ARITHMETIC. DEFINITIONS. 1. A SINGLE THING is called one or a unit. 2. A NUMBER is a unit, or a collection of units. The unit is called the base of the collection. The primary base of every number is the unit one. 3. Each of the words, or terms, one, two, three, four, &c., denotes how many things are taken. These terms are generally called numbers; though, in fact, they are but the names of numbers. 4. The term, one, has no reference to the kind of thing to which it is applied and is called an abstract unit. 5. An abstract number is one whose unit is abstract: thus, three, four, six, &c., are abstract numbers. 6. The term, one foot, refers to a single foot, and is called a denominate unit: hence, 7. A denominate number is one whose unit is named, or denominated: thus, three feet, four dollars, five pounds, are denominate numbers. These numbers are also called concrete numbers. 1. What is a single thing called? 2. What is a number? What is the unit called? What is the primary base of every number? 3. What does each of the words, one, two, three, denote? What are these words generally called? What are they, in fact? 4. Has the term one any reference to the thing to which it may be applied? What is it called? 5. What is an abstract number? Give examples of abstract numbers. 6. What does the term one foot refer to? What is it called? 7. What is a denominate number? Give examples of denominate numbers. What are denominate numbers, also called? 8. A SIMPLE NUMBER is a single collection of units. 9. QUANTITY is any thing which can be increased, diminished and measured. 10. SCIENCE treats of the properties and relations of things: ART is the practical application of the principles of Science. 11. ARITHMETIC treats of numbers. It is a science when it makes known the properties and relations of numbers; and an art, when it applies principles of science to practical purposes. 12. A PROPOSITION is something to be done, or demonstrated. 13. An ANALYSIS is an examination of the separate parts of a proposition. 14. An OPERATION is the act of doing something with numbers. The number obtained by an operation is called a result, or answer. 15. A RULE is a direction for performing an operation, and may be deduced either from an analysis or a demonstration. 16. There are five fundamental processes of Arithmetic: Notation and Numeration, Addition, Subtraction, Multiplication and Division. EXPRESSING NUMBERS. 17. There are three methods of expressing numbers: 1st. By words, or common language; 2d. By capital letters, called the Roman method; 3d. By figures, called the Arabic method. 8. What is a simple number? 9. What is quantity? 10. Of what does Science treat? What is Art? 11. Of what does Arithmetic treat? When is it a science? When an art? 12. What is a Proposition? 13. What is an Analysis 14. What is an Operation? What is the number obtained called? 15. What is a Rule? How may it be deduced? 16. How many fundamental rules are there? What are they? 17. How many methods are there of expressing numbers? What are they? |