; (b) Mathematics each of the integers in a Pythagorean triple, corresponding to the sides of a plane right-angled triangle (cf. Pythagorean triple n.); also in extended use.

ΚΠ

1600 Abp. G. Abbot Expos. Prophet Ionah xviii. 387 Those come within this compasse, who do tye the euent of things to Pythagorean numbers, as the chaunges of states and kingdomes to the ends of seuen yeares, and of nine yeares, being multiplied vp and downe.

1757 G. Colman Connoisseur (ed. 2) IV. 100 The mystery..was as dark and unfathomable as the Pythagorean number, or the secret doctrines of Trismegist.

1858 W. Whewell Hist. Sci. Ideas i. ii. 77 Things shared the nature of the Platonic Ideas ‘by participation’, while they shared the nature of Pythagorean Numbers ‘by imitation’.

1879 Scribner's Monthly Apr. 896/1 Twelve is the Pythagorean number of man and humanity.

1912 Science 7 June 880/1 Pythagoras gave a general rule by means of which one can find any desired number of such solutions, and hence these triplets are often called Pythagorean numbers.

1929 Amer. Math. Monthly 36 286 Consecutive rectangular triangles..each having for its sides the Pythagorean numbers h, (h²−1)/2, (h²+1)/2, where h is the hypotenuse of the preceding triangle [etc.].

1984 Coll. Math. Jrnl. 15 325 Although the problem of constructing quadruples of Pythagorean numbers might seem harder and more complicated than the original task of finding Pythagorean triples, it is easier to solve the equation with four unknowns x² + y² + z² = w².

1996 S. H. Nasr Relig. & Order of Nature iii. 83 Pythagorean mathematics was a means of uniting rather than dividing, and Pythagorean numbers and geometric patterns are so many reflections of Unity.

Pythagorean proposition n. Mathematics = Pythagorean theorem n.

ΚΠ

1852 B. Peirce Elem. Treat. Plane & Spherical Trigonom. 8 We have, by the Pythagorean proposition, in the right triangle ABC, [etc.].

1895 Amer. Math. Monthly 2 341 Thirty-nine diagrams to illustrate as many different demonstrations of the Pythagorean Proposition.

1996 Math. Mag. 69 45 (title) The Pythagorean proposition: a proof by means of calculus.

Pythagorean system n. Astronomy the cosmological system associated with Pythagoras (often ascribed to the Pythagorean Philolaus of Croton), in which the earth, the other planets, and the sun orbit a central fire and there is another object (a counter-earth) in orbit between the earth and the central fire.The system has occasionally been confused with the Copernican system.

ΚΠ

1694 Philos. Trans. (Royal Soc.) 18 101 Since the Pythagorean System of the World has been revived by Copernicus, [etc.].

1747 D. Jennings Introd. Use of Globes ii. i. 45 The Pythagorean System has generally been received by the greatest Mathematicians and Philosophers, ever since the Revival of it by Copernicus.

1842 Treat. Mod. Geogr. (Brothers of Christian Schools) 280 The Pythagorean system being overthrown, the opinions of Aristotle were supported by all the philosophers of antiquity.

1976 Brit. Jrnl. Philos. Sci. 27 410 The problem here is simply one of a lack of information first concerning the details of pre-Platonic astronomy (especially the Pythagorean system later associated with the name of Philolaus).

Pythagorean theorem n. Mathematics = Pythagoras' theorem n. at Pythagoras n.

ΚΠ

1743 E. Stone New Math. Dict. (ed. 2) Pythagorean theorem, is the 47th Prop. of the first Book of Euclid.

1869 J. Davis tr. B. Auerbach Villa on Rhine v. iv. 291 He went through the fourth conjugation in a stiff, gawky manner; explained the Pythagorean theorem, and recited a lot more of the most incoherent stuff.

1993 R. J. Pond Introd. Engin. Technol. (ed. 2) vi. 135 The Pythagorean theorem can be used to prove that a triangle with sides equalling 3 x 4 x 5 will form a right angle opposite the side of length 5.

Pythagorean triple n. any set of three integers which satisfies the equation x² + y² = z², corresponding to the sides of a plane right-angled triangle (cf. Pythagoras' theorem n. at Pythagoras n.).

