ROMAN NOTATION. The Romans, and other ancient nations, for want of being acquainted with the method of notation now used, which was first introduced into Europe by the Arabs about the year 1000, expressed numbers by means of the seven following capital letters of the alphabet: Numbers I. And by repeating and combining these, any of the intermediate, or higher numbers, were denoted as follows: 200. 800. 2000. Also annexing a letter, or letters, of a lower value to one of a higher, denoted their sum: And if a letter of a lower value were put before one of a higher, it denoted their difference: As IV. Also, in the titles of some old books, we find 10 put for D, or 500; and for every such annexed, the value is increased tenfold; as 100 is 5000, 1000 is 50000, &c.; cro is also put for м, or 1000; and for every such c and o, the value is increased as before. Thus, cc1ɔɔ is 10000, and ccc1ɔɔɔ is 100000. And if a bar be put over any number, it increases its value 1000 fold. Thus, v is 5000, x is 10000, L is 50000, and c 100000, &c. 8 Write down in words, or read the following:-3 12 17 25 68 104 246 415 1421 68003 7483542 20742156 875631 986147 84734219 462185321 510639274 971360487 To express Numbers by Figures. RULE. (1.) Write down a sufficient number of ciphers, and divide them into periods; (2.) Then beginning at the left, place in their proper positions under the ciphers, the significant figures necessary for expressing the proposed number; (3.) If any places remain unoccupied, let them be filled with ciphers. Hence to express five hundred and three million and thirty thousand six hundred and four, proceed as under :— 000,000,000 5 3 3 6 4, and thence by filling the unoccupied places, 503,030,604. By practice, the learner will soon be able to dispense with the ciphers. wwww... Write down in figures, forty-two-Two hundred and thirty one- -Five hundred and seven- -One thousand and twenty-two- -Seven thousand, nine hundred and seventy-four Three thousand and nine-Twenty thousand and ninety-three- Five hundred and fifty thousand and ninety— -Six millions, five thousand, and three-Eighty-four millions, seven hundred-Eleven millions, nine thousand and one- -One billion, ten millions, two hundred thousand--One billion-One trillion. SIMPLE ADDITION Teacheth to add two or more sums together, to make one whole or total sum; or Addition is the collecting of several numbers into one sum. ADDITION TABLE. 1 and 1 are 22 and 1 are 33 and 1 are 44 and 1 are 55 and 1 are 66 and 1 are 7 1 2.. 65.. 2 3.. 75 74.. 4.. 85 2.. 8 3.. 2.. 32 2.. 43 76 3.. 42 3.. 53 3.. 86.. 9 4.. 4.. 96.. 4.. 10 5 5.. 5.. 106 .. 5.. 11 6.. 6.. 105.. 7.. 82 .. 7.115.. 7 and 1 are 818 and 1 are 99 and 1 are 10 10and10are2011 & 11are2212 & 12are24 7 .. 2.. 98 9.. 13 5 9.. 15 10 134 10 145 10 16 166.. 11 .. 17 11 10.. 11..21 11 12..23 12 13..25 14..26 25 12.. 15..27 17 9.. 168 3 119 3 12 10 4.. 129 4 13 10 179.. 7. 10.. 178 .. 10 .. 189 7 .. 11 .. 188 11 .. 199.. 17.. 12.. 198 .. 12.. 20,9 6. 15 10.. 14.. 24 11 .. 15.. 26 12 ..16..28 15.. 25 11 .. 16.. 27 12.. 17.. 29 7.. 16 10.. 16.. 26 11 .. 17.. 28 12 .. 18.. 30 18.. 29 12.. 19.. 31 19.. 30 12.. 20..32) 20..31 12 21..33 8.. 17 10.. 17.. 27 11 .. 9 .. 18 10 .. 18.. 28 11 .. 10 19 10 .. 19.. 29 11 .. 11 20 10..20.. 30 11 .. 21..32 12.. 22..34 12.. 21 10 21..31 11 22..33 12 23..35 SIMPLE EXERCISES. 1. Proceed the same as in Exercise 4, 5, &c., p. 8. 2. Here are 2 books, I put 1 more to them, how many are there now? I add 2 more-or 3 more, &c., &c. 3. Here are 3 slates, I put 2 more to them, or 3, or 4, &c. Here are 4 slates, I put 3 more to them, how many are there now? 4. Here are 10 lines | | | | 10 or 4, &c., how many will there be? , if I add 1, or 2, or 3, 5. Here I make a sign +, what does it mean? Ans. lt means plus, or more; it is the sign of adding to, as when I put 1 book to 2 books, it makes altogether 3. Thus I write +, which means 2 added to 1, and makes 3. 