Geometry

a branch of mathematics that treats of figures and space. The name is Greek, signifying earth measurement. The science is thought to have grown out of land surveying. It was developed first in Mesopotamia and in Egypt, both regions in which it was necessary to reestablish boundaries between fields, after the great inundations that occur each year. The Greeks were noted mathematicians. The textbook of plane and solid geometry now used in schools is essentially that written by Euclid, a professor of mathematics in the Greek university of Alexandria, Egypt, who flourished about 300-270 B. C. He taught and wrote in the Greek language. His geometry was divided into thirteen books, which were preceded by definitions and axioms.

The study of geometry is of exceptional value in teaching students to think and to speak accurately. In geometry a statement is worthless unless absolutely accurate. The conclusions of geometry are also exceedingly satisfactory. We may say of Nero that he was cruel, and yet later find it necessary to modify our opinion; but the geometrical statement that the three angles of a triangle are together equal to two right angles may be proved beyond question, and is true for all time, of all triangles. One cannot be absolutely certain of the spelling of a word, for custom changes. The chemist must be on the lookout constantly, lest some unexpected circumstance prevent chemical action taking place as expected; but when two straight lines cross each other, the opposite angles formed are always equal. They can't be otherwise. For this reason geometry is spoken of as an exact study. It is also exceedingly practical. The builder finds that a timber forming a triangle with two other timbers is not only a rigid frame, but the only rigid frame known. Geometry gives the reason; a triangle cannot change its shape without changing the length of at least one side. Geometry also furnishes the only method of constructing an exact right angle, that is, of turning a square corner. The rules of mensuration are supplied by geometry. Without geometry the rules for finding the area of a triangle, a rectangle, or a circle, as well as those for finding the solid contents of spheres and other solids, would be mere guesswork.

See Cube; Conic Section; Triangle; Euclid; Pythagoras; Hexagon

George I (1660-1727), elector of Hanover and king of Great Britain. In 1698 he inherited the German electorate of Hanover. On the death of Queen Anne in 1714 he was selected by Parliament for the throne of England and Scotland. Through his mother, Sophia, he was a great grandson of James I. When he ascended the throne of England he was fifty-four years old. He could not speak a word of English and had no desire to become an Englishman. He brought a number of German favorites with him and created a great deal of dissatisfaction. He was a man of simple, plain manners, however, with natural good sense and ideas of justice that pleased the common people well. As he was not an ambitious man, and being unfamiliar with the language, the government fell naturally into the hands of a body of ministers, now known as the cabinet or ministry. This transfer of power from the king to Parliament and its executive committee had been going on rapidly: the peculiar conditions just referred to hastened it to completion. From that time on, the sovereignty of Great Britain become more of an honorary position than otherwise. The king now exercises far less authority than the president of the United States.

George II (1683-1760), king of Great Britain and elector of Hanover. He ascended the British throne on the death of his father in 1727. Like his father, he thought more of Hanover than he did of his English court. During the early part of his reign the real ruler of England was Walpole, who pursued a vigorous foreign policy. A second rising of the Highlanders took place in 1745 in favor of the Stuart prince, Charles Edward. The French and Indian War, of which we read in our American history, took place during his reign, though peace was not formally declared until 1763, three years after his death. William Pitt was the great Englishman of this later period. George II was considered a man of very ordinary ability, without a liking for literature of science. In money matters he was termed stingy. He was obstinate, quick tempered, and conceited; but, unlike some of the Stuart kings, he was truthful and of respectable character.

George III (1738-1820), king of Great Britain and elector of Hanover. He was the grandson of George II. He ascended the throne in 1760. He was the first of the Hanoverian line who was born in England. He is the King George of whom so much is said in the history of the American Revolution. He appears to have been a shortsighted, stubborn man. He was fond of reading and took an interest in agriculture and useful inventions. He appears to have been impatient because the lines of government had passed from the sovereign into the hands of a cabinet. It is said that he spent large sums of money in bribing influential members of Parliament to do his bidding and to carry out his views, rather than the wishes of his ministers.

The American colonies secured their independence during the reign of George III. This loss of America must not be supposed to have occupied so great a place in public attention or in the mind of the king as Americans are disposed to consider. With large interests in other parts of the world, and a powerful enemy just across the English Channel, George III and his Parliament had many other questions to consider that seemed to them of more importance than the management of a few struggling colonies forty days distant. Nevertheless King George was distressed by the revolt of the American colonies. When, after the peace of 1783, John Adams appeared at the court of St. James as minister of the United States, King George received him kindly and was much affected by Minister Adams' expressions of good will toward the mother country. When the American ambassador addressed him in respectful and affectionate language, his reply was full of feeling.

"Sir," he said, "the circumstances of this audience are so extraordinary, the language you have now held is so extremely proper, and the feelings you have discovered so justly adapted to the occasion, that I must say that I not only receive with pleasure the assurance of the friendly dispositions of the United States, but that I am very glad the choice has fallen upon you to be their minister. I wish you, sir, to believe and that it may be understood in America, that I have done nothing in the late contest but what I thought myself indispensably bound to do by the duty which I owe to my people. I will be very frank with you. I was the last to consent to the separation; but the separation having been made, and having become inevitable, I have always said, as I say now, that I would be the first to meet the friendship of the United States as an independent power. The moment I see such sentiments and language as yours prevail, and a disposition to give to this country the preference, that moment I shall say, let the circumstances of language, religion, and blood have their natural and full effect."