ΚΠ

1940 Amer. Math. Monthly 47 718 Let (a, b, c) be any P.T. (Pythagorean Triple, i.e.,a, b, c integers, b >c, and a² = b² + c²).

1998 P. M. Higgins Math. for Curious iv. 85 A (6, 8, 10) triangle is similar to the (3, 4, 5)... But there are some genuinely different Pythagorean triples, such as (5, 12, 13) and (8, 15, 17).

Pythagorean triplet n. = Pythagorean triple n.

ΚΠ

1912 Science 7 June 880/1 These triplets are often called Pythagorean numbers.]

1925 G. D. Birkhoff Origin, Nature, & Infl. Relativity 102 Imagine a clock traveling as fast as light. The Pythagorean rule shows that the corresponding Pythagorean triplet is 1, 0, 1. Hence, contraction of measuring sticks to nil and a complete stopping of clocks takes place in motion with the velocity of light.

1989 Math. Mag. 62 342 Some of these [sc. diophantine equations]..have no nontrivial solutions; whereas others, such as x² + y² = z² (Pythagorean triplets)..have an infinite number of integral solutions.

Derivatives

† Pythagoreanly adv. Obsolete rare in a Pythagorean manner.

ΘΚΠ

the mind > mental capacity > philosophy > ancient Greek philosophy > pre-Socratic schools of philosophy > [adverb] > specific schools

pythagorically1588

Pythagoreanly1596

atomically1659

1596 T. Nashe Haue with you to Saffron-Walden Ep. Ded. sig. C^v I will tutour thee so Pythagoreanly how to husband them in al companies.

This entry has been updated (OED Third Edition, December 2007; most recently modified version published online March 2022).

