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ably as a commoner, and a young Paston, of the family of the Paston letters, as an Oppidan (about 1479).

The earliest indication of the number of the Oppidans, who rather than the scholars have made the school famous, is in the will of Provost Lupton, provost from 1504 to 1540. Most of the college buildings and the whole of the great quadrangle except the chapel were built by him or in his time. First came in 15031504"Long Chamber," in which all the seventy scholars slept in one long room, now cut up into separate rooms, and which

"Contrived a double debt to pay,

Bedrooms by night and living-rooms by day." Next, about 1512, a new, now Old or Lower School, in 1515 the chantry on the north side of the church, known as Lupton's chantry, in which he and many later provosts lie buried, and in 1517 the Provost's Lodgings and the great red-brick central tower called Lupton's Tower. By his will, Feb. 23, 1540, Lupton gave a hundreth children of the town 8d. a piece." There is no other indication of numbers till the first extant school list, that for 1678, when there were 207 boys, including the choristers. Only one was a nobleman, the Scotch Earl of Stirling, and there were three baronets. Sir Robert Walpole, the first Etonian Prime Minister, was a colleger, and was on the roll of King's College in 1695. In the next school list, that for 1718, the numbers had risen to 399. The first William Pitt, afterwards Earl of Chatham, was there in 1717. The numbers sank again to 244 in 1745, went up to 498 in 1766, of whom 50 were sons of peers, down to 230 in 1770 after a rebellion in which 156 boys left the school, including a future Prime Minister, William Grenville, who was sent back by his father to be flogged and expelled. In 1836 the numbers stood at 444, while ten years later they were 777, in 1891, 1007, and in 1908, 1045.

Of the curriculum of the school no very definite information is forthcoming before the sixteenth century. But we know that it consisted in the study of the Latin classics and the writing of Latin verses from the record of a payment of 10d. in 1474 "for the binding of a school-book, viz. Ovid," and from a letter of William Paston in 1479 in which he gives a specimen of his versifying. In 1486 a school Vergil was recovered which had been furtively taken away, apparently by a dismissed headmaster. In 1528 the "Form order and usage taught in the Grammar School at Eton" was directed to be followed in the free grammar school at Cuckfield, Sussex, enlarged in that year and the "Form" is annexed to the deed of endowment. It gives the curriculum in six classes. The first class learnt Stanbridge's Latin Grammar Rules in English, and did "small and easy Latins." The second did Cato's Moralia, the third and fourth Terence and Erasmus' Colloquies, the fifth and sixth

Vergil, Sallust, Horace, and Ovid. They all wrote Latin prose and verse. No Greek is mentioned. But a little earlier the Vulgaria of William Horman (q.v.), headmaster of Eton 1485-1495 and, after an interval at Winchester as headmaster, 1495-1501, fellow and viceprovost of Eton, published in 1519, give evidence of Greek being taught there; and Sir Thomas Pope, founder of Trinity College, Oxford, writing in 1556, says Greek was taught at Eton when he was a boy there. No Greek occurs in the time-table sent by Dr. Cox, headmaster in 1530, to Saffron Walden School in Essex. Even in the time-table of Malim, headmaster in 1561, Greek grammar was only learned by the two highest forms, VI and VII, and no Greek authors are mentioned. It is not till some notes of Anthony à Wood's, made about 1669, that Demosthenes, Homer, and Zenophon" appear among the authors read. At that time Greek prose was practiced by translations out of Latin into Greek. In 1765 Dr. James' time-table shows that the Sixth Form translated Homer into Latin verse. Theocritus, Aristophanes, and Greek plays were read. Latin verses were still the chief object. French was taught out of school, as was also drawing. It was not till 1851 that mathematics was made a part of the regular school work, nor till 1869 that natural science was introduced, and the mathematical, science, and French masters were raised to the same status as the classical masters. Under Dr. Warre (1884-1905), the unity of the school was supposed to be preserved by a community of bondage to the Greek Testament, being read by all for one hour every Monday morning. Now, under Dr. Edward Lyttelton, it is possible to be admitted to Eton without "compulsory Greek," and to pass through it with German instead of Greek in the Army Class - a rather recent addition to the school which produced the Duke of Wellington and Earl Roberts in the regular classical mill. The Army Classes number over 100 boys. Classics still predominate, 184 out of the first 240 boys specializing in classics, which now include, however, French, English history, and English literature, as well as mathematics and classics proper.

