DESIGNED FOR ACADEMIES AND SCHOOLS; UNITING THE INDUCTIVE REASONING OF THE FRENCH ENGLISH SYSTEM. AUTHOR OF FIRST LESSONS IN ARITHMETIC, UNIVERSITY ARITHMETIC ; INTEGRAL CALCULUS. NEW YORK: No. 51 JOHN-STREET. BOARD OF COMMISSIONERS OF PUBLIC SCHOOLS, BALTIMORE, August, 1842. At a meeting of the Board of Camininsióners of Public Schools, Baltimore, to hear the report of the Book Committee, upon Davies' Elementary Series. The celowing resolution was offered, and adopt ed: Resolved, - That Davies' FIRST LESSONS IN ARITHMETIC, DAVIES' JAMES LUCAS, Commissioners. JOHN F. TILYARD, Clerk. 35347 CHAMBER OF THE CONTROLLERS OF PUBLIC SCHOOLS, FIRST SCHOOL DISTRICT OF PENNSYLVANIA. Philadelphia, September 15, 1842. Resolved, -That Davies' FIRST LESSONS IN ARITHMETIC, and Davies' THOMAS B. FLORENCE, Secretary. Entered, according to Act of Congress, in the year 1847, BY CHARLES DAVIES, District of New York. Stereotyped by New York. C. A. ALVORD, Printer, PREFACE. SCIENCE has been well defined to be knowledge reduced to order ; that is, knowledge so classified and arranged as to be easily remembered, readily referred to, and advantageously applied. ARITHMETIC is the science of numbers, and a correct and accurate knowledge of it is one of the most important elements of a liberal or practical oducation. It is the corner-stone of the exact and mixed sciences, and the first subject in a well-arranged course of instruction to which the reasoning powers of the mind are applied—yet in all that relates to the uses and applications of numbers, it is the guide and daily companion of the mechanic and man of business. These two objects have been kept constantly in view in the preparation of this work-yiz. : 1. To present to the young mind, unacquainted with the inethods of exact reasoning, the elementary principles of arithmetic in their simplest form and combination. II. To explain and illustrate the various applications of arithmetic in the transactions of business, and thus make known its great practical utility. To attain the first of these ends the following method has been adopted. 1. To present to the mind every now idea by a simple question, and then to express the idea in general terms under the form of a definition or principle. 2. When a sufficient number of ideas are thus fixed in the mind, they are combined, forming a proposition or rule ; so that the separate elements are arranged in the order of exact reasoning, as fast as they are learned. 3. An entire system of Mental or Oral Arithmetic has been earried forward in connection with the text, by means of a connected series of questions placed at the bottom of each page ; and if these, or their equivalents, are carefully put by the teacher, the pupil will understand the reasoning in every process, and at the same time cultivate the powers of analysis and abstraction. 4. The better to attain these objects, the Arithmetic has been divided into paragraphs or sections, each containing a number of connected principles and these paragraphs constituto a series of dependant propositions that make up the entire system of reasoning which the work develops. The Oral Arithmetic corresponds with these connected propositions. The subject of Fractions, will perhaps best illustrate the advantages of this method. In regard to the second part, the table of contents, under the head of “ APPLICATIONS TO BUSINESS," and “MENSURATION," shows how large a portion of the work has been given to what may justly be termed the PRACTICAL AND USEFUL. The First Lessons in Arithmetic, the School Arithmetic, and the University Arithmetic, embrace a series of works on the subject of numbers which are designed to meet the wants of different classes of pupils. The first work is for beginners. It treats of the simplest properties of numbers, and although but the alphabet of the science, yet that alphabet is the basis of all subsequent combinations. The School Arithmetic is an entire and complete treatise, and embraces all the subjects usually taught in academies and schools. The University Arithmetic is also a treatise of itself. It contains much that is found in the School Arithmetic, but the reasoning is more elaborate and the difficult and hidden properties of numbers more fully developed. The proof of the four ground rules by means of the Properties of the 9's, the subject of Circulating or Repeating Decimals,-of Coins, Currencies, and general Exchanges of Bookkoeping by Double Entry, are all treated in the larger work, which may be studied to great advantage by higher classes and all who desire to obtain a thorough and full knowledge of the wonderful properties of numbers and their numerous applications. New YORK, June, 1847. ! CONTENTS. PIRST FIVE RULES. Subtraction of Simple Numbers.... Applications in Addition and Subtraction.. Multiplication of Simple Numbers |