单词	pythagorean
释义	Pythagoreann.adj. Brit. /ˌpʌɪθaɡəˈriːən/, /pʌɪˌθaɡəˈriːən/, /pɪˌθaɡəˈriːən/, U.S. /pᵻˌθæɡəˈriən/, /paɪˌθæɡəˈriən/ Forms: 1500s Pithagorean, 1500s Pythagorien, 1500s 1900s– Pythagoran, 1500s–1600s Pithagorian, 1500s–1700s 1900s– Pythagorian, 1500s– Pythagorean, 1600s Phythagorean, 1600s Pithgorean, 1600s–1700s 1900s– Phythagorian. Origin: A borrowing from Latin, combined with an English element. Partly also a borrowing from French. Etymons: Latin Pȳthagorēus , -an suffix; French Pythagorien. Etymology: < classical Latin Pȳthagorēus, Pȳthagorīus of or relating to Pythagoras or his philosophy, (noun) follower of Pythagoras ( < ancient Greek Πυθαγόρειος of or relating to Pythagoras or his philosophy, (noun) follower of Pythagoras < Πυθαγόρας , the name of Pythagoras (see Pythagoras n.) + -ειος , suffix forming adjectives) + -an suffix (compare -ean suffix, -ian suffix). As adjective originally via Middle French, French Pythagorien (1559 in the passage translated in quot. 1579 at sense B. 1a); compare Middle French Pythagorien, noun (1546).According to Diogenes Laertius ( Lives of Philosophers 1. 12), ‘Pythagoras was the first person who invented the term philosophy, and called himself a philosopher’ (φιλοσοφίαν δὲ πρῶτος ὠνόμασε Πυθαγόρας καὶ ἑαυτὸν φιλόσοφον ). Pythagoras (of Samos) left no writings, but to him and his followers are ascribed traditions of thought both religious and scientific. Pythagoras is said to have introduced the doctrine of transmigration of souls into Greece, and his religious influence is reflected in the cult organization of the Pythagorean society, with periods of initiation, secret doctrines and passwords, special dietary restrictions, and burial rites. Aristotle reports that for the Pythagoreans all things are numbers or imitate numbers. One of the mathematical discoveries attributed to Pythagoras is the theorem of the right-angled triangle (see Pythagoras n.). In music Pythagoras is said to have discovered the ratios representing the length of strings corresponding to the octave and the basic harmonies (the fifth and the fourth). The same ratios are presumably reflected in the music of the spheres, which Pythagoras alone was said to hear. Pythagorean analysis of the courses of the sun, moon, and stars into circular motions was not set aside until the 17th cent. In early use (up to the 18th cent.) also stressed on the third syllable. A. n. 1. An admirer or disciple of Pythagoras; a student or adherent of the philosophical ideas of Pythagoras or his followers. Chiefly in plural with the. ΘΚΠ the mind > mental capacity > philosophy > ancient Greek philosophy > pre-Socratic schools of philosophy > [noun] > Presocratic philosopher or adherent > of specific schools Ionic1483 Pythagorean1531 Pythagorist1576 Italic1594 physiologer1598 Democritean1603 atomist1610 Pythagoric1652 physiologist1653 acousmatic1660 mathematic1660 Pythagorite1660 Anaxagorean1678 Anaximandrian1678 atomic1678 Heraclitic1678 Parmenidean1678 Pythagorician1678 hylopathian1809 atomician1850 neopythagorean1891 1531 T. Elyot Bk. named Gouernour ii. xi. sig. S5^v Two Pythagoriens, that is to say studentes of Pythagoras lerninge. 1550 W. Lynne tr. J. Carion Thre Bks. Cronicles ii. f. xxxvii The Pythagorians [L. Pythagorici] taughte their doctrines priuatly amonge themselues. 1598 J. Marston Certaine Satyres in Metamorph. Pigmalions Image 28 Giue him his fiddle once againe, Or he's more mute then a Pythagoran. a1612 J. Harington Epigrams (1618) i. 68 An vse there was among some Pithagorians, If we giue credit to the best Historians: How they..Did keepe a wondrous strict and sparing dyet. 1678 R. Cudworth True Intellect. Syst. Universe i. iv. 225 Aristotle..was not occasioned to do that..because it was a Doctrine then Generally Received, but only because he had a mind, odiously to impute such a thing to the Pythagoreans. 1737 W. Whiston tr. Josephus Antiq. Jews xv. x, in tr. Josephus Genuine Wks. 501 These men [sc. Essens] live the same kind of life as do those whom the Greeks call Pythagoreans. 1759 A. Smith Theory Moral Sentiments vii. §ii. i. 422 In this consisted that compleat virtue, that perfect propriety of conduct, which Plato, after some of the antient Pythagoreans, denominated Justice. 1846 T. W. Jenkyn Baxter's Wks. Pref. 50 Those who understand..what Tetractysm was to the Pythagoreans will..comprehend what Triadism was to Baxter. 1876 G. Bancroft Hist. U.S. (rev. ed.) I. i. 5 Nearly three centuries before the Christian era, Aristotle, following the lessons of the Pythagoreans, had taught that the earth is a sphere. 