PREFACE. This work is designed to furnish Schools with a methodical, comprehen. sive and practical system of Arithmetic; in which it has been the study of the Authors to render it a useful and easy text-book for Instructors, and also to convey instruction in an easy, concise and familiar manner to the pupil. The Authors are not disposed to derogate the merits of any system of Aríthmetic now before the public, of which there is a great variety, and many meritorious works; none of which, perhaps, has received a greater share of public patronage than Daboll's Schoolmaster's Assistant : But it must be obvious to teachers of Arithmetic, and also to men of business, that Arithmetics written some thirty or forty years ago, however complete they were considered at that time, are now become more or less obsolete. One objection to those which were written about the time Federal Money was coming into use, is, that they are too much intermixed with, and contain more of the old currency or Sterling Money, than is necessary at the present day. Another objection to those of long standing is, a deficiency of proper illustrations of the rules and examples. To remedy these defects, a variety of Arithmetics have been compiled by different authors and published within a few years past. But for the use of Schools generally, there are in the opinion of experienced teachers some objections to them all: for while the older publications have pursued too much of an arbitrary, dogmatic course of instruction; other more modern writers have pursued almost wholly the inductive or mental plan, leaving the pupil to solve without proper and concise rules nearly all questions in Arithmetic; and thus in endeavoring to correct one error, have, as regards Common Schools, run into another as great. A small introduction to the ground rules of Arithmetic, on the inductive or mental plan, may be useful: but considering that our Common Schools are made up principally of the children of mechanics, farmers, and working-men, whose time, allotted them to obtain a knowledge of Arithmetic and other branches of literature, is but a few months in each year, for a short period of years; to require them to perform the various operations in Arithmetic without plain, concise rules and illustrations, is as inconsistent as it would be to require each laboring man in the community, to make every implement of his particular trade, before he could enter upon the business of his occupation. In the execution and arrangement of “DABOLL'S COMPLETE SCHOOLMASTER'S ASSISTANT,” now offered to the public, it has been the object of the Authors alike to guard against the dogmatic course pursued in Arithmetics of long standing, and also the deficiency of concise rules, so apparent in some of the more modern ones. In this work the Authors have given a short introduction to the first rules, on the inductive or mental plan of instruction, after which, it has been their object to give the rules, examples and illustrations, in a manner so clear and familiar as to be easily comprehended by the pupils, and also, to convey to their minds the reason of the same. They have also pursued a course of questioning on the rules, which will be found beneficial to the pupil, and convenient to the instructor. It is not the design of this work, to call forth the deep research of men of science, but rather to develope to the juvenile mind, a plain, easy and pleasing ascent, in the science of practical Arithmetic. The arrangement of the rules and examples in this work is such as is believed to be the most proper. Addition and Subtraction of Federal Money are placed immediately after Addition and Subtraction of whole numbers. Reduction, Multiplication and Division of Federal Money, with simple and concise rules for finding the cost of goods, &c. when the price is an aliquot or even part of a dollar, are placed immediately after Division of whole numbers. In Reduction Ascending and Descending, the answers to the questions are not set down, as they alternately prove each other. Fractions, Vulgar and Decimal, have received that attention which their importance demands; being simplified and illustrated in such a manner as to render the study of them pleasing and interesting to the pupil. In Simple Interest several short rules are given. Also explanatory ob. servations, and remarks on casting Interest on notes, bonds, &c. where endorsements have been made. The rule called Practice is omitted, except so much as is now necessary in business. That part of the rule formerly called “Tare and Tret” which relates to