PYRUVIC See also:

• ACID (from the Lat. root ac-, sharp; acere, to be sour)

ACID, or PYRORACEMIC ACID  , See also:

• CH3CO(4)

CH3CO•See also:

• CO2H

CO2H, an organic See also:

• ACID (from the Lat. root ac-, sharp; acere, to be sour)

acid first obtained by J . See also:

• BERZELIUS, JONS JAKOB (1779-1848)

Berzelius by the dry See also:

• DISTILLATION (from the Lat. distillare, more correctly destillare, to drop or trickle down)

distillation of tartaric or racemic acids (Pogg . See also:

• ANN

Ann., 1835, 36, p . I) . It may be prepared by boiling a-dichlorpropionic acid with See also:

• SILVER

silver See also:

• OXIDE

oxide; by the See also:

• HYDROLYSIS (Gr. 6Swp, water, Anew, to loosen)

hydrolysis of acetyl See also:

• CYANIDE

cyanide with hydrochloric acid (J . Claisen and J . See also:

• SHADWELL, THOMAS (c. 1642-1692)

Shadwell, Ber., 1878 . Ir, pp . 62o, 1563); and by warming oxalacetic ester with a so% See also:

• SOLUTION (from Lat. solvere, to loosen, dissolve)

solution of sulphuric acid . It is usually made by distilling tartaric acid with See also:

• POTASSIUM [symbol K (from kalium), atomic weight 39.114 0=16)]

potassium bisulphate at about 200—250° C., the crude product being after-wards fractionated . It is a liquid which boils at about 165° C . (with partial decomposition) ; it may be solidified, and when pure melts at 13.6° C .

(L . See also:

• SIMON, ABRAHAM (1622-1692)
• SIMON, JULES FRANCOIS (1814–1896)
• SIMON, RICHARD (1638–1712)
• SIMON, SIR JOHN (1816–1904)
• SIMON, THOMAS (c. 1623-1665)

Simon See also:

• BULL
• BULL, GEORGE (1634–1710)
• BULL, JOHN (c. 1562–1628)
• BULL, OLE BORNEMANN (18ro-188o)

Bull . See also:

• SOC

Soc . Chim., 1895 [31, 13, p . 335) . It is readily soluble in See also:

• WATER

water, See also:

• ALCOHOL

alcohol and See also:

• ETHER, (C2H5)2O

ether . It reduces ammoniacal silver solutions . When heated with hydrochloric acid to See also:

• LOO (formerly called " Lanterloo," Fr. lanturlu, the refrain of a popular 17th-century song)

loo° C. it yields See also:

• CARBON (symbol C, atomic weight 12)

carbon dioxide and pyrotartaric acid, C5H804, and when warmed with dilute sulphuric acid to 15o° C. it gives carbon dioxide and acetaldehyde . See also:

• SODIUM [symbol Na, from Lat. natrium; atomic weight 23.00 (0=16)]

Sodium See also:

• AMALGAM

amalgam or See also:

• ZINC

zinc and hydrochloric acid reduce it to lactic acid, whilst hydriodic acid gives propionic acid . It readily condenses with aromatic See also:

• HYDROCARBONS

hydrocarbons in the presence of sulphuric acid . It is somewhat readily oxidized; nitric acid gives carbonic and oxalic acids, and chromic acid, carbonic and acetic acids . It forms a well-crystallized See also:

• HYDRAZONE

hydrazone with phenylhydrazine; and a-nitroso but this entanglement with politics led in the end to the dismemberment and suppression of the society .

The authorities differ hopelessly in See also:

• CHRONOLOGY (Gr. xpovo?oyfa, computation of time, xp6vos)

chronology, but according to the See also:

• BALANCE (derived through the Fr. from the Late Lat. bilantia, an apparatus for weighing, from bi, two, and lanx, a dish or scale)

balance of See also:

• EVIDENCE (Lat. evidentia, evideri, to appear clearly)

evidence the first reaction against the Pythagoreans took See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place in the lifetime of See also:

• PYTHAGORAS
• PYTHAGORAS (6th century B.C.)

