CONTENTS. When the sum of a column does not exceed 9, When the sum of a column exceeds 9, When a figure in the lower number is larger than that above it, 43 Illustration of the principle of borrowing, SECTION VIL The standard unit of Weight of the United States, The standard unit of Length of the United States, The standard unit of Liquid Measure of the United States, When the number of articles, and the cost of the whole When the price of one article and the cost of the whole are given, to find the number of articles, Applications of Federal Money to Bills, &c., Simple Proportion, or Rule of Three, Simple Proportion by Cancellation, Applications of Square Root, ARITHMETIC. SECTION I. ART. 1. ARITHMETIO is the science of numbers. OBS. Arithmetic is sometimes regarded both as a science and an art; a science, because it explains the relations and properties of numbers; an art, because it shows how to apply them to the practical concerns of life. 2. Any single thing, as a peach, a rose, a book, is called a unit, or one; if another single thing is put with it, the collection is called two; if another still, it is called three; if another, four; if another, five, &c. The terms, one, two, three, &c., by which we express how many single things or units are under consideration, are the names of numbers. Hence, 3. NUMBER signifies a unit, or a collection of units. Numbers are expressed by words, by letters, and by figures. Note.-The questions on the observations may be omitted, by beginners, till review, if deemed advisable by the Teacher. NOTATION. 4. NOTATION is the art of expressing numbers by letters or figures. There are two methods of notation in use, the Roman and the Arabic. QUESTIONS.-1. What is Arithmetic? 2. What is a single thing called? If another is put with it, what is the collection called? If another, what? What are the terms one, two, three, &c.? 3. What, then, is number? How are numbers expressed? 4. What is Notation? How many methods of notation are in use? |