trett, cloff, and sutile, is omitted, it being entirely obsolete. A short demonstration of the Square and Cube Roots is given; and the rules for working Arithmetical and Geometrical Progression, will be found very plain and concise. After going through the various rules, a collection of useful and entertaining questions is given for exercise. The Appendix contains a variety of useful Problems in Mensuration, &c. Also a concise method of BOOK-KEEPING, adapted to the Business of Farmers, Mechanics, &c. Some of the late writers on Arithmetic, have wholly expunged the old currency of Sterling Money ; but considering the increasing facilities to commerce, and the contiguity of these States to the British dominions; the Au. thors have thought proper to retain enough of Sterling Money, to show its use and nature. TABLE OF CONTENTS. Multiplication of Federal Money, To reduce fractions to their lowest terms, To change a whole or mixed number to an improper fraction, To change an improper fraction to a whole or mixed number, 'To multiply a whole number by a fraction, To multiply a fraction by a whole number, To divide a fraction by a whole number, . To reduce a given quantity to a fraction, . To find the value of a fraction in whole numbers, To find the greatest common divisor of two numbers, To find the least common multiple of two or more numbers, Reduction of Vulgar Fractions, Addition of Vulgar Fractions, . Subtraction of Vulgar Fractions, Multiplication of Vulgar Fractions, Rule of Three Ďirect in Vulgar Fractions, Commission, Brokerage, Insurance, &c. Compound Interest by Decimals, Extraction of the Square Root, Annuities at Compound Interest, APPENDIX.--SUPERFICES. To find the area of a Parallelogram, or long square, To find the solidity of a cube, To find the contents of any regular solid, The breadth and thickness given, to find how much in length will To measure a cylinder, pyramids and cones, To find how many solid feet a round stick of timber will make, &c. 239 To find the contents of a globe, and vessel, 239, 240 To find how many bricks a building of given size will contain, 240 ADDITION TABLE: 1 are 2 and 1 are 31 3 and are 41 4 and I are 5 and 1 are 6 2 and 2 are 4 3 and 2 are 5! 4 and 2 are 6 5 and 2 are 7 2 and 3 are 5 3 and 3 are 6 4 and 3 are 75 and 3 are 8 2 and 4 are 6 3 and 4 are 7 4 and 4 are 8! 5 and 4 are 9 2 and 5 are 7 3 and 5 are 8l 4 and 5 are 9 5 and 5 are 10 2 and 6 are 8l 3 and 6 are 9 4 and 6 are 10 5 and 6 are 11 2 and 7 are 9 3 and 7 are 104 and n are 11 5 and 7 are 12 2 and 8 are 10 3 and 8 are 11 4 and 8 are 12) 5 and 8 are 13 2 and 9 are 11) 3 and 9 are 12 4 and 9 are 13 5 and 9 are 14 2 and 10 are 12 3 and 10 are 134 and 10 are 14/ 5 and 10 are 15 2 and 11 are 13 3 and 11 are 14 4 and 11 are 15) 5 and 11 are 16 2 and 12 are 14 3 and 12 are 15 4 and 12 are 16) 5 and 12 are 17 6 and 1 are 77 and 1 are 81 8 and 9 9 and 1 are 10 6 and 2 are 81 7 and 2 are 9 8 and 2 are 10 9 and 2 are 11 6 and 3 are 9 7 and 3 are 108 and 3 are 11| 9 and 3 are 12 6 and 4 are 10 7 and 4 are 11 8 and 4 are 12 9 and 4 are 13 6 and 5 are 117 and 5 are 12 8 and 5 are 13 9 and 5 are 14 6 and 6 are 12 7 and 6 are 13 8 and 6 are 14 9 and 6 are 15 6 and 7 are 13 7 and n are 14 8 and 7 are 15 9 and 7 are 16 6 and 8 are 14 7 and 8 are 15 8 and 8 are 16 9 and 8 are 17 6 and 9 are 15 7 and 9 are 16 8 and 9 are 17 9 and 9 are 18 6 and 10 are 167 and 10 are 17 8 and 10 are 18 9 and 10 are 19 6 and 11 are 17 7 and 11 are 18 8 and 11 are 19 9 and 11 are 20 6 and 12 are 181 7 and 12 are 19 8 and 12 are 2019 and 12 are 21 10 and I are 1110 and 10 are 20/11 and are 18112 and 4 are 16 10 and 2 are 12 10 and 11 are 21/11 and 8 are 19 12 and 5 are 17 10 and 3 are 1310 and 12 are 22 11 and 9 are 2012 and 6 are 18 10 and 4 are 1411 and 1 are 1211 and 10 are 21 12 and 7 are 19 10 and 5 are 1511 and 2 are 13 11 and 11 are 22 12 and 8 are 20 10 and 6 are 16 11 and 3 are 1411 and 12 are 23 12 and 9 are 21 10 and 7 are 17 11 and 4 are 15/12 and I are 13 12 and 10 are 22 10 and 8 are 1811 and 5 are 16 12 and 2 are 14 12 and 11 are 23 10 and 9 are 1911 and 6 are 1712 and 3 are 15 12 and 12 are 24 Signs. A cross + with one line perpendicular and the other horizontal, is the sign of addition. It shows that the numbers between which it is placed are to be added together. It is sometimes read plus, which is a Latin word signifying more. It also denotes a remainder after division. Two horizontal parallel lines =, are the sign of equality. It signifies that the number before it is equal to the number after it. Thus, 100 cents=1 dollar ; read, 100 cents are |