1939 Fortune Nov. 115/1 The Pythagoreans..swore by the ‘holy tectractys’ illustrated above—which represents the number 10, and shows at a glance the 1+2+3+4=10. 1972 M. Kline Math. Thought iii. 28 There are no written works by the Pythagoreans; we know about them through the writings of others. 2003 S. Trépanier Empedocles iv. 118 Pythagoreans..were an actual community, founded on the authority of a genuine historical individual, but seemingly without any fixed text. 2. allusively. A person whose beliefs or practices (esp. as regards dietary restrictions) accord with or resemble those of Pythagoras or his followers. ΘΚΠ the world > food and drink > food > consumption of food or drink > eating > following specific diet > [noun] > vegetarianism or veganism > vegetarian or vegan Pythagorean1819 Grahamite1834 vegetarian1842 pythagorizer1875 veg1884 fruitarian1893 nutarian1909 nut-fooder1917 lacto-ovo-vegetarian1940 vegan1944 veggie1955 1599 T. Nashe Lenten Stuffe 31 The Rhomish rotten Pithagoreans or Carthusian friers, that mumpe on nothing but fishe. 1683 R. Dixon Canidia 136 Beans and Bacon are no Meat, For a Pythagorean to eat. 1709–10 R. Steele Tatler No. 134. ⁋1 This ancient Pythagorean, who has as much Honesty as any Man living, but good Nature to an Excess. 1819 W. Cobbett Year's Resid. U.S.A. ii. xii. 256 Nor have even the Pythagoreans a much better battery against us. Sir Richard Phillips..does, indeed, eat neither flesh, fish, nor fowl... But..his shoes and breeches and gloves are made of the skins of animals. 1854 H. D. Thoreau Walden 175 Not that I wanted beans to eat, for I am by nature a Pythagorean. 1935 Times 4 Mar. 4/5 In food value, the result..does not equal the vegetables they [sc. trappers] could grow in the time: but they are not Pythagoreans, and look at it in quite another light. 2000 Amer. Scholar Autumn 87 Pythagoras's regimen, which, for obscure reasons, banned beans as well as meat, was so exemplary that for more than two thousand years those who abstained at least from flesh were called Pythagoreans. B. adj. 1. a. Of, relating to, or characteristic of Pythagoras, his followers, or their philosophy.In early quots. often with reference to Pythagoras' belief in the transmigration of souls. ΘΚΠ the mind > mental capacity > philosophy > ancient Greek philosophy > pre-Socratic schools of philosophy > [adjective] > specific schools or philosophers Pythagorical1570 Pythagorean1579 Anaxagorean1586 Pythagoric1589 Empedoclean1599 Democritean1603 Democritala1617 Democritical1650 atomical1653 Italic1662 Democritish1668 Anaximandrian1678 atomic1678 Democritic1678 Heraclitic1678 hylopathian1678 Parmenidean1678 Heracliticala1688 atomistic1695 Eleatic1695 atomistical1707 acousmatic1753 Pythagorico-Platonic1760 Zenonic1779 Heraclitean1791 neopythagorean1863 1579 T. North tr. Plutarch Liues 1036 Archytas the Pythagorian Philosopher [Fr. Archytas philosophe Pythagorien; Gk. τοὺς περὶ Αρχύταν Πυθαγορικούς]. 1602 J. Marston Antonios Reuenge iii. ii. sig. F If Pythagorian Axiomes be true, Of spirits transmigration. 1649 J. Ogilby tr. Virgil Georgics (1684) iv. 116 (note) Upon this Pythagorean Opinion, ‘That Bees derive from a Celestial strain’. 1733 T. Ridgley Body of Divinity II. lxxxvii. 181/2 And then he represents them as speaking, according to the Pythagorean and Platonick way, concerning the body's being the prison of the soul, and its remaining when released from it. 1785 T. Reid Ess. Intellect. Powers iv. ii The Platonic system of ideas..was the invention of the Pythagorean school. 1839 Times 7 Dec. 7/5 The festivals of the goddess Fornax..took place at Rome on the same day as the Quirinalia, with offerings of barley and barley cakes, the former sprinkled with salt according to the Pythagorean rights of Numa. 1877 W. E. H. Lecky Hist. European Morals (ed. 3) I. 335 The Pythagorean and Neoplatonic schools revived the feeling of religious reverence, inculcated humility. 1912 G. Kapp Electr. viii. 210 The well-known Pythagorean axiom that the sum of the squares of the kathetes in a rectangular triangle is equal to the square of the hypotenuse. 1973 Sci. Amer. Apr. 103/2–3 As for intuitionists, they have in effect returned to the Pythagorean position that the natural numbers must be accepted without further analysis. 