29. The following table will exemplify this truth, and the pupil can point out the different values which a digit admits of, as well as express the law of variation :— 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 999999999 30. Read and write in words the following numbers: 84; 973; 8542: 73961; 340609; 8760464; 55478035; 341275648. The larger the number is, the greater the difficulty of reading it; but this difficulty vanishes if the number be divided into periods of three figures, commencing at the right, till not more than three remain. Then read each period by itself, beginning at the left, and call the periods after their units, thus : 464,789,485,321,543, which number is thus read, 464 trillions 789 billions 485 millions 321 thousands 543 units, or briefly 543. 31. Write down in figures the following numbers: sixty-four, two hundred and forty-nine, eight thousand four hundred and twenty-four, forty-six thousand seven hundred and sixteen, six hundred and forty thousand four hundred and ninety-four, five millions four hundred and forty-four thousand seven hundred and eighty-nine. 32. In the Roman notation, seven capital letters were used to express numbers, these letters were- 33. When any letter is followed by one of less or equal value, the expression is equal to their simple values taken together; but when a letter precedes one of greater value, together they express the difference of their simple values; thus the series of natural numbers, from one to a thousand, is denoted : I. II. III. IV. V. VI. VII. VIII. IX. X. XI. 34. To increase a number a thousand fold, a line is drawn over the top of a letter. Thus, 5000 is written, V or Iɔɔ; 70000 is written, LXX.; 2001000 is written, MMM. 35. The Roman characters are used at the present day, first, to number the chapters and the several parts into which books are divided; sometimes to show the year of publication of a work, and the paging of prefaces; secondly, in inscriptions for monuments and in epitaphs; thirdly, in numismatics, the science of medals and coins. 36. EXERCISES IN NUMERATION. Write down in words the following numbers :-5, 8, 12, 17, 24, 26, 37, 49, 76, 87, 90, 99, 101, 241, 176, 087, 008, 245, 574, 809, 977, 047, 999, 1005, 1014, 1346, 1787, 2007, 3745, 9846, 10609, 10428, 82307, 110349, 137008 540423, 837457, 806004, 7640006, 7607760, 6900070, 24803765, 900706539, 6476300088, 807050700603. 37. EXERCISES IN NOTATION. Express the following numbers in figures :-Forty-five, three hundred and sixty-five, six hundred and eight, one thousand and seventy-five, three thousand nine hundred and nine, seventyeight thousand and seven, eight hundred and four thousand four hundred and fifty-four, five millions three hundred and forty thousand nine hundred and eleven, three hundred and four millions seven hundred and forty thousand four hundred, eighty-four billions seven millions three hundred thousand and ninety. 38. EXERCISES IN ROMAN NOTATION. 14, 28, 74, 80, 96, 99, 107, 194, 345, 609, 7000, 9080, 5704, 5555, 60000, 33333, 800000, 659186, 999999. 39. Express in Arabic figures :-XV. XIX. XXIV. XXXVII. XCIX. LV. LXXXI. CL. CXC. CCCX. DLX. DXCIV. MDCCXCIX. VIII. LXDCVI. LVDLV. DCCLXXVIIDCCLXXVII. 40. Every process in Arithmetic consists in the increase or diminution of numbers. 41. These processes are various, but they can be reduced to four, which are called fundamental, because all the others depend on them. 42. The fundamental operations are: Addition, Subtraction, Multiplication, and Division, the last two being shorter methods of the first and second. ADDITION. 43. I had in my purse fifteen shillings; my father gives me seven shillings and my mother five shillings more. How many shall I have altogether? To find the answer I have to put these three numbers of shillings together, or to add them up; and the process is called addition. 44. Therefore, addition is the process of collecting several numbers together. 45. The number resulting from addition is called the sum. 46. The sum of 6 and 4 is 10, which is expressed: 6+4=10. The sign signifies plus or and; and the sign is called the sign of equality, denoting that the quantity on the left is equal to that on the right. The sum of two numbers in the first vertical and the first horizontal column is found at the concourse of these two columns. The learner must afterwards be questioned in different order In the following exercise, add up the numbers outside the brackets to those that are within; let it be done both in writing This is to be continued until the pupil answers readily ques- |