PUBLISHER'S NOTICE. WHEREVER used, Felter's admirable Text-books have been pronounced by practical Teachers to contain the most perfect system of arithmetical instruction published. The grading of the books is simple, systematic, and complete, and peculiar to the series. The works are the result of a long experience and service in the school-room, and it is believed they will meet the requirements of every grade of schools. The series consists of the following books: Felter's First Lessons in Arithmetic. (Illustrated.) Felter's Intermediate Arithmetic. Felter's Grammar-School Arithmetic. Felter's Intellectual Arithmetic. Felter's High-School Arithmetic.* (In preparation.) FOR TEACHERS. Felter's Manual of Instruction. FELTER'S FIRST LESSONS is illustrated with more than sixty original engravings executed in the finest style of art, and forms one of the most attractive books for the young ever published. FELTER'S PRIMARY is also elegantly illustrated with a number of suggestive engravings, illustrating the Fundamental Rules and Denominate Tables. FELTER'S GRAMMAR - SCHOOL follows the INTERMEDIATE, and it is believed to contain the best and most practical collection of problems, involving the transactions of the market, the store, the bank, the counting - house, and the mechanic, ever before offered to teachers. N. B. For the use of those who prefer it, the INTermediate and GramMAR-SCHOOL books are bound in one volume, and called the "PRACTICAL." Copies, postage paid, of any of the series sent to any Teacher for EXAMINATION on the receipt of ONE-HALF the usual retail price. Correspondence solicited. *This book is intended expressly for High-Schools and Universities, where particular attention is given to the theory of numbers and advanced commercial instruction. * To the Teacher. Children generally enter school at about the age of six or of seven years, and seldom finish the subject of Commercial Arithmetic before the age of fifteen or sixteen. This volume, which is meant to follow the INTERMEDIATE ARITHMETIC, is designed to occupy pupils during three years, and give them complete instruction in all common business transactions, as well as a special preparation for those who wish to enter a course of study in the higher mathematics. The Author suggests the following nine-year course of study in Arithmetic with the use of this book. N. B.-Nothing is to be gained and much may be lost by hurrying scholars on from subject to subject, and from book to book. TEACH EACH SUBJECT THOROUGHLY BEFORE LEAVING IT. * Experience proves that the age of seven is preferable, by far, for the good of the pupil, in the matter of mental discipline, as well as of economy in time. ARITHMETIC. SECTION I. DEFINITIONS, NOTATION, AND NUMERATION. 1. A Unit.-One of any kind of things is called a unit; as 1 apple, 1 cow, 1 peach, 1 dozen, 1 fourth. ILLUSTRATION.*-Since 1 cow, 1 peach, represent each a single thing, they are therefore, units. 2. A Number.-An expression that tells how many is called a number; as, 1 3, 5, 4 horses, 7 apples, 5 ninths. 3. A Concrete or Denominate Number.-A unit. or a collection of units, the kind of which is expressed, is called a concrete or denominate number; as, 1 bird, 7 sheep, 13 pears, 3 elevenths, 2 ounces. 4. An Abstract Number.-A unit or a collection of units, the kind of which is not expressed, is called an abstract number; as, 1, 7, 8, 6. 5. Arithmetic treats of numbers; as, 4 apples and 3 apples are 7 apples; 8 less 5 are 3. *NOTE FOR THE TEACHER.-The pupil should be required to illustrate at the black-board, each of the definitions in the work, in the same way. NOTATION AND NUMERATION. 6. Notation.- A method of expressing numbers either by words, letters, or figures, is called notation. 7. The Roman method uses the letters I, V, X, L, C, D, M; and is chiefly used in numbering the chapters, sections, and other divisions of books. (a.) TABLE OF THE ROMAN NOTATION. (b.) All other numbers are expressed by the use of these letters repeated or combined, as: 1. XL. Read the following numbers from the book at recitation : The teacher should by no means omit to question the class thoroughly on each subject; and by illustrations and suggestions to develop in the mind of the pupil a clear conception of the idea contained in the definition, proposition, or problem, before requiring it to be committed to memory. The following notes and hints are merely suggestive, and are not intended to be either systematic or complete. No book can take the place of a living teacher, neither can any teacher follow any prescribed method of instruction, for by so doing he sacrifices that individuality which is essential to success. (c.) The value of a letter is repeated as many times as the letter itself is repeated; as, XXX, thirty; CC, two hundred. (d.) If a letter of less value be written before a letter of greater value, the value of the less is subtracted from that of the greater; as, X., ten, IX, nine; L., fifty, XL., forty. (e.) If a letter of less value be written after a letter of greater value, the value of the less is added to that of the greater; as, V., five, VI,, six, M., one thouand, MD., fifteen hundred. (f.) A dash (—) placed over a letter or a combination of letters repeats the value a thousand times; as, X., ten, X., ten thousand; XII., twelve, XII., twelve thousand. 8. The Arabic Notation is generally used in arithmetic. It consists of ten characters, or figures, nine of which are called digits, and have each a simple and a local value. They are: 9. The Simple Value of a figure is the one expressed by it when standing alone, or in the units' place of a number. 10. The Local Value of a figure is that which depends upon the place which the figure occupies in a number; thus, in 37, the figure 3 denotes thirty; and in 904, 9 denotes nine hundred 11. The Naught or Cipher (0) has no value, but is used to show that the place of a denomination is vacant; thus, in the number 6074, the place of hundreds being vacant it is occupied by a cipher. NUMERATION. 12. Numeration is the art of naming in order, the places occupied by the figures which represent a number. |