It was of course a libel when Huxley said that Eton only taught good manners and a gentlemanly proficiency in cricket. It is not even certain whether its cultivation of cricket

to use the word as including games and sports in general--is due to its being the school of the aristocracy, or whether it is the school of the aristocracy because of its cultivation of cricket. It was always to a large extent the school of the court because of the royal patronage extended to it, and its neighborhood to Windsor and to London; but until the second half of the eighteenth century it was less the school of the aristocracy in general than Winchester in the seventeenth or than Westminster in the eighteenth century. It became pre

eminently the school of the aristocracy because of the beauty of its site, the superiority of its buildings, and the charm of its spacious playing fields, but chiefly because on the whole the boys were much better treated than at other schools. The system of dames' houses had already begun in 1561, when Malim says that there were monitors at each "hostises" (hostess') house "to stop chiding or wrangling and to enforce talking Latin." The houses being of moderate size and kept by ladies, much less barbarism flourished there than in Long Chamber at Eton or at Westminster or the much more barrack-like Commoners at Winchester or "schoolhouse" at Rugby.

As early as 1506 the famous playing fields, playing meads, or playing lees, as they were at first and more properly called, since they were grass meadows and not fields, i.e. arable land, occur in the accounts. Before that there was little encouragement of games, and the only forms of exercise were a march out to Montem, later known as Salt Hill, a hill about a mile from the college, with special outings for getting may on May Day and gathering nuts in September. Little of either could be gathered by the school now. About the same time the boys began to perform plays, a Latin play, presented by the master at Christmas, with a little later an English play presented by the usher. From Horman's Vulgaria (1519) we gather that the boys learned to swim and play football "with a ball full of wind," quoits, and tennis. Cricket does not appear before the reign of Elizabeth, and then as a town game at Guilford in Surrey. By Elizabeth's reign Montem had sunk into an annual celebration at which new boys were initiated with actual and Attic salt; and afterwards became a mock-military march at which the salt took the form of guineas, collected from passers-by and those who came to see the fun, for the benefit of the captain of the school, the head colleger. Robert Boyle, "father of chemistry and uncle of the Earl of Cork," when at Eton about 1630, played at tops and ball and was given sweets by the provost. In 1765 cricket, fives, and tennis are the principal games mentioned in the Nuga Etonenses (Eton Trifles) of that year. But battledore and shuttlecock, peg-tops, hop-scotch, marbles, hoops, puss-in-the-corner, hunt-the-hare, and chuck-farthing are also mentioned. It is a disputed point incapable of definite solution, whether, when Gray, in his Ode on a Distant Prospect of Eton College, written 1742, asks" who chase the rolling circle's speed he meant who bowls hoops, or who runs after the cricket ball. These "who urge the flying ball" were no doubt the football players. It was not till the nineteenth century that the playing of cricket became a cult and rowing a profession. The former began with the matches against Harrow School, first started in 1822, and against Winchester College in

1826, and still played annually, the latter since 1854 at Winchester and Eton alternately, the former at Lord's Cricket Ground, London. Boating as a profession and not a mere amusement began with races against Westminster School in 1826, and continued till 1848, when the Thames steamboats stopped Westminster rowing. Since then Henley Regatta has been the object of the Eton eight. Though some other schools, such as Bedford, Radley, and to a small extent Winchester and Cheltenham, now row, the Oxford and Cambridge boat race still depends chiefly on which university is, for the time, favored by the Eton oarsmen. At football Eton has two games of its own, at the Wall," the grand match between Collegers and Oppidans being played on Nov. 30, and the field game, which is one of the elements from which the Association game was developed at Oxford. A Rugby football team and an Association team are now started for some interschool matches. Tennis has disappeared. Rackets reigns in its stead.

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But great as the part played by games has been in making the Etonian and the English public school system, it is after all to the excellence of its teaching that Eton has owed its position. Even in the days when Keate (c. 1830) pretended to teach 198 boys in one form, the lessons being often interrupted by singing and throwing paper pellets or even stones, the out-of-school teaching by my tutor " was most efficient for those who chose to learn. Many of the tutors inspired in the boys a far more lasting love of letters and a more effective stimulant than the more ordered and systematic compulsion of class teaching. The names of George Canning, Prime Minister in 1827, the Marquess Wellesley, Governor-General of India, of Gladstone, three times Prime Minister, and Lord Chief Justice Coleridge, as eminent in learning, in the school magazines, and the school debating society, commonly called pop," as they were in afterlife in the House of Commons or the law courts, are alone enough to show that Eton education was no bad one.

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The advertisement thus received from its ten prime ministers, its twenty-two governorgenerals of India, and its innumerable cabinet ministers, attracted "the thanes," and the thanes attracted the rest. On the whole, Eton has led and still leads the van of the public schools on its merits. The authorities there have on the whole been more amenable to public opinion and more pervious to new ideas than those of other prominent schools, especially in the domestic life of the boys, but also in the adoption of new subjects and new methods in teaching. A. F. L.

