OTHE NORTH AMERICAN ARITHMETIC. PART THIRD, FOR ADVANCED SCHOLARS. BY FREDERICK EMERSON, BOSTON: JENKS, PALMER & CO. HARVARD COLLEGE LIBRARY FROM THE LIBRARY OF MRS. ELLEN HAVEN ROSS JUNE 28, 1938 Entered according to act of Congress, in the year 1834, by Frederick Emerson, in the Clerk's Office of the District Court of the District of Massachusetts. RECOMMENDATIONS. CAMBRIDGE, Oct. 31, 1834, To the Publishers of Emerson's Arithmetic.-Gentlemen-I have examined the Third Part of Mr. Emerson's Arithmetic, with great pleasure. The perspicuity of its arrangement, and the clearness and brevity of its explanations, combined with its happy adaptation to the purposes of practical business are its great recommendations. I hope it will soon be introduced into all our schools, and take place of the ill-digested Treatises, to which our instructers have hitherto been compelled to resort. Respectfully, BENJAMIN PEIRCE, [Professor of Mathematics and Nat. Philo. Harvard University. BOSTON, Nov. 10, 1834. To the Publishers of Emerson's Arithmetic.-I have carefully examined the Third Part of the North American Arithmetic, by Mr. Emerson; and am so well satisfied that it is the best treatise upon the subject, with which I am acquainted, that I have determined to introduce it as a text-book into my school. Very respectfully, &c., yours, E. BAILEY, [Principal of the Young Ladies' High School, Boston.] From the Boston Public Schoolmasters. BOSTON, Nov. 16, 1834. We have considered it our duty to render ourselves acquainted with the more prominent systems of Arithmetic, published for the use of schools, and to fix on some work which appears to unite the greatest advantages, and report the same to the School Committee of Boston, for adoption in the Public Schools. After the most careful examination, we have, without any hesitancy, come to the conclusion, that Emerson's North American Arithmetic [First, Second, and Third Parts] is the work best suited to the wants of all classes of scholars, and most convenient for the purposes of instruction. Accordingly, we have petitioned for the adoption of this work in the Public Schools. P. MACKINTOSH, JR. JAMES ROBINSON. OTIS PIERCE. ABEL WHEEeler. LEVI CONANT. J. FAIRBANK. Orders of the Boston School Committee. At a Meeting of the School Committee, Nov. 18, 1834, Ordered, That Emerson's North American Arithmetic, Second_and Third Parts, be substituted in the Writing Schools, for Colburn's First Lessons and Sequel.* Ordered, That the Arithmetics now in use be permitted to their present owners; but that whenever a scholar shall have occasion to purchase a new one, the North American Arithmetic shall be required. Attest, S. F. M'CLEARY, Secretary. *The FIRST PART was already adopted, by a previous order. PREFACE. THE work now presented, is the last of a series of books, ander the general title of THE NORTH AMERICAN ARITH METIC, and severally denominated Part First, Part Second, and Part Third. PART FIRST is a small book, designed for the use of children between five and eight years of age, and suited to the convenience of class-teaching in primary schools. PART SECOND consists of a course of oral and written exercises united, embracing sufficient theory and practice of arithmetic for all the purposes of common business. PART THIRD Comprises a brief view of the elementary principles of arithmetic, and a full development of its higher operations. Although it is especially prepared to succeed the use of Part Second, it may be conveniently taken up by scholars, whose acquirements in arithmetic are considerably less than the exercises in Part Second are calculated to afford. While preparing this book, I have kept in prominent view, two classes of scholars; viz.—those who are to prosecute a full course of mathematical studies, and those who are to embark in commerce. In attempting to place arithmetic, as a science, before the scholar in that light, which shall prepare him for the proper requirements of college, I nave found it convenient to draw a large portion of the examples for illustration and practice, from mercantile transactions; and thus pure and mercantile arithmetic are united. No attention has been spared, to render the mercantile information here presented, correct and adequate. Being convinced, that many of the statements relative to commerce, which appear in books of arithmetic, have been transmitted down from ancient publications, and are now erroneous, I have drawn new data from the counting-room, the insurance office, the custom-house, and the laws of the present times The article on Foreign Exchange is comparatively extensive, and I hope it will be found to justify the confidence of merchants. Its statements correspond to those of the British 'Universal Cambist,' conformably with our value of foreign coins, as fixed by Act of Congress, in 1834. Although a knowledge of arithmetic may, in general, be well appreciated as a valuable acquisition, yet the effect produced on intellectual character, by the exercises necessary for acquiring that knowledge, is not always duly considered. In these exercises, the mental effort required in discovering the true relations of the data, tends to strengthen the power of comprehension, and leads to a habit of investigating; the certainty of the processes, and the indisputable correctness of the results, give clearness and activity of thought; and, in the systematic arrangement necessary to be observed in performing solutions, the mind is disciplined to order, and accustomed to that connected view of things, so indispensable to the formation of a sound judgment. These advantages, however, depend on the manner in which the science is taught; and they are gained, or lost, in proportion as the teaching is rational, or superficial. Arithmetic, more than any other branch of learning, has suffered from the influence of circumstances. Being the vade-mecum of the shop-keeper, it has too often been viewed as the peculiar accomplishment of the accountant, and neglected by the classical student. The popular supposition, that a compendious treatise can be more easily mastered than a copious one, has led to the use of textbooks, which are deficient, both in elucidation and exercises. But these evils seem now to be dissipating.-The elements of arithmetic have become a subject of primary instruction; and teachers of higher schools, wno nave adopted an elevated course of study, are no longer satisfied with books of indifferent character. It has been my belief, that a treatise on arithmetic might be so constructed, that the learner should find no means of proceeding in the exercises, without mastering the subject in his own mind, as he advances; and, that he should still be enabled to proceed through the entire course, without requiring any instruction from his tutor. Induced by this belief, I commenced preparing The North American Arithmetic about five years since; and the only apology I shall offer, for not earlier presenting its several Parts to the public, is the unwillingness that they should pass from my hands, while I could see opportunity for their improvement. Boston, October 1834. F. EMERSON. A KEY to this work (for teachers only) is published separately. ARITHMETIC. ARTICLE I. DEFINITIONS OF QUANTITY, NUMBERS, AND ARITHMETIC. QUANTITY is that property of any thing which may be increased or diminished-it is magnitude or multitude. It is magnitude when presented in a mass or continuity; as, a quantity of water, a quantity of cloth. It is multitude when presented in the assemblage of several things; as, a quantity of pens, a quantity of hats. The dea of quantity is not, however, confined to visible objects; it has reference to every thing that is susceptible of being more or less. NUMBERS are the expressions of quantity. Their names are, One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, &c. In quantities of multitude, One expresses a UNIT; that is, an entire, single thing; as one pen, one hat. Then each succeeding number expresses one unit more than the next preceding. In quantities of magnitude, a certain known quantity is first assumed as a measure, and considered the unit; as one gallon, one yard. Then each cucceeding number expresses a quantity equal to as many times the unit, as the number indicates. Hence, the value of any number depends upon the value of its unity. When the unit is applied to any particular thing, it is called a concrete unit; and numbers consisting of concrete |