1994 J. North Fontana Hist. Astron. & Cosmol. vii. 167 Not only is the Indian doctrine reminiscent of Pythagorean and Stoic teaching, but the yugas themselves are almost all divisible by the third power of sixty, that is, 216 000. b. That follows or accords with the lifestyle advocated by Pythagoras or his followers; spec. vegetarian. ΘΚΠ the world > food and drink > food > consumption of food or drink > eating > following specific diet > [adjective] > vegetarian or vegan Pythagorical1570 Pythagorean1651 vegetable1812 vegetarian1847 vegetizing1857 vegetant1858 veg1884 lacto-ovo-vegetarian1940 veggie1942 vegan1944 1651 Bp. J. Taylor XXVIII Serm. x. 129 His little garden made for..the feasting of a few Pythagorean herbe-eaters. 1693 J. Dryden tr. Juvenal in J. Dryden et al. tr. Juvenal Satires iii. 47 There, love the Fork; thy Garden cultivate; And give thy frugal Friends a Pythagorean Treat [L. unde epulum possis centum dare Pythagoreis]. 1700 T. Tryon Lett. xii. 67 If you can perswade your self to lead a Philosophical and Pythagorian Life, in Meats, Drinks, Exercises and Communications. 1739 M. Browne Poems 299 Herbs by culinary Art prepare, For thy plain Board, Pythagorean Fare. 1822 T. Taylor tr. Apuleius Metamorphosis i. 322 Desirous of imitating the Pythagorean abstinence and chastity. 1852 H. Melville Pierre xxii. 408 Nor shall all thy Pythagorean and Shellian dietings on appleparings, dried prunes, and crumbs of oat-meal cracker, ever fit thy body for heaven. 1931 Amer. Hist. Rev. 36 638 ‘He is a sick man,’ observed an acquaintance of this vegetarian, Pythagorean, ecstatic noble. 2000 Amer. Scholar 69 85 Airline food has probably done more..to persuade our neighbors to pass up meat. Is there sociological significance to the fact that the best-selling novel of the 1990s..tells the story of a livestock farmer's wife who falls in love with a Pythagorean stranger? 2. Music. Also with lower-case initial. Designating a system of pitch-relationships attributed to Pythagoras and based on simple arithmetical ratios, for example those for the octave (2:1), fifth (3:2), and others derived from them. Hence: of or relating to the diatonic scale based on these; relating to any interval derivable from the same calculations, as Pythagorean hemitone, Pythagorean third. See also Pythagorean comma n. at Compounds. ΘΚΠ society > leisure > the arts > music > musical sound > pitch > interval > [adjective] > others Pythagorean1653 diazeuctic1698 redundant1753 direct1828 parallel1876 1653 H. Moseley in Ld. Brouncker tr. R. Descartes Excellent Compend. Musick To Rdr. sig. a4^v Please you, to understand Him to be such, as hath..swallowed the whole Theory of Musick; i. e. haveing profoundly speculated the Pythagorean Scheme of the various Sounds arising from various Hammers, beaten on an Anvill, respective to their different Weights. 1694 W. Holder Treat. Harmony vi. 152 The Pythagoreans, not using Tone Minor, but two Equal Tones Major, in a Fourth, were forced to take a lesser Interval for the Hemitone; which is call'd their Limma, or Pythagorean Hemitone. 1800 M. Young Anal. Princip. Nat. Philos. 291 This latter interval was anciently called the Pythagorean Hemitone, because the Pythagoreans did not use the minor tone. 1878 W. H. Stone Sci. Basis Music v. 52 The third of the Greek scale was made by four fifths taken upwards, and is still called a Pythagorean third. 1881 Musical Times Aug. 410/2 To the Greeks it [sc. the major third] was unpleasing, under most conditions, and in just or in pythagorean intonation. 1952 Galpin Soc. Jrnl. 5 37 A similar close correlation lies between the notes W and X..and the Pythagorean hemitone..which differ by only one-thirtieth of an equal-tempered semitone. 2008 Nature 8 May 161/3 A scale defined by pythagorean proportions in C will be increasingly out of tune the farther the key moves away from C. †3. Metamorphosed, transformed. Obsolete. rare. ΘΚΠ the world > time > change > change to something else, transformation > [adjective] > transformed transformed1413 transmutate?a1475 leavened1587 trans-shaped1602 Pythagoreana1667 transfigured1678 metamorphosed1730 transmuted1749 transmogrifiedc1832 transnatural1907 metamorphosized1948 born-again1977 a1667 A. Cowley Verses Several Occasions 42 in Wks. (1668) This Pythagorean Ship (for it may claim Without presumption so deserv'd a Name, By knowledge once and transformation now). Compounds † Pythagorean bean n. Obsolete the sacred lotus, Nelumbo nucifera; (also) the fruit of this plant (cf. Egyptian bean n. at Egyptian adj. and n. Compounds 1). ΚΠ 1846 Penny Cycl. Suppl. II. 352/1 N[elumbia] speciosum, Pythagorean Bean, has a polypetalous corolla and anthers drawn out beyond the cells into a club-shaped appendage. 