TUBLIC LIBRARY Entered, according to Act of Congress, 19th June, 1833, by Charles Davies, in the Clerk's office of the Southern Dis. trict of New York. 3 PREFACE. A CORRECT and accurate knowledge of Arithmetic is one of the most important elements of a liberal or practical edu. cation. The public should, therefore, receive with indulgence every attempt that may be made to improve this department of instruction. The Elementary Treatise, which is here presented, has been prepared with care, though the author by no means in. dulges the belief that it is free from faults. He has endeav. ored to render the subject as plain as it is capable of being made, and, at the same time, to treat it as briefly as possible. The reasons for most of the rules are given. It was not, however, thought best to demonstrate the rules for the ex. traction of roots, nor that for finding the sum of a geometri. cal series. The name, Compound Numbers, which has heretofore been given to all numbers in which the kind of unit is ex. pressed, has been changed to that of Denominate Numbers. This change has not been made with any ambitious spirit of innovation, but because it is deemed an improvement. It is not easy to form an idea of what is meant by the term, Com. pound Number, and especially so, when we find it applied to such numbers as £3, $3, 3s. Why is £3° a compound num. ber any more than 3? If it be answered, that £3 is composed or compounded of three single pounds, that does not remove the difficulty, for 3 is also composed of three units 1. Is it not then the better way to call the first a denominate num. ber, and the other a simple number, as is done in $ 71. Mr. Hasler, in his Arithmetic, has called this class of numbers, Denominate Fractions. Some of the examples in the Rule of Three, and most of those at the end of the book, have been selected from Hut. ton's and Walkingame's Arithmetics. Military Academy, 4 SUGGESTIONS TO TEACHERS. Tax first object has been to fix in the mind of the pupil a clear idea of a unit, this being regarded as the basis of all correct knowledge of Arithmetic. Each subject is divided into sections, and at the end of the subject, a series of questions is appended. All the questions which refer to the same section, are arranged together, and are intended to suggest to the pupil all that he is required to learn from the particular section to which they refer. The pupil should be able to answer all the ques. tions in his own language, and to understand perfectly the reasons of the answers. The parts to be committed to memory are printed in Italic, to distinguish them from those parts that are merely explanatory. 5 TABLE OF CONTENTS. Pago Subtraction of Simple Numbers, Multiplication of Simple Numbers, Reduction of Denominate Numbers, Addition of Denominate Numbers, Subtraction of Denominate Numbers, Multiplication of Denominate Numbera, Division of Denominate Numbers, Reduction of Vulgar Fractions, Reduction of Denominato Fractions, Subtraction of Vulgar Fractions, Multiplication of Vulgar Fractions, |