6. Observe what I write, | |+|||=||||| 2 8 means that the sum of 2 and 3 is equal to 5. Hence this sign, =, means equal to. GENERAL OR SLATE EXERCISES. -hundreds cotens units RULE. Write the numbers under each other, units under units, tens under tens, hundreds under hundreds, &c. :then add the figures in the right hand column together; thus 2 and 1 make 3, 3 and 4 make 7. Put down 7. Proceed to the next column, 3 and 4 make 7, 7 and 3 make 10. Put 241 down the cipher of the number 10. Take the 1 of the 10, and add it to the next column, thus 1 and 6 make 7, 7 and 2 make 9, and 9 and 1 make 10. Therefore put down 10. The number 1007 is called the sum. 632 1007 PROOF. First, begin at the top of the sum, and reckon the figures downwards, the same as you add them up, and if the same as the first, the sum is supposed to be right. Second, draw a line below the uppermost row, add all the rest together, setting their sum under the number to be proved; add the last line found to the top line cut off, and if the sum be the same as that found by the first addition, the work is right.* * Prove also thus:-Add all the figures in the first line; and having rejected as many nines as are contained in their sum, set down the excess of nines opposite; do so with each of the lines; then if the excess of nines in this sum, taken as before, be equal to the excess of nines in the total sum, the work is right. The Tutor will by a mere glance perceive the answer to each of these exercises. 1. What is the sum of 18+2+3+10+3? Ans. 36. 2. Required the sum of 200+242 +611+576+321+ 599+624. Ans 3173. 3. What is the sum of 1621+5437+8961+3876+ 4289+6248 +9987+1204 ? Ans. 41623. 4. Produce the sum of 10581+10999+44376+89467 +346819+432178. two Ans. 934420. 5. My Son was born in 1834, when will he be sixtyyears of age ? Ans. In the year 1896. 6. Add the age of the world before Christ, 4004 to the year 1852, and tell the age of the world. Ans. 5856. 7. In the year 1849 I took the lease of a farm for 99 years, when will the lease be out ? Ans. 1948. 8. A Railway train had 10 passenger carriages; the first two contained 60 persons, the second two 57, the next three 91, and the rest 78. How many passengers were in the train ? Ans. 286. 9. Last year I planted 3342 oaks, 7482 ashes, 5942 elms, 7321 firs, 891 birches, 724 beeches; how many did I plant in all ? Ans. 25702. 10. I paid to one of my creditors £257, to another £2361, to another £5624, to another £78, to another £10576, to another £7990, which left in the Bank £10453, how much had I at first? Ans. £37339. 11. Received from A nine hundred and twenty-eight pounds, from B thirty-six, from C five thousand, from D seven hundred and thirteen, from E twenty-five thousand four hundred and eighty-eight, from F ninety-seven, from G seven thousand eight hundred and sixty-five, and from H forty-three thousand and two; how many pounds did 12. An army consisted of 8 battalions of foot, and 4 squadrons of horse: A's battalion consisted of 464 men, B's 372, C's 846, D's 563, E's 279, F's 625, G's 368, and H's 429; R's squadron was 658, S's 271, T's 463, and U's 587; how many horse and foot were in the army ? Ans. 3946 foot, 1979 horse. 13. A Woollen Draper sold 75 yards of cloth on Monday, 94 on Tuesday, 65 on Wednesday, 59 on Thursday, and the same quantity on Friday, and 116 on Saturday; how many yards of cloth did he sell during the week? Ans. 468. SIMPLE SUBTRACTION. SUBTRACTION is the method of finding the difference of any two numbers, of the same denomination, by taking the less from the greater. The greater number is called the Minuend; the less the Subtrahend; and the number found is called the Difference or Remainder. Subtraction is indicated by called minus, or negative sign. Thus 4-3-1, i. e. 4 minus or less 3, equal to 1. SIMPLE EXERCISES. 1. Proceed as directed page 9, Exercises 7 to 11. 2. A boy had 4 oranges, he gave me 2, how many had he left? 3. A woman had 9 eggs in her basket, I took 3 out, and paid for them; how many remained in the basket? [Here the Teacher may show the meaning of Subtraction; it means the taking out or away of one number from another. 4. A girl had 6 pence, and spent 2 pence, how many pence had she then left? 5. Add four and 5 by counting your fingers. Take 3 away, how many remain ? 6. If I buy a lb. of sugar for 5 pence, how much will the grocer give me out of 6 pence? 7. Here are 12 lines | | | | | | | | | | | |, 12; if I take 2 away, or 3, or 4, &c., how many will remain? The Teacher should continue these and similar questions, till his Pupils become well acquainted with Addition and Subtraction. |