1884 Jrnl. & Proc. Royal Soc. New South Wales 17 101 The flower is supposed to be the Lotus figured on Egyptian and Indian monuments, and the fruit is said to be the ‘Pythagorean Bean’. Pythagorean comma n. Music the difference in pitch between twelve intervals of a perfect pitch above a given note and seven octaves above the same note; an interval of this size.The ratio of the two frequencies is 531441:524288, or 3¹²:2¹⁹. ΚΠ 1784 J. Keeble Theory of Harmonics ii. 125 In the same manner we may proceed to discover by these tables all other intervals, however remote: as for instance, the Pythagorean comma..which is a comparison of a multiple of the first root, with the fifth of the twelfth power. 1875 London, Edinb., & Dublin Philos. Mag. 4th Ser. 50 169 In one of these, which is preferred, all the fifths except one are perfect, the remaining one erring of course by a Pythagorean comma. 1963 Jrnl. Aesthetics 22 189 Pythagoreans are usually credited with dividing the octave by a fourth and a fifth, constructing a scale using the whole-tone 8:9, and discovering the ‘pythagorean comma’ or difference between 12 fifths and 7 octaves. Pythagorean letter n. the capital form of the Greek letter upsilon (Υ), esp. used as a symbol of the divergent paths of virtue and vice. ΚΠ 1618 G. Chapman tr. Hesiod Georgicks i.14 And this paineful passage to Vertue Virgil imitated in his translation of the Pythagorean letter, Y. 1789 M. Madan tr. Persius Satires v, in New & Literal Transl. Juvenal & Persius II. 404 Compitum is a place where two or more ways meet.—The poet here alludes to the Pythagorean letter Y. 1851 Encycl. Americana (new ed.) XIII. 296/1 Y, in its Greek form (Υ), is also called the Pythagorean letter, because the Pythagoreans were said to signify by it the proceeding of the duad out of the monad, or the sacred triad..or the dividing road of life. 1929 S. Angus Relig. Quests Graeco-Roman World xvii. 308 The symbolic Pythagorean letter Upsilon divides the scene into two sections: on the right Virtue is seated as a woman with a little child. 1989 D. A. Carozza & H. J. Shey Petrarch's Secretum 146 The Pythagorean letter was ‘Y’, which by its form became in the Middle Ages a symbol for man's life. At a certain point every man makes a decisive step in the direction of virtue or pleasure. Pythagorean lyre n. chiefly poetic a lyre with eight strings, said to have been invented by Pythagoras. ΚΠ 1770 Musical Entertainment 5 How sweet with thee, blest Bard! When Spring descends..To listen to thy muse's varied song; Whether she paints the happy, golden age, Or touches light the Pythagorean lyre. 1851 Encycl. Americana (new ed.) X. 443/2 Tradition makes him the inventor of a musical [instrument] (Pythagorean lyre, octochordum Pythagoræ), which, after his death, was engraved in brass, and preserved in the temple of Juno at Samos. 1959 A. J. McVan tr. A. Machado in Antonio Machado 187 In the silence the Pythagorean lyre throbs, remote, rainbow in light, the light that fills my useless stereoscope. 2000 E. Loomis tr. A. Machado in tr. R. Dario & A. Machado El Nica & Don Antonio 124 And to the illusionist who sighs under the supreme order, and to the one who dreams the Pythagorean lyre in his hand. Pythagorean number n. (a) a number as conceived in cosmic or mystical terms by Pythagoras or his followers; (b) Mathematics each of the integers in a Pythagorean triple, corresponding to the sides of a plane right-angled triangle (cf. Pythagorean triple n.); also in extended use. ΚΠ 1600 Abp. G. Abbot Expos. Prophet Ionah xviii. 387 Those come within this compasse, who do tye the euent of things to Pythagorean numbers, as the chaunges of states and kingdomes to the ends of seuen yeares, and of nine yeares, being multiplied vp and downe. 1757 G. Colman Connoisseur (ed. 2) IV. 100 The mystery..was as dark and unfathomable as the Pythagorean number, or the secret doctrines of Trismegist. 1858 W. Whewell Hist. Sci. Ideas i. ii. 77 Things shared the nature of the Platonic Ideas ‘by participation’, while they shared the nature of Pythagorean Numbers ‘by imitation’. 1879 Scribner's Monthly Apr. 896/1 Twelve is the Pythagorean number of man and humanity. 1912 Science 7 June 880/1 Pythagoras gave a general rule by means of which one can find any desired number of such solutions, and hence these triplets are often called Pythagorean numbers. 