Part, a portion is reserved for the Second Part, which will treat of Fractions and the higher departments of the science. No abstract rules have been introduced, but the various modes of working examples have been carefully elucidated. This plan has been adopted from the persuasion that Arithmetic when taught by rules, fails to awaken, and bring into active play, the reasoning powers of children. And further, that no rules, however carefully drawn up, can produce in youthful minds that clear comprehension of the reason of arithmetical operations which results from the synthetic explanation of the successive steps of a solution. By the use of this Manual, it is confidently believed that a young person, of ordinary capacity, will be able to acquire a well-grounded knowledge of the Elementary Principles of Arithmetic; and with this conviction it is now respectfully submitted to the public. Royal Naval Schools, December, 1849. E. H. ARITHMETIC. 1. ARITHMETIC teaches us the method of computing by numbers. 2. Suppose that you had to count a number of apples-say twenty-and that you began by saying one, and then proceeded by saying two, three, four, five, and so on till you had counted them all. apple is here called the unit. One Again, if you had to count a number of books, one book would be called the unit; the number of boys in the school,-a boy would be the unit; the number of panes of glass in the school-room windows,-a pane of glass would be the unit. If you had to measure the number of yards in a piece of cloth, a yard of cloth would be the unit; the number of gallons in a large vessel of water,-a gallon of water would be the unit, and so on. Any thing may be a unit,-a length, a weight, or a time, as the case may be, but it can be a unit only for things of its own kind, as the unit is one of the things that are counted or measured. If a school consisted of fifty boys and fifty girls, a boy would be the unit in the number of boys, and a girl the unit in the number of girls; but if we said there were one hundred children in the school, then a child, which means either boy or girl, would be the unit. We speak of a hundred head of cattle, though some of them may be horses, some cows, and some sheep; or a hundred head of game, though some may A be pheasants, some hares, and some rabbits, &c.; in each case we mean one hundred separate heads of animals. Any of the above units, or a single article of any kind, as a penny, a shilling, a pound, a yard, &c., is represented in calculation by the symbol 1, called one, which is itself the unit of arithmetic, every other number being a collection of ones or units. 3. If we had to count a number of persons or things, as men, women, boys, girls, books, slates, pens, birds, trees, apples, &c.,-the number counted could be represented by short upright lines; for example, suppose I begin to count my fingers, holding them up one after the other, and that I place in groups upon a slate or black board as many short upright lines as there are fingers held up at the same time. This being done, the groups of lines will appear thus: Now if I had to count a hundred or more articles of any kind, and to represent them by means of short lines, the writing down of so many lines would not only be troublesome, but the difficulty of readily seeing how many were written would lead to confusion and, consequently, to mistakes. In order to avoid this inconvenience, numbers are expressed by means of the following ten signs or figures, whose names and the number of marks for which they stand are placed over them. Nought, 0, called also cipher or zero, has no value, |