Pythagoras after the victory gained by See also:

• CROTONA, CROTO

Crotona over See also:

• SYBARIS

Sybaris in 5io . Dissensions seem to have arisen about the See also:

• ALLOTMENT (from O. Fr. a and toter, to divide by lot)

allotment of the conquered territory, and an adverse party was formed in Crotona under the leadership of Cylon . This was probably the cause of Pythagoras's withdrawal to See also:

• METAPONTUM (Gr. Meraaovrtov, mod. Metaponto)

Metapontum, which an almost unanimous tradition assigns as the place of his See also:

• DEATH

death in the end of the 6th or the beginning of the 5th See also:

• CENTURY (from Lat. centuria, a division of a hundred men)

century . The See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order appears to have continued powerful in Magna Graecia till the See also:

• MIDDLE

middle of the 5th century, when it was violently trampled out . The See also:

• MEETING (from " to meet," to come together, assemble, 0. Eng. metals ; cf. Du. moeten, Swed. mota, Goth. gamotjan, &c., derivatives of the Teut. word for a meeting, seen in O. Eng. Wit, moot, an assembly of the people; cf. witanagemot)

meeting-houses of the Pythagoreans were everywhere sacked and burned; mention is made in particular of "the See also:

• HOUSE
• HOUSE (O. Eng. hiss, a word common to Teutonic languages, cf. Dut. huis, Ger. Haus; in Gothic it is only found in gudhiss, a temple; it may be ultimately connected with the root of " hide," conceal)

house of See also:

• MILO
• MILO, TITUS ANNIUS

Milo" in Crotona, where fifty or sixty leading Pythagoreans were surprised and slain . The persecution to which the brotherhood was subjected throughout Magna Graecia was the immediate cause of the spread of the See also:

• PYTHAGOREAN

Pythagorean See also:

• PHILOSOPHY (Gr. gthos, fond of, and vo4 (a, wisdom)

philosophy in See also:

• GREECE

Greece proper . See also:

• PHILOLAUS (b. c. 48o)

Philolaus, who resided at See also:

• THEBES (anciently &Oat, Thebae, or in poetry sometimes Oif3a, in modern Greek Phiva, or, according to the corrected pronunciation, Thivae)
• THEBES (e 3a1)
• THEBES, ROMANCE OF

Thebes in the end of the 5th century (cf . See also:

• PLATO

Plato, See also:

• PHAEDO

Phaedo, 6i D), was the author of the first written exposition of the See also:

• SYSTEM

system . Lysis, the instructor of See also:

• EPAMINONDAS (c. 418-362)

Epaminondas, was another of these refugees . This Theban Pythagoreanism had an important See also:

• INFLUENCE (Late Lat. influentia, from influere, to flow in)

influence upon Plato's thought, and Philolaus had also disciples in the stricter sense . But as a philosophic school Pythagoreanism became See also:

• EXTINCT

extinct in Greece about the middle of the 4th century . In See also:

• ITALY
• ITALY (Italia)

Italy-where, after a temporary suppression, it attained a new importance in the See also:

• PERSON, OFFENCES AGAINST THE

person of See also:

• ARCHYTAS (c. 428—347 B.C.)

Archytas of See also:

• TARENTUM
• TARENTUM (Gr. rapas)

Tarentum—the school finally disappeared about the same See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time .

See also:

• ARISTOTLE
• ARISTOTLE (384-322 B.C.)

Aristotle in his accounts of Pythagorean doctrines never refers to Pythagoras but always with a studied vagueness to " the Pythagoreans" (oi rcaXouµovoc HvOayopewi) . Nevertheless, certain doctrines may be traced to the founder's teaching . Foremost among these is the -theory of the See also:

• IMMORTALITY (Lat. in-, not, mortalis, mortal, from mors, death)

immortality and transmigration of the soul (see See also:

• METEMPSYCHOSIS (Gr. µF El.4/1Xco rts)

METEMPSYCHOSIS) . Pythagoras's teaching on this point is connected by one of the most trustworthy authorities with the See also:

• DOCTRINE

doctrine of the kinship of all living beings; and in the See also:

• LIGHT

light of anthropological See also:

• RESEARCH (O. Fr. recerche, from recercher, re- and cercer, mod. chercher, to search; Late Lat. circare, to go round in a circle, to explore)

research it is easy to recognize the See also:

• CLOSE
• CLOSE (from Lat. clausum, shut)
• CLOSE, MAXWELL HENRY (1822-1903)

close relationship of the two beliefs . The Pythagorean See also:

• RULE

rule of See also:

• ABSTINENCE (from Lat. abstinere, to abstain)

abstinence from flesh is thus, in its origin, a See also:

• TABOO (also written tapu and tabu)

taboo resting upon the See also:

• BLOOD

blood-brotherhood of men and beasts; and the same See also:

• LINE

line of thought shows a number of the Pythagorean rules of See also:

• LIFE

life which we find embedded in the different traditions to be genuine taboos belonging to a similar level of See also:

• PRIMITIVE

primitive thought . The moral and religious application which Pythagoras gave to the doctrine of transmigration continued to be the teaching of the school . The view of the See also:

• BODY

body (u& a) as the See also:

• TOMB (Gr. Tuµ/3a, Tuµ(3os, probably allied to Lat. tumulus, literally a swelling, tumere, to swell)

tomb (o ia) of the soul, and the See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of philosophy in the Phaedo as a meditation of death, are expressly connected by Plato with the teaching of Philolaus; and the See also:

• STRAIN (through O. Fr. straindre, estraindre, mod. i treindre, from Lat. stringere, to draw tight, related to stress, stretch, string, &c.)

strain of See also:

• ASCETICISM

asceticism and other worldliness which meets us here and elsewhere in Plato is usually traced to Pythagorean influence . Plato's mythical descriptions of a future life of retribution and purificatory wandering can also be shown to reproduce Pythagorean teaching, though the sub-stance of them may have been See also:

• DRAWN

drawn from a See also:

• COMMON

common source in the Mysteries . The scientific doctrines of the Pythagorean school have no apparent connexion with the religious See also:

• MYSTICISM (from Or. µuety, to shut the eyes; µuorrts, one initiated into the mysteries)

mysticism of the society or their rules of living . They have their origin in the same disinterested See also:

• DESIRE

desire of knowledge which gave rise to the other philosophical See also:

• SCHOOLS

schools of Greece, and the See also:

• IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

idea of " philosophy " or the "theoretic life" as a method of emancipation from the evils of See also:

• MAN
• MAN, ISLE OF (anc. Mona)

man's See also:

• PRESENT

present See also:

• STATE
• STATE, GREAT OFFICERS OF

state of existence, though a genuine Pythagorean conception, is clearly an afterthought . The discourses and speculations of the Pythagoreans all connect themselves with the idea of number, and the school holds an important place in the See also:

• HISTORY

history of mathematical and astronomical See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

science . An unimpeached tradition carries back the Pythagorean theory of See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

numbers to the teaching of the founder himself .

Working on hints contained in the See also:

• OLDEST

oldest traditions, See also:

• RECENT

recent investigators have shown that the discoveries attributed to Pythagoras connect themselves with a primitive numerical symbolism, according to which numbers were represented by dots arranged in symmetrical patterns, such as are still to be seen in the marking of See also:

• DICE (plural of die, O. Fr. de, derived from Lat. dare, to give)

dice or See also:

• DOMINOES

dominoes . Each See also:

• PATTERN

pattern of See also:

• UNITS, DIMENSIONS OF
• UNITS, PHYSICAL

units becomes on this See also:

• PLAN
• PLAN (from Lat. planes, flat)

plan a fresh unit . The " See also:

• HOLY

holy tetractys," by which the later Pythagoreans used to swear, was a figure of this See also:

• KIND (O. E. ge-cynde, from the same root as is seen in " kin," supra)

kind representing the number to as the triangle of 4, and showing at a glance that I + 2 + 3 + 4 = 10 . The sums of the See also:

• SERIES (a Latin word from serere, to join)

series of any successive numbers may be graphically represented in a similar way, and are hence spoken of as " triangular numbers," while the sums of the series of successive See also:

• ODD (in middle English odde, from old Norwegian oddi, an angle of a triangle; the old Norwegian oddamann is used of the third man who gives a casting vote in a dispute)

odd numbers are called " square numbers," and those of successive even numbers "oblong numbers"; thus 3 and 5 added to the unit give a figure of this description -.1 . while 4 and 6, added to 2, are thus • represented .1 - Such a method of representing number in areas leads naturally to problems of a geometrical nature, and as the See also:

• PRACTICAL

practical use of the right-angled triangle was already See also:

• FAMILIAR (through the Fr. familier, from Lat. familiaris, of or belonging to the familia, family)

familiar in the arts and crafts, there is no See also:

• REASON (Lat. ratio, through French raison)

reason to dispute the well-established tradition which assigns to Pythagoras the See also:

• DISCOVERY

discovery of the See also:

• PRO

pro-position that in such a triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides . And it is probably also correct to attribute to him the discovery of the See also:

• HARMONIC

harmonic intervals which underlie the See also:

• PRODUCTION (Lat. productionem, from producere, to pro-duce)

production of musical sounds . Impressed by this reduction of musical sounds to numbers and by the presence of numerical relations in every See also:

• DEPARTMENT (Fr. departement, from departir, to separate into parts)

department of phenomena, Pythagoras and his See also:

• EARLY
• EARLY, JUBAL ANDERSON (1816-1894)

early followers enunciated the doctrine that " all things are numbers." Numbers seemed to them, as Aristotle put it, to be the first things in the whole of nature, and they supposed the elements of numbers to be the elements of all things, and the whole See also:

• HEAVEN (0. Eng. hefen, heofon, heofone; this word appears in O.S. hevan; the High. Ger. word appears in Ger. Himmel, Dutch hemel; there does not seem to be any connexion between the two words, and the ultimate derivation of the word is unknown; the sugges

heaven to be a musical See also:

• SCALE
• SCALE (1) A

scale and a number (See also:

• META

Meta . A . 986a) . Numbers, in other words, were conceived at that early See also:

• STAGE (Fr. 6/age; from Lat. stare, to stand)

stage of thought not as relations or qualities predicable of things, but as themselves constituting the substance or essence of the phenomena—the rational reality to which the appearances of sense are reducible . But the development of these ideas into a comprehensive meta-See also:

• PHYSICAL

physical system was no doubt the See also:

• WORK

work of Philolaus in the latter See also:

• PART

part of the 5th century . His formulation of the theory implies a knowledge of the teaching of Parmenides and See also:

• EMPEDOCLES (c. 490–430 B.C.)

Empedocles, and had itself in turn a See also:

• GREAT

great influence upon Plato . The " elements of numbers," of which Aristotle speaks in the passage quoted above, were, according to the Pythagoreans, the Odd and the Even, which they identified with the Limit and the Unlimited; and Aristotle distinctly says that they did not treat these as " priorities of certain other substances" such as See also:

• FIRE (in O. Eng. f j'r; the word is common to West German languages, cf. Dutch vuur, Ger. Feuer; the pre-Teutonic form is seen in Sanskrit pu, pavaka, and Gr. irup; the ultimate origin is usually taken to be a root meaning to purify, cf. Lat. purus)

fire, water or anything else of that sort, but that the unlimited itself and the one were the reality of the things of which they were predicated, and that is why they said that number was " the reality of everything " (Meta .

A . 587) . Numbers, therefore, are spatially conceived, " one " being identified with the point in the sense of a unit having position and magnitude . From combinations of such units the higher numbers and geometrical figures arise—" two " being identified with the line, " three " with the See also:

• SURFACE

surface, and " four " with the solid—and the Pythagoreans proceeded to explain the elements of Empedocles as built up out of geometrical figures in the manner followed by Plato in the See also:

• TIMAEUS (c. 345—c. 250 B.e.)