George III was not a great man; he is not a favorite with American readers; but we may well afford some kindly feeling for our last king. The critical American historian and publicist, Ford, says of him:

In his private life he exactly fulfilled the popular ideal of a good ruler. In an age when society was recklessly dissolute, he was chaste in conduct, temperate in diet, and simple in manners. While irreligion abounded, he kept a virtuous home, whose days, beginning with family prayer, were passed in laborious performance of duty. But though a good man, George was a bad ruler. His public conduct, at the best, was marked by the narrowness and trickery of a small politician, rather than by the tact and broad outlook of a statesman.

Although it has been stated in some quarters that King George was not fond of literature or art, it is certain that he was a tireless book-collector, and that he fostered the British Museum, leaving to it, in fact, his fine private library. When about to take up a residence at Weymouth he wrote his bookseller, the list is still extant in his own handwriting, to send him a parcel of books including a two-volume Bible, a religious work called The New Whole Duty of Man, The Annual Register in 25 volumes, Blackstone's Commentaries, Johnson's Dictionary, a French Dictionary, three collections of poems extending to 87 volumes, Shakespeare's plays, histories of England and France, two volumes of Voltaire, the works of Jonathan Swift, and a few other books in English and in French--none in German, none in Latin or Greek, none in science. See Hanover; Victoria

George IV (1762-1830), king of Great Britain and Ireland and Hanover. He was the son of George III and Charlotte Sophia, a German princess. He was married without his father's consent to a Mrs. Fitzherbert in 1785, and in 1795 he was married with royal consent to his cousin Caroline of Brunswick. Prince George belonged to a wild set of young men, including Fox and Sheridan, leaders of the Whigs. This is the prince whose partisans caused the arrest and imprisonment for a year of two editors who had the impertinence to say a rival paper had been guilty of exaggeration in calling the Prince of Wales an Adonis. He was rather a handsome man. He dressed in the height of fashion and delighted in the title of "the first gentleman in Europe." The man whose esteem he most desired was "Beau" Brummel, leader of court fashions.

He was made regent in 1811, and succeeded his father in 1820. He refused to permit his queen to take part in the coronation exercises; and sued for divorce. It speaks well for the nation that the suit was not granted, even to a royal successor of Henry VIII. On his accession George forsook his early Whig friends and looked with favor on the Tories. Robert Peel and the Duke of Wellington, a warrior, not a statesman, were the leading Tories.

The reign of George IV is rather an ignoble one. The Tories basked in the reputation won by the successful ending of the Napoleonic wars. War taxes were continued almost to the verge of confiscation. Among the measures to be commended was the enfranchisement of Catholics in 1829, and an overhauling of the penal laws. In 1823 the death penalty was removed from a hundred offenses.

One of the best things that can be said of George IV is that he presented the British Museum with 65,250 volumes, 20,000 pamphlets, and a "superb array" of maps, topographical drawings, and prints. He died without issue, and was succeeded by his brother, William IV.

George III died in 1820 and George IV be came king. The new monarch was a man of low principles and dissolute habits. He married a Roman Catholic lady in secret but disowned her in order to obtain the crown. Later he married a German princess in order to induce parliament to pay his debts, but he soon neglected and illtreated her and finally sought a divorce. He was always deeply in debt and took little part in the government except occasionally to interpose his influence in opposition to reforms. He was of fine appearance and always dressed in the height of fashion and was therefore sometimes very unworthily called "the first gentleman in Europe." He was amiable and disinclined to severity in punishments; but taken all in all he was one of the sovereigns of whom England can be least proud in all the long line.--E. P. Cheney.

Poor crazy George III died in 1820, and for the next ten years the crown was worn by George IV, "the first gentleman in Europe." More accurately, he was the first dandy and the first scamp. But his head was as wooden to all reform ideas as had been his father's, and it was with great difficulty that he was driven, in 1827, to assent to the measure for allowing Roman Catholics to sit in Parliament. George died in 1830, and his brother, a bluff and rather honest sailor, succeeded as William IV.--H. P. Judson, Europe in the Nineteenth Century.

George V, king of the United Kingdom of Great Britain and Ireland. Son of Edward VII and Alexandra, eldest daughter of King Christian IX of Denmark. He was born June 3, 1865, at Marlborough House. July 6, 1893, he married Victoria May, daughter of the Duke of Teck. Six children were born of this marriage--five sons and one daughter. The heir apparent, Edward Albert, was born June 23, 1894. George V succeeded his father, May 6, 1910, an elder. brother having died in 1892.

Prince George's training was that of a sailor. He spent five years in cruising. He is said to have taken pains to forget the foreign languages taught him in school and to be able to converse in English only. In 1892, when his brother died, he became heir apparent, and took his seat in the House of Lords as Duke of York. The prince became Duke of Cornwall when his father took the throne, and soon thereafter started on a tour of the colonies. He opened the first Parliament of the Commonwealth of Australia. In celebration of his safe return from the tour he was entertained by the London corporation at Guildhall on December 5, 1901; on which occasion he advised England to "wake up." In the fall of 1905 he went to India and when he returned there was another celebration. On this occasion he said that "the task of governing India will be made the easier if we, on our part, infuse into it a wider element of sympathy." Among the good qualities attributed to King George are that he is fond of a quiet evening at home, that he studies public questions and delivers practical addresses, and that he is in sympathy with the colonies of the empire. By all accounts, he is not fond of sport nor of court gaiety. George Eliot. See Cross; Mrs. Mary Ann Evans