An Explanation of some of the Marks and Characters made use of in Arithmetic. extraction of? ✔ or 2√ 3 √ Significations. = $ 1. The sign of equality; as, 100cts 4 = 2; The sign of subtraction; as, 6- Numbers placed like a fraction likewise The sign that the square root of that number is required; thus, 29 = 3; that is, the square root of 9 is equal to 3. The sign that the cube root of that number is required; thus, 3/64-4; that is, the cube root of 64 is equal to 4. &c. ERRATA. Page 15, 15th line from the bottom, for four read one. 34, 12th line from the top, for 262 rem. read 162 remainder. 102, 8th line from the top, for roods read rods. 102, 7th sum, for 2p. in the Ans. read 20p. 140, 4th sum, for d. in the answer read id. 146, 3d sum in case 4th, read for answer 5C, 3qrs. 10lbs.t 155, in example for illustration, read 1422 for 1442. 156, 2d sum, for the rem. read 157, 2d sum, for the anwer read for 22. 336 for $ 366. 182, 8th sum, for O's stock, read 170 for 120. 189, in example for illustration, draw the line under the 4th quantity instead of between the 3d and 4th. Subtraction of Vulgar Fractions read Subtraction of Deci 2d answer for 8lbs at 4cts. read 2lbs. at 4cts. ARITHMETIC. ARITHMETIC is the art, science, or knowledge of computing numbers, (which consist of one or more quantities,) and has five principal or fundamental rules; viz. Notation or Numeration, Addition, Subtraction, Multiplication and Division; each of which will be treated of. NUMERATION.. Numeration teacheth to read or express the true value of any number; consequently any proposed number can be written down according to its value, which is done by placing in due order, the following characters or figures. 1 2 8 9 0 one two three four five six seven eight nine cipher 3 4 5 6 7 The last is called a cipher which, by itself, is nought; but when it stands to the right of one or more of the characters or figures mentioned, it increases the figure or figures in a tenfold proportion, as 10 stands for ten, 120 for one hundred and twenty. The value of the other characters or figures when standing alone, may be understood as follows: 1 is of itself but one, as one yard, one penny, &c. 2 is two ones, 3 three ones, &c. till you get to 9, which in value is nine ones, as 1 yard or 1 penny nine times told. Beside the simple value of figures here explained each has a value depending upon the place it stands in. One figure standing by itself expresses its own value as before explained, but when combined with one or more figures the value is increased according to the number and situation of the figures mentioned, and may be understood by strictly attending to the table constructed for this purpose, which you will find hereafter inserted. But to illustrate it plainly, observe that beginning at the right hand and reckoning to the left, the first figure represents its own value, that in the second place ten times its simple value, and so on, the value of each figure being ten times the value of the last mentioned. The first is called units, the second tens, the third hundreds, the fourth thousands, &c. as you will see in the table. For farther illustration, attend to what follows; let 3854 be the number under consideration; this in value is three thousand eight hundred and fifty-four, and may be thus understood, beginning at the right hand and reckoning (as has been observed,) to the left. The right hand figure is 4, which is no more in value than four times one; the next is 5, and increases the number in a tenfold proportion, that is 5 times 10 are 50 which, with the 4, makes 54; the next figure is 8, which is 10 times greater than the last and is increased by 100 times its simple value; this makes 800, and connected with the 54, makes 854; the last figure 3 is reckoned in the same proportion, and is 10 times greater than the last, or 1000 times its simple value, which is 3000; this, connected with the other figures, makes what was first mentioned, viz. 3854. Another illustration; suppose 45369 be the number whose value is to be determined, you may understand it thus: This last example may be read thus, nine, sixty-nine, three hundred and sixty-nine, five thousand three hundred and sixtynine, forty-five thousand three hundred and sixty-nine. As soon as the following table is learned, there will be no great difficulty in comprehending the value of as many figures as will be necessary. You will perceive that the first place of figures, is units, the second tens, the third hundreds, &c. By this table nine places of figures can be enumerated; which for common use will be sufficient; but to enumerate a larger number, the following may be observed. When a number of figures is given to be read, it will be found convenient to divide them into as many periods of six figures each as you can, reckoning from right to left; the first period being called units, the second millions, the third billions, &c. as in the following table. 7 Period. 6 Period. 5 Period. 4 Period. 3 Period. 2 Period. 1 Period. 946.258; 713.395; 173.826; 143.697; 495.213; 191.216; 493.121; The foregoing figures may be read thus. Nine hundred and forty-six thousand two hundred and fiftyeight sextillions; seven hundred and thirteen thousand three hundred and ninety-five quintillions; one hundred and seventythree thousand eight hundred and twenty-six quadrillions; four hundred and forty-three thousand six hundred and ninety-seven trillions; four hundred and ninety-five thousand two hundred and thirteen billions; one hundred and ninety-one thousand two hundred and sixteen millions; four hundred and ninety-three thousand one hundred and twenty-one. Note.-Billions are substituted for millions. of millions. Trillions for millions of millions of millions. Quadrillions for millions of millions of millions of millions, &c. There are others that might be mentioned besides those in the last table, viz. Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, &c. the value of which are determined in the same manner as those mentioned above. APPLICATION. RULE. Remember to begin at the right hand; write unit place of units, tens in the place of tens, hundreds in the place of hundreds, and so continue on to the left, writing each figure according to its proper value in numeration. Take care that you supply the places that would come in order, with ciphers, when they are omitted in the question. EXAMPLES. Write down in figures the following numbers. Sixteen. Two hundred and sixteen. Five thousand two hundred and sixteen. Sixty-four thousand two hundred and sixteen. Nine hundred and eight thousand three hundred and fifty seven. One million. Three millions two hundred and sixty-eight thousand seven hundred and forty-one. Three hundred and thirty-three thousand and five. Six hundred and forty millions one hundred and one thousand and four. Twenty-two millions three hundred and nine thousand and ninety-seven. Nine thousand nine hundred and ninety-nine. Write down in words the following numbers. 5, 4345, 66, 927, 21492, 213145, 121, 425925, 100000000, 709, 3040, 9002, 50434, 160029, 3040864, 910703, 36002009. ADDITION AND SUBTRACTION TABLE. 1 2 3 4 5 2 4 5 6 7 6 7 8 9 10 11 12 8 9 10 11 12 13 14 3 5 6 7 8 9 10 11 12 13 14 15 4 6 7 8 9 10 11 12 13 14 15 16 5 7 8 9 10 11 12 13 14 15 16 17 6 8 9 10 11 12 13 14 15 16 17 18!! 7 9 10 11 12 13 14 15 16 17 18 19. 810 11 12 13 14 15 16 17|18|19|20| 9 11 12 13 14 15 16 17 18 19 20 21 10 12 13 14 15 16 17 18 19 20 21 22 11 13 14 15 16 17 18 19 20 21 22 23 12 14 15 16 17 18 19 20 21 22 23 24 |