short and plain manner, and each rule is illustrated, with a few easy and familiar examples, gradually proceeding from that which is simple, to such as are more abstruse and difficult. 3d. Clearness and precision in the definitions, directions, and examples. Carefully explaining every technical term when first used, and thereby guarding against ambiguity and uncertainty. 4th. Brevity in each part, so that every thing useless, or unimportant, may be excluded; in order that the work may find its way into schools at the cheapest rate; that parents, when examining the schoolbooks of their children, may not find, whilst one part is worn out, the other is untouched, and half the price of the book entirely lost. How far these objects have been obtained, must be left to the decision of time. Should the work be found to aid the progress of scholars, in acquiring a practical knowledge of this useful science-to save expenses in a book, so many of which are required; and be found a useful assistant to merchants, mechanics, and farmers, as well as in some degree to lessen the labor of teachers in this branch of the sciences; the compiler will have obtained his object. NOTICE TO THE FOURTH EDITION. THE favorable reception, and wide circulation, of the former edi. tions of the Western Calculator, stimulate the author to make it still more deserving of public patronage. He has, therefore, at the suggestion of several respectable teachers, given sundry additional questions to some of the rules; and also some other alterations, which several years' experience in teaching has pointed out. The greatest care has been taken to prevent errors from appearing in this edition. Pittsburgh, February 1, 1823. APHORISMS FOR THE SCHOLAR'S CAREFUL CONSIDERATION AND ATTENTION. KNOWLEDGE is the chief distinction between wise men and fools; between the philosopher and the savage. The common and necessary transactions of business cannot be conducted with profit or honesty, without the knowledge of Arithmetic. He who is ignorant of this science must often be the dupe of knaves, and pay dear for his ignorance. Banish from your mind, idleness and sloth, frivolity and trifling; they are the great enemies of improvement. Make study your inclination and delight; set your hearts upon knowledge. Accustom your mind to investigation and reflection; determine to understand every thing as you go along. Commit every rule accurately to memory, and never rest satisfied until you can apply it. As much as possible do every thing yourself; one thing found out by your own study, will be of more real use than twenty told you by your teacher. Be not discouraged by seeming difficulties; patience and application will make them plain. Endeavor to be always the best scholar in your class, and to have the fewest mistakes, or blots, in your book. "The wise shall inherit honor, but shame shall be the promotion of fools." A 2 EXPLANATION OF THE SEVERAL CHARACTERS EMPLOYED FOR THE SAKE OF BREVITY, IN THIS TREATISE. Two parallel lines, signifying equality: as, 100 cents= 1 dollar; that is, 100 cents are equal to 1 dollar. +Signifying more, or addition: as, 6+4=10; that is, 6 and 4 added make 10. This character is called Plus. -A single line, signifying less, or subtraction as, 6-4 This character is × Signifying Multiplication: as, 2 x 4-8; that is, 2 multiplied by 4 is equal to 8. Signifying Division: as, 6÷3=2; that is, 6 divided by 3 is equal to 2. Signifying Proportion: as, 2:46:12; that is, as 2 is to 4, so is 6 to 12; or, that there is the same proportion between 6 and 12, as there is between 2 and 4. 2 ✔or Signifying the square root of the number before which it is placed: as, √64=8; that is, the square root of 64 is 8. Signifying the cube root: as, 64-4; that is, the cube root of 64 is 4. A Vinculum, or chain: denoting the several quantities over which it is placed, are to be considered as one simple quantity THE WESTERN CALCULATOR. PART 1. ARITHMETIC IN WHOLE NUMBERS. ARITHMETIC is the art, or science, of computing by numbers, and is generally divided into five principal parts, or primary rules: viz. Numeration, Addition, Subtraction, Multiplication, and Division. SECTION 1. OF NUMERATION. NUMERATION (or, as it is often called, Notation) is the art of expressing any given or supposed number, by the ten following characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The first of these is called a cipher, the rest are termed digits or figures. These nine digits are divided into three periods, three ir. each period. The first period includes units, tens, and hundreds. The second period includes thousands, tens of thousands, hundreds of thousands. The third period includes millions, tens of millions, hundreds of millions. Note. The cipher is also called nought and zero. They are all Arabic characters. The relative value of each period, and the different figures in each period, may be learned from the following After the foregoing table, with the preceding definitions and explanations, are well explained by the teacher, and accurately committed to memory by the pupil, let him next proceed To write Numbers, Observing carefully the following RULE. Write down first, the given sum, in such figures as express its value, and then supply the deficiencies therein with ciphers Application. Write down in figures the following numbers. 1. Sixteen. 2. Forty-nine. |