See DORMITORIES; GRAMMAR SCHOOLS, ENGLISH; PUBLIC SCHOOLS; ATHLETICS, EDUCA

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EUCLID (EUKLEIDES). The greatest teacher of geometry of ancient times, and the author of one of the world's most influential textbooks. Practically all that is known of his life is given by Proclus (410-485 A.D.) (q.v.), who says:

Not much younger than these [Hermotimus of Colophon, and Philippus of Mende, who were pupils of Plato] is Euclid, who composed the Elements, collecting many of the theorems of Eudoxus (q.v.), perfecting many of those of Theætetus, and also demonstrating with perfect certainty what his predecessors had but insufficiently proved. He flourished in the time of the first Ptolemy, for Archimedes (q.v.), who closely followed the first [i.e. Ptolemy the First, or Ptolemy Soter], speaks of Euclid. Furthermore it is related that Ptolemy one time demanded of him if there was in geometry no shorter way than that of the Elements; to whom he replied that there was no royal road to geometry. He was therefore younger than the pupils of Plato, but older than Eratosthenes and Archimedes; for the latter were contemporaries with one another, as Eratosthenes somewhere says." Another Greek writer, Stobus, tells a story that expresses the educational value placed by Euclid upon geometry: Someone who had begun to study geometry with Euclid, when he had learned the first theorem, asked, 'But what shall I get by learning these things?' Euclid called his slave, and said, 'Give him three pence, since he must make gain out of what he learns.'"

From the first of these fragments we gather that Euclid lived after the pupils of Plato (who died in 347 B.C.), and before Archimedes (who was born c. 287 B.C.), and in the reign of Ptolemy Soter (who reigned from 306 to 283 B.C.). He must therefore have flourished about 300 B.C. He probably studied at Athens, and certainly taught at the great school of Alexandria, in Egypt. He wrote not merely on geometry, but also on the theory of numbers and other mathematical subjects. It is, however, by his Elements that he is chiefly known. Proclus, in speaking of this work, says that there are "in the whole of geometry certain leading theorems, bearing to those which follow the relation of a principle, all-pervading, and furnishing proofs of many properties. VOL. II-2 L

Such theorems are called by the name of elements, and their function may be compared to that of the letters of the alphabet in relation to language, letters being indeed called by the same name in Greek" (σroxea, stoicheia). This characterizes the work of Euclid, a collection of the basic propositions of geometry, and chiefly of plane geometry, arranged in logical sequence. Euclid included in plane geometry between 160 and 175 propositions, the manuscripts varying in details. The distinctive feature of his work, compared with modern textbooks, is that he mingles his problems and theorems, endeavoring always to show how a figure is to be constructed before he considers any theorems relating to that figure. We, on the other hand, usually assume the possibility of constructing the figures, until we have a body of theorems upon which the proofs that our constructions are correct can be built. Euclid's treatment of proportion is purely geometric, and is considered too difficult for beginning pupils to-day, being replaced by an algebraic treatment. This modern method is confessedly less mathematically rigorous than the ancient one.

While we have in modern times improved the phraseology of Euclid, simplified the treatment of a few propositions, and made more usable textbooks for beginners, we have not improved upon the rigor of Euclid, nor have we materially changed his basic propositions. Although he was not completely rigorous in all of his steps, he was more nearly so than modern textbook makers, and his geometry is liable to remain for all time as a standard upon which others can improve in details of bookmaking, but upon which no one will greatly improve in the essential features. D. E. S. See ALEXANDRIA, UNIVERSITY OF.

References:

BALL, W. W. R. Short History of Mathematics. (London, 1908.)

CANTOR, M. Geschichte der Mathematik. (Leipzig,
1894-1908.)

FRANKLAND, W. B. Story of Euclid. (London, 1902.)
HEATH, T. L. Euclid's Elements. (Cambridge, 1908.)
SMITH, T. Euclid, his Life and System. (New York,
1902.)

EUDOXUS (408-355 B.c.). --A distinguished mathematician of the Athenian school. He was born at Cnidus, studied at Tarentum under the Pythagoreans, went to Egypt with Plato, and finally taught at Athens. To him seems to have been due most of the fifth book of Euclid (q.v.), the book that treats of proportion. He was much interested in the theory of the " golden section," the division of a line in extreme and mean ratio. He also perfected the "method of exhaustions" in geometry, which had been suggested by Bryson about 430 B.C. Essentially this means that, in the case of the circle, we may inscribe and circumscribe regular polygons, continually doubling the number of sides, and approaching 513

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