1929 Amer. Math. Monthly 36 286 Consecutive rectangular triangles..each having for its sides the Pythagorean numbers h, (h²−1)/2, (h²+1)/2, where h is the hypotenuse of the preceding triangle [etc.]. 1984 Coll. Math. Jrnl. 15 325 Although the problem of constructing quadruples of Pythagorean numbers might seem harder and more complicated than the original task of finding Pythagorean triples, it is easier to solve the equation with four unknowns x² + y² + z² = w². 1996 S. H. Nasr Relig. & Order of Nature iii. 83 Pythagorean mathematics was a means of uniting rather than dividing, and Pythagorean numbers and geometric patterns are so many reflections of Unity. Pythagorean proposition n. Mathematics = Pythagorean theorem n. ΚΠ 1852 B. Peirce Elem. Treat. Plane & Spherical Trigonom. 8 We have, by the Pythagorean proposition, in the right triangle ABC, [etc.]. 1895 Amer. Math. Monthly 2 341 Thirty-nine diagrams to illustrate as many different demonstrations of the Pythagorean Proposition. 1996 Math. Mag. 69 45 (title) The Pythagorean proposition: a proof by means of calculus. Pythagorean system n. Astronomy the cosmological system associated with Pythagoras (often ascribed to the Pythagorean Philolaus of Croton), in which the earth, the other planets, and the sun orbit a central fire and there is another object (a counter-earth) in orbit between the earth and the central fire.The system has occasionally been confused with the Copernican system. ΚΠ 1694 Philos. Trans. (Royal Soc.) 18 101 Since the Pythagorean System of the World has been revived by Copernicus, [etc.]. 1747 D. Jennings Introd. Use of Globes ii. i. 45 The Pythagorean System has generally been received by the greatest Mathematicians and Philosophers, ever since the Revival of it by Copernicus. 1842 Treat. Mod. Geogr. (Brothers of Christian Schools) 280 The Pythagorean system being overthrown, the opinions of Aristotle were supported by all the philosophers of antiquity. 1976 Brit. Jrnl. Philos. Sci. 27 410 The problem here is simply one of a lack of information first concerning the details of pre-Platonic astronomy (especially the Pythagorean system later associated with the name of Philolaus). Pythagorean theorem n. Mathematics = Pythagoras' theorem n. at Pythagoras n. ΚΠ 1743 E. Stone New Math. Dict. (ed. 2) Pythagorean theorem, is the 47th Prop. of the first Book of Euclid. 1869 J. Davis tr. B. Auerbach Villa on Rhine v. iv. 291 He went through the fourth conjugation in a stiff, gawky manner; explained the Pythagorean theorem, and recited a lot more of the most incoherent stuff. 1993 R. J. Pond Introd. Engin. Technol. (ed. 2) vi. 135 The Pythagorean theorem can be used to prove that a triangle with sides equalling 3 x 4 x 5 will form a right angle opposite the side of length 5. Pythagorean triple n. any set of three integers which satisfies the equation x² + y² = z², corresponding to the sides of a plane right-angled triangle (cf. Pythagoras' theorem n. at Pythagoras n.). ΚΠ 1940 Amer. Math. Monthly 47 718 Let (a, b, c) be any P.T. (Pythagorean Triple, i.e.,a, b, c integers, b >c, and a² = b² + c²). 1998 P. M. Higgins Math. for Curious iv. 85 A (6, 8, 10) triangle is similar to the (3, 4, 5)... But there are some genuinely different Pythagorean triples, such as (5, 12, 13) and (8, 15, 17). Pythagorean triplet n. = Pythagorean triple n. ΚΠ 1912 Science 7 June 880/1 These triplets are often called Pythagorean numbers.] 1925 G. D. Birkhoff Origin, Nature, & Infl. Relativity 102 Imagine a clock traveling as fast as light. The Pythagorean rule shows that the corresponding Pythagorean triplet is 1, 0, 1. Hence, contraction of measuring sticks to nil and a complete stopping of clocks takes place in motion with the velocity of light. 1989 Math. Mag. 62 342 Some of these [sc. diophantine equations]..have no nontrivial solutions; whereas others, such as x² + y² = z² (Pythagorean triplets)..have an infinite number of integral solutions. Derivatives † Pythagoreanly adv. Obsolete rare in a Pythagorean manner. ΘΚΠ the mind > mental capacity > philosophy > ancient Greek philosophy > pre-Socratic schools of philosophy > [adverb] > specific schools pythagorically1588 Pythagoreanly1596 atomically1659 1596 T. Nashe Haue with you to Saffron-Walden Ep. Ded. sig. C^v I will tutour thee so Pythagoreanly how to husband them in al companies. This entry has been updated (OED Third Edition, December 2007; most recently modified version published online March 2022). < n.adj.1531
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