Timaeus . The See also:

• IDENTIFICATION (Lat. idem, the same)

identification of the numerical opposites, the Odd and the Even, with the Limit and the Unlimited—otherwise difficult to explain—may perhaps be understood, as See also:

• BURNET
• BURNET, GILBERT (1643-1715)
• BURNET, THOMAS (1635-1715)

Burnet suggests, by reference to the arrangement of the units or "terms" (8poi) in patterns . " When the odd is divided into two equal parts," he quotes from See also:

• STOBAEUS, JOANNES

Stobaeus, " a unit is See also:

• LEFT

left over in the middle; but when the even is so divided, an empty See also:

• FIELD (a word common to many West German languages, cf. Ger. Feld, Dutch veld, possibly cognate with O.E. f olde, the earth, and ultimately with root of the Gr. irAaror, broad)
• FIELD, CYRUS WEST (1819-1892)
• FIELD, DAVID DUDLEY (18o5-1894)
• FIELD, EUGENE (1850-1895)
• FIELD, FREDERICK (18o1—1885)
• FIELD, HENRY MARTYN (1822-1907)
• FIELD, JOHN (1782—1837)
• FIELD, MARSHALL (183 1906)
• FIELD, NATHAN (1587—1633)
• FIELD, STEPHEN JOHNSON (1816-1899)
• FIELD, WILLIAM VENTRIS FIELD, BARON (1813-1907)

field is left over, without a See also:

• MASTER (Lat. magister, related to tnagis, more, as the corresponding minister is to minus, less; the English form is due partly to the O. Eng. maegister, and partly to O. Fr. maistre, mod. maitre; cf. Du. meester, Ger. Meister, Ital. maestro)

master and without a number, showing that it is defective and incomplete." The idea of opposites, derived, perhaps, originally from Heracleitus, was See also:

• DEVELOPED

developed by the Pythagoreans in a See also:

• LIST (O.E. lisle, a Teutonic word, cf. Dut. lust, Ger. Leiste, adapted in Ital. lista and Fr. lisle)
• LIST, FRIEDRICH (1789-1846)

list of ten fundamental oppositions, bearing a certain resemblance to the tables of categories framed by later philosophers, but in its arbitrary mingling of mathematical, physical and ethical contrasts characteristic of the uncritical beginnings of speculative thought: (I) limited and unlimited, (2) odd and even, (3)one and many,(4)right and left, (5) male and See also:

• FEMALE

female, (6) See also:

• REST (O. Eng. rest, reste, bed, cognate with other Teutonic forms, e.g. Ger. Rast, Riiste, rest, and probably Gothic Rasta, league, i.e. resting or stopping place)

rest and See also:

• MOTION (Lat. motio, from movere, to move)
• MOTION, LAWS OF

motion, (7) straight and curved, (8) light and darkness, (9) See also:

• GOOD, JOHN MASON (1764-1827)

good and evil, (to) square and oblong . To the Pythagoreans, as to Heracleitus, the universe was in a sense the realized See also:

• UNION
• UNION (known locally as Union Hill and officially as Town of Union)

union of these opposites, but interpretations of Pythagoreanism which represent the whole system as founded on the opposition of unity and duality, and proceed to identify this with the opposition of See also:

• FORM (Lat. forma)

form and See also:

• MATTER

matter, of divine activity and passive material, betray on the surface their See also:

• POST

post-Platonic origin . Still more is this the See also:

• CASE
• CASE, JOHN (d. 1600)

case when in Neoplatonic See also:

• FASHION (adapted from Fr. facon, agon, Lat. factio, making, facere, to do or make)

fashion they go on to derive this See also:

• ORIGINAL

original opposition from the supreme unity or See also:

• GOD

God . The further speculations of the Pythagoreans on the subject of number rest mainly on analogies, which often become capricious and tend to lose themselves at last in a barren symbolism . " Seven" is called aap8Evos and 'AOitv,t, because within the See also:

• DECADE (from Gr. Oka, ten)

decade it has neither factors nor product . " Five," on the other See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

hand, signifies See also:

• MARRIAGE

marriage, because it is the union of the first masculine with the first feminine number (3+2, unity being considered as a number apart) . The thought already becomes more fanciful when " one " is identified with reason, because it is unchangeable; " two " with See also:

• OPINION (Lat. opinio, from opinari, to think)

opinion, because it is unlimited and indeterminate; " four " with See also:

• JUSTICE (Lat. justitia)

justice, because it is the first square number, the product of equals .

