X 183. Sixth line from the top, at the end, for 5, read = 5a. 184. Second line from the top, near the end, for 188. Example, paragraph 485, third line, for a2 a2+ab, and for 144 96, read 144 +96. · ab, read 189. Examples, some of the exponents have slipped down in the printing. 214. Last line of paragraph 557, for 5833-8 5832-8 read 2 222. Nineteenth line of paragraph 572, for third time, read third term. 224. Eleventh line from the bottom, for = 14, read 1⁄2 = 14. 225. Seventh line, for 8 y 28, read 8 X 21. 225. Last line but one in paragraph 577, for shorter, read shortened. 228. Example, paragraph 588, for 55, read 55. 308. Examples, paragraph 804, for 36721. 12s. 4d. and 36841. 3s. 4d, read 36721. 12s. Id. and 36841. 3s. ld. 312. First line of paragraph 814, for (2:52), read (2-5)2, and on the eighth line of the same paragraph, for (1)2 read (1)2. This instrument, which is referred to in paragraph 26, consists of a frame of wood, in which are fixed 10 parallel wires, on each of which are ten moveable balls, and may be used with great effect in performing small operations by a system of palpable arithmetic, similar to that used by the Chinese. By it may be performed operations in any of the four cardinal rules. On the first wire, are exhibited the fives in ten; on the second, the fours in ten; on the fifth wire it is shown that six taken from ten leaves four, &c. &c. This brief description of the instrument will be sufficient to show the manner of using it. Multiplicationand Division of large Numbers, Of Prime Numbers, of Multiples, of Sub-multi- ples, and of the Method of performing Short Whole Numbers, as distinguished from Compound Numbers and Fractions, ARITHMETIC MADE EASY. CHAPTER I. INTRODUCTION. 1. The term Arithmetic is derived from the Greek, and it means the art of numbering and of calculating in numbers. 2. Arithmetic is a science as well as an art, and of all the arts and sciences there is none so generally useful in the common concerns of life. A thorough knowledge of it must be of the utmost importance to every one, whatever be his station in society; but to those engaged in trade or commerce, however trivial, it is indispensable. Beside the general utility of this branch of knowledge, it has another recommendation; it is easy of attainment. 3. In the progress of the work, I shall not only give the general rules of performance, and show their application to practical examples, but also clearly develope the principles on which these rules are founded, and on which the application of them is made; and thereby enable the student clearly to perceive the reason for every operation which he may perform. This cannot, however, be effected without attention and application on his part. He must carefully observe every fact, and compare these facts. From a knowledge of particular facts, he will arrive at a knowledge of general facts, and thus general principles will become firmly fixed in his mind. A mere mechanical performance is not sufficient. As I observed above, Arithmetic is a science as well as an art: he must, therefore, study as well as figure. He should never put down a figure without considering what is to be the result, for one wrong figure will throw a whole question into derangement. 4. Every operation is governed by certain principles, and when these principles are clearly understood, the result is certain. How necessary is it, then, that the student should understand them? 5. The practice of Arithmetic consists, first, of the Writing and Reading of Figures, which may be called the language of B Arithmetic; and, secondly, of the calculation of numbers, written or conceived. The first of these divisions will form the subject of the following chapter. CHAPTER II. NOTATION AND NUMERATION. 6. NOTATION* is the art of expressing numbers in figures. 7. NUMERATIONt is the art of reading or enumerating numbers when expressed in figures. 8. For the purpose of expressing number, we have ten signs or characters. By these we are enabled to express all numbers, however large, or however small. 9. These characters are as follow: 1 One 3 Three 5 Five | 7 Seven | 9 Nine Four 6 Six 8 Eight 0 Cypher Of these characters, nine are called significant figures, to distinguish them from nought, or cypher. These significant figures have a certain fixed value in themselves, besides a relative value, which they acquire from position. Any of these figures, when placed alone, is of a certain fixed value, representing only the number which is assigned to it in the above table. The figure 6, for example, when so placed, means only six, and is called a simple number; but join to it another figure, 2, for instance, and its value becomes conditional, depending on its relative position with regard to the annexed figure. If the 2 be placed on the left of it, thus, 26, the value of the 6 remains unchanged; it expresses only six, and the two figures taken together express twenty-six. But change their position; place the 6 on the left of the 2, thus, 62, and the 6 becomes increased in value ten-fold; it now expresses sixty, and the 2, two, and the two figures taken together express sixty-two, and form a compound|| number. Annex another figure, thus, 620, and the 6 now expresses six hundred, and the 2, twenty. Both figures have acquired a still further augmentation of value-they are increased again ten times, and would continue to increase in the same ratio,** by every addition of a figure to the right hand. *Notation, from the Latin not-a, a mark. + Numeration, from the Latio numer-us, a number. Character, from a Greek word which signifies a mark or stamp. Significant; expressive, important, from the Latin sign-um, a mark, a sign, a seal. Compound, formed by the union of two or more; mingled; from com, with or together, and pon-o, to put, to place. ¶ Augmentation, the act of increasing. ✶✶ Ratio meaus in the same rate, proportion, or by the same difference. |