TVI. We have a shorter method still, which is in very general use, as will appear by observing what follows: Q. What are these characters called? A. Figures. .1. .3. .4. ..5. ..6. ..7. ..8. ..9. Q. By what other name are they sometimes called? A. The 9 digits. Q. What is this method of expressing numbers called ' A. The Arabic method. Q. Why so called? A. Because the Arabs are supposed to have invented it.* Let me see you write down on the slate, in figures, the numbers one, two, three, four, five, six, seven, eight, nine. Q. To express ten, as we have no one character that will do it, what two characters do we make use of to represent this number? A. The first character, 1, and 0, or cipher; thus, 10. Q. What place does the 0, or cipher, in this case take? A. The units' place. Q. What place does the figure 1 take? A. A new place. Q. What is this new place called? A. The tens' place. Q. Write down in figures, on the slate, the number ten; now take away the 1, and what will be left? A. Nothing but 0, or cipher. Q. What is the value of this 0, or cipher, thus standing alone? 4. No value. Q. Now place the 0 at the right of the figure 1, and what will it become? A. Ten, (10.) Q. How many times is the figure 1 increased by the 0, or cipher? A. Ten times. Q. What effect, then, has a cipher in all cases when placed at the right of figures? A. It increases the value ten times. Q. In what proportion is this increase said to be? A. Tenfold proportion. * Q. How was it obtained from the Arabs? A. The Moors communicated it to the Spaniards, and John of Basingstoke, Archdeacon of Leicester, introduced it into England; hence its introduction into our own country. Q. About what time was it introduced into England? A. About the midile of the eleventh century. Q. How extensively is it now used? A. All over the civilized orld. As you have probably learned by this time how to write down ten in figures, by the help of a cipher, and learned also the value of this cipher, we will now proceed to higher numbers; and to begin let me see you write down in figures, on the slate, the following numbers, viz. One ten and one unit, or eleven,. Two tens,. Three tens,.. Four tens, .11 .12 .13 ..14 ...15 ....16 ...17 ..18 ..19 ...or twenty,. ..20 ....or thirty,. .30 ...or forty, .40 ...or fifty, .50 ...or sixty, .60 ....or ninety, Q. Here we see the value of the cipher again; for, by placing a cipher at the right of ten, it becomes one hundred, (100,) that is, ten tens should we place another cipher still at the right of the 100, (thus, 1000,) what would it become? A. One thousand, (1000). : Q. From what you have now seen of the value of figures, what may 2 and 5 be made to stand for? A. 25 or 52. Q. What is this different value called, which arises from the figures being placed or located differently? A. Their local value. Q. What would be the value of the five written alone? A. Simply 5. Q. What is the value, then, of a figure standing alone? A. The simple value. Q. How many values do figures appear to have? A. Two. Q. What are they? A. Simple and local. Q. Now, as it takes 10 units to make one ten, or one in the next left hand place, and 10 teng to make 100, how do figures appear to increase by being removed one place farther to the left? A. In a tenfold proportion from right to left. You must have acquired, by this time, some considerable knowledge of figures: let me examine you a little; and, in the first place, let me see you write down on the slate the figure 8. Q. What do you call it? A. 8 units. Q. What do you call them both, and how are they read 4. 8 units and 2 tens read twenty-eight. Write at the left of the 28 the figure 8, (thus, 828.) Q. What do you call the three figures now, and how are they read? A. 8 units, 2 tens, and 8 hundreds, read eight hundred and twenty-eight. Write at the left of 823 the figure 1, (thus, 1828.) Q. What do you call the 4 figures now, and how read? A. 8 units, 2 tens, 8 hundreds, and 1 thousands, read one thousand eight hundred and twenty-eight. Q. We have now been combining, or placing figures together till we have obtained the number 1828, representing the number of years it is since Christ appeared on earth, to the present time. We might continue to put figures together in this way that would express higher numbers still, up to billions, &c That you may be able to form some idea of the power of figures, let me tell you that there is not a billion of seconds in thirty thousand years; notwithstanding there are 60 seconds in every minute, 60 minutes in every hour, 24 hours in every day, and in a solar year, 365 days, 5 hours, 48 minutes, and about 48 seconds. Should we continue to go on as we began, in combining inore figures still, it would be very inconvenient; to avoid this we have a rule by which we can read almost any number of figures, ever so large. What is this rule called. A. Numeration. Q. What is the reading, or expressing a number by figures as now shown, called? A. Notation or Numeration. RULE. I. From the above illustrations, how does it appear that you must begin to numerate? A. Begin at the right hand. II. At which hand would you begin to read? A. The left. III. What is the first figure at the right hand, or first place, called? . Units. What is the second figure, or second place, called? A. Tens What is the third place called? A. Hundreds. What is the fourth place called? A. Thousands. IV. In reading, what value do you give those figures which were called units in numerating? A. Units. V. What value do you give tens? A. Tens. VI. What value do you give hundreds, thousands, &c 4. Hundreds, thousands, &c. 1. Repeat the Numeration Table. 0, read-One billion. 0 0, read-Two hundred thous. mills. 4 0 0 0 0 0 0 0 0 8 0 0 0 0 0, read-Seven millions. 0, read-Eight hundred thousand. 2 0 0, read-Two hundred. 4, read-Four." Questions on the Table. Here let the teacher cover over the written numbers only on the right of the table above, and ask the pupil the following questions, viz. What is the value of 4? Of 3 and one cipher? Of 2 and 2 ciphers? and so on, up to the top of the table. Q. What is the meaning of annex? A. To place after. Q. What is the meaning of prefix? A. To place before. Note. Let the scholar write down in figures, the answers to the following Questions on his slate at recitation. Q. How much does 1, with 1 cipher annexed, stand for? A. Ten. Q. Why? A. Because the 1 is tens when I numerate. Numerate the 10 and see. Q. What does 1 with 3 ciphers stand for? A. One thousand. Q. Why? A. Because when I numerate by saying units, tens, hundreds, thousands, the 1 comes thousands. Q. What does 5 with five ciphers stand for? A. Five hin dred thousand. Why? A. Because when I numerate, the 5 comes hundreds of thousands. Numerate and see. Q. What does 8 with 6 ciphers stand for? A. 8 millions. Numerate and see. Q. How do you read the figures 624 ? A. Six hundred and twenty-four. Q. Why do you say 6 hundred? Q. What does 6278 stand for? A. Six thousand two hundred and seventy-eight. Q. How do you know that the 6 is 6 thousand? Q. How do you read the figures 56768? How do you read 27365? How do you read 654212? Express in words the following numbers. Note.-The pupil may learn the value of each succeeding number by a for 75000100=Seventy-five millions and one hundred. 83000800 Express in figures the following numbers. Sixty-One hundred and twenty-five. Three thousand three hundred and thirty three. Three millions, three hundred thirty-three thousand, three hundred and thirty-three. Thirty millions. Three hundred millions and twenty-five. |