The See also:

• ASTRONOMY (from Gr. &arpov, a star, and v ,usiv, to classify or arrange)

astronomy of the Pythagoreans was their most notable contribution to scientific thought, and its importance lies in the fact that they were the first to conceive the See also:

• EARTH
• EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. 'pq'e, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in
• EARTH, FIGURE OF
• EARTH, FIGURE OF THE

earth as a globe, self-supported in empty space, revolving with the other See also:

• PLANETS, MINOR

planets See also:

• ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rond)

round a central luminary . They thus anticipated the See also:

• HELIOCENTRIC

heliocentric theory, and See also:

• COPERNICUS (or KOPPERNIGK), NICOLAUS (1473-1543)

Copernicus has left it on See also:

• RECORD (Lat. recordari, to recall to mind, from cor, heart or mind)

record that the Pythagorean doctrine of the planetary See also:

• MOVEMENT

movement of the earth gave him the first hint of its true See also:

• HYPOTHESIS (from Gr. inrorcOivat, to put under; cf. Lat. suppositio, from sub-ponere)

hypothesis . The Pythagoreans did not, however, put the See also:

• SUN
• SUN (0. Eng. sonne, Ger. sonne. Fr. soleil, Lat. sol, Gr. ijXior, from which comes helio- in various English compounds)

sun in the centre of the system . That place was filled by the central fire to which they gave the names of See also:

• HESTIA

Hestia, the See also:

• HEARTH (a word which appears in various forms in several Teutonic languages, cf. Dutch haard, German Herd, in the sense of " floor ")

hearth of the universe, the See also:

• WATCH (in O. Eng. wcecce, a keeping guard or watching, from wacian, to guard, watch, wacan, to wake)

watch-See also:

• TOWER (Lat. turris; Fr. tour, clocker; Ital. torre; Ger. Thurm)

tower of See also:

• ZEUS

Zeus, and other mythological expressions . It had then been recently discovered that the See also:

• MOON (a common Teutonic word, cf. Ger. Mond, Du. maan, Dan. maane, &c., and cognate with such Indo-Germanic forms as Gr. µlip, Sans. ma's, Irish mi, &c.; Lat. uses luna, i.e. lucna, the shining one, lucere, to shine, for the moon, but preserves the word i
• MOON, SIR RICHARD, 1ST BARONET (1814-1899)

moon shone by reflected light, and the Pythagoreans (adapting a theory of Empedocles), explained the light of the sun also as due to reflection from the central fire . Round this fire revolve ten bodies, first the Antichthon or See also:

• COUNTER

counter-earth, then the earth, followed in order by the moon, the sun, the five then known planets and the heaven of the fixed stars . The central fire and the counter-earth are invisible to us because the See also:

• SIDE
• SIDE (mod. Eski Adalia)

side of the earth on which we live is always turned away from them, and our light and See also:

• HEAT (0. E. haktu, which like " hot," Old Eng. hat, is from the Teutonic type haita, hit, to be hot; cf. Ger. hitze, heiss; Dutch, hitte, heet, &c.)

heat come to us, as already stated, by reflection from the sun . When the earth is on the same side of the central fire as the sun, the side of the earth on which we live is turned towards the sun and we have See also:

• DAY (O. Eng. dreg, Ger. Tag; according to the New English Dictionary, " in no way related to the Lat. dies")
• DAY, JOHN (1574-1640?)
• DAY, THOMAS (1748-1789)

day; when the earth and the sun are on opposite sides of the central fire we are turned away from the sun and it is See also:

• NIGHT

night . The distance of the revolving orbs from the central fire was determined according to See also:

• SIMPLE

simple numerical relations, and the Pythagoreans combined their astronomical and their musical discoveries in the famous doctrine of " the See also:

• HARMONY (Gr. dpµovia, a concord of musical sounds, dpA'ew to join; &plan midi (sc. TeXvil)

harmony of the See also:

• SPHERES, MUSIC OF THE

spheres." The velocities of the bodies depend upon their distances from the centre, the slower and nearer bodies giving out a deep See also:

• NOTE
• NOTE (Lat. nota, mark, sign, from noscere, to know)

note and the swifter a high note, the See also:

• CONCERT (through the French from Lat. con-, with, and certare, to strive)

concert of the whole yielding the See also:

• COSMIC (from Gr. Kovµos, order or universe)

cosmic See also:

• OCTAVE (from Lat. octavus, eighth, octo, eight)

octave . The reason why we do not hear this See also:

• MUSIC

music is that we are like men in a See also:

• SMITH
• SMITH, ADAM (1723–1790)
• SMITH, ALEXANDER (183o-1867)
• SMITH, ANDREW JACKSON (1815-1897)
• SMITH, CHARLES EMORY (1842–1908)
• SMITH, CHARLES FERGUSON (1807–1862)
• SMITH, CHARLOTTE (1749-1806)
• SMITH, COLVIN (1795—1875)
• SMITH, EDMUND KIRBY (1824-1893)
• SMITH, G
• SMITH, GEORGE (1789-1846)
• SMITH, GEORGE (184o-1876)
• SMITH, GEORGE ADAM (1856- )
• SMITH, GERRIT (1797–1874)
• SMITH, GOLDWIN (1823-191o)
• SMITH, HENRY BOYNTON (1815-1877)
• SMITH, HENRY JOHN STEPHEN (1826-1883)
• SMITH, HENRY PRESERVED (1847– )
• SMITH, JAMES (1775–1839)
• SMITH, JOHN (1579-1631)
• SMITH, JOHN RAPHAEL (1752–1812)
• SMITH, JOSEPH, JR
• SMITH, MORGAN LEWIS (1822–1874)
• SMITH, RICHARD BAIRD (1818-1861)
• SMITH, ROBERT (1689-1768)
• SMITH, SIR HENRY GEORGE WAKELYN
• SMITH, SIR THOMAS (1513-1577)
• SMITH, SIR WILLIAM (1813-1893)
• SMITH, SIR WILLIAM SIDNEY (1764-1840)
• SMITH, SYDNEY (1771-1845)
• SMITH, THOMAS SOUTHWOOD (1788-1861)
• SMITH, WILLIAM (1769-1839)
• SMITH, WILLIAM (c. 1730-1819)
• SMITH, WILLIAM (fl. 1596)
• SMITH, WILLIAM FARRAR (1824—1903)
• SMITH, WILLIAM HENRY (1808—1872)
• SMITH, WILLIAM HENRY (1825—1891)
• SMITH, WILLIAM ROBERTSON (1846-'894)

smith's forge, who cease to be aware of a See also:

• SOUND
• SOUND, THE (Danish Oresund)

sound which they constantly hear and are never in a position to contrast with silence . AuTHoRITrns.—See also:

• ZELLER, EDUARD (1814-1908)

Zeller's account of Pythagoreanism in his Philosophie der Griechen gives a full account of the See also:

• SOURCES

sources, with See also:

• CRITICAL (in alphabetical order of authors)

critical references in the notes to the numerous monographs on the subject, but the labour and ingenuity of more recent scholars has succeeded in clearing up a number of points since he wrote . Diels, Doxographi graeci (1879), and See also:

• DIE
• DIE (Fr. de, from Lat. datum, given)

Die Fragmente der Vorsokratiker, vol. i .

(2nd ed., 1906) . See also:

• GOMPERZ, THEODOR (1832– )

Gomperz, See also:

• GREEK
• GREEK, ETRUSCAN AND

Greek Thinkers, vol. i., and especially Burnet's Early Greek Philosophy (2nd ed., 1908), give the results of the latest investigations . Tannery's Science hellene; Milhaud's La . Science grecque and Philosophes geometees; Cantor's History of See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

Mathematics; and See also:

• GOW, NIEL (1727-1807)

Gow's See also:

• SHORT, FRANCIS JOB (1857– )

Short History of Greek Mathematics, refer to the mathematical and physical doctrines of the school . (A . S .