sixty, eighty thousand and eighty-eight, two hundred thousand and twenty-one. (8.) Three millions and three, two millions and twenty, seventy-five millions and sixty-four, six hundred and twenty-nine millions sixty-one thousand and eight, seven hundred and eighty-four millions three hundred and forty-five thousand two hundred and eighty-two. (9.) Five hundred thousand eight hundred and sixtyfour millions two hundred and fifty thousand five hundred and nine, eight hundred and sixty-one thousand three hundred and forty-four millions five hundred and ninety-five thousand one hundred and one, four billions sixty-four millions eight thousand and seventy. (10.) Nineteen billions eighteen millions seventeen thousand and fifteen, seventy-one billions five hundred and five millions sixty thousand and seven, thirty-five billions seven thousand and nineteen millions four thousaud five hundred and eleven, six hundred and fortythree billions two hundred and forty-two thousand three hundred and seventy-five millions eight hundred and nine thousand five hundred and seventy-two. III. (1.) What is the smallest number which can be expressed by three figures? what is the largest ? (2.) What is the smallest number which can be expressed by six figures? what is the largest ? (3.) What is a thousand thousands called? what, a million millions? (4.) Read the heights of the following mountains :— Ben Nevis, 4406 feet; Mt. Blanc, 15744 feet; Mt. Everest, the highest in the Himalaya range, 29000 feet; Mt. Hood, the highest in N. America, 18000 feet; Aconcaqua, the highest of the Andes, 23910 feet. (5.) Read the following areas :-England, 58000 sq. miles; Scotland, 31000 sq. miles; Ireland, 33000 sq. miles; British Empire, 8600000 sq. miles; land surface of the globe, 51500000 sq. miles. (6.) Express the following numbers in figures :-the Caucasian race consists of five hundred millions; the Mongolian, of four hundred and ninety millions; the Negro, of one hundred millions; the Malay, of sixty-eight millions; the American Indian, of sixteen millions; the population of the globe, of one thousand two hundred and fifteen millions. (7.) Express the following numbers in figures :-the distance of the planet Mercury from the sun is thirtyfive millions six hundred and forty-nine thousand miles; of Venus, sixty-six millions six hundred and fourteen thousand miles; of the earth, ninety-two millions and ninety-three thousand miles; of Mars, one hundred and forty millions three hundred and twenty-two thousand miles; of Jupiter, four hundred and seventy-nine millions one hundred and forty-one thousand miles. (8.) The distance of Uranus from the sun is one thousand seven hundred and sixty-six millions five hundred and sixty-five thousand miles; of Neptune, two-thousand seven hundred and sixty-six millions one hundred and thirty-three thousand miles. (9.) The distance of the nearest fixed star from the earth is twenty-one billions of miles. (10.) A star of the 16th magnitude is supposed to be thirty-three thousand nine hundred and eight billions of miles distant. ROMAN NUMERALS. I. = 1, II. = 2, III. = = 3, IV. = 4, V. = 5, VI. = = 7, VIII. = 6, = 8, IX. = VII. : 9, X. = 10, L. = 50, C. = 100, D. or I. = 500, M. or CIO. =1000, CCCC. or CD. A letter placed before another of greater value is subtracted from it, as IV. = 4, but after one of equal or greater value is added, as XX. = €20, XI. = 11. as A line over a letter increases its value a thousandfold, IV. (1.) Read-V., VII., IV., VI., X., IX., XI., VIII. XII., I., III., II. (2.) C., XC., CX., CL., CXX., CCIX., CCXIX., XL.. LVIII., LXXII. (3.) MD., MCCCC., D., C., MDCCXL., MDCLXXIX., MDCCCLXXII. (4.) Express in Roman numerals:-3, 6, 9, 10, 11, 12, 18, 17, 16, 19, 21. (5.) 36, 43, 75, 84, 97, 204, 506, 829, 1450, 1873. (6.) Express the following dates in Roman numerals:Grecian History-Homer lived 850 B.C. First Olympiad, 776 B.C. Battle of Marathon, 490 B.C. Athenian supre macy, 449 B.C. (7.) Capture of Athens by Spartans, 404 B.C. Retreat of the "ten thousand," 400 B.C. Aristotle flourished, 366 B.C. Philip became king of Macedon, 359 B.C. conquered by the Romans, 146 B.C. Greece End of End of (8.) Roman History-Rome founded, 753 B.C. kingdom, 509 B.C. Julius Cæsar born, 100 B.C. Republic, 30 B.C. Christianity established at Rome, 324 A.D. Fall of Empire, 470 a.d. (9) History of the Middle ages-Birth of Mohammed, 571 A.D. Charlemagne becomes Emperor of the West, 800 A.D. Arabic numerals introduced into Europe, 991 A.D. First Crusade, 1096 A.D.; end of the Crusades, 1291 A.D. Swiss independence, 1307 A.D. Columbus discovered America, 1492 A.D. (10) Heptarchy completed in England, 582 A.D. Monarchy established in England, 827 A.D. Battle of Hastings, 1066 A.D. Henry II, first of the Plantagenet line, ascended the throne, 1154 A.D. House of Commons first summoned, 1265 A.D. Battle of Bannockburn, 1314 A.D. Henry IV., first of the Lancastrian line, 1399 A.D. Edward IV., first of the House of York, 1461 A.D. Henry VII., first of the Tudor line, 1485 a.d. Sign+, PLUS. plus-sum. a. 2+2 + 2 &c. ADDITION, Terms to be explained :—Addition— MENTAL EXERCISES. 3 +3 +3 &c. 4 +4 +4 &c., and so with the other numerals. b. 3 + 4 + 6 + 7 &c. c. What two numbers added together are equal to 5? to 10? to 18? to 21? &c. What three numbers added together are equal to 12? to 25? to 48? &c. d. 12 +13 + 15 + 17 &c.; and similar exercises. |