NEW AND EASY INTRODUCTION TO THE MATHEMATICS: CONTAINING, I. A SYSTEM OF THEORETICAL AND PRACTICAL ARITHMETIC, In which the Rules are simplified, the Theory of them is the labor of the Teacher. II. RULES FOR THE MENSURATION OF SUPERFICES AND SOLIDS, with their application to various prac- propriate examples. III. RULES FOR SOLVING A NUMBER OF USEFUL AND INTER IV. A COLLECTION OF INTERESTING MATHEMATICAL QUES- TIONS FOR EXERCISE. V. USEFUL TABLES, &C. DESIGNED FOR THE USE OF Schools, Academies, and Private Learners. BY IRA WANZER. "Make the rough path of Science plain to find, DANBURY, CONN. PRINTED AND PUBLISHED BY W. & M. YALE, SOLD AT THEIR BOOKSTORE, AND BY THE PRINCIPAL BOOK- SELLERS IN THE UNITED STATES. DISTRICT OF CONNECTICUT, ss. BE IT REMEMBERED, That on the twenty-fifth day of March, Anno Domini 1831, IRA WANZER, of the said District, bath deposited in this office the title of a Book, the title of which is in the words following, to wit: "A new and easy INTRODUCTION to the MATHEMATICS: Containing, 1. A System of THEORETICAL and PRACTICAL ARITHMETIC, in which the Rules are simplified, the Theory of them is explained, and the methods of operation are amply illustrated by many examples and familiar explanations, calculated to facilitate the improvement of the Learner and diminish the labor of the Teacher.-II. Rules for the Mensuration of Superfites and Solids, with their application to various practical purposes-illustrated by appropriate examples. III. Rules for solving a number of useful and interesting Mathematical, Philosophical and Chronological Problems. IV. A collection of interesting Mathematical Questions for exercise. - V. Useful Tables, &c.--Designed for the use of Schools, Academies, and private Learners. By IRA WANZER. Make the rough path of Science plain to find, And through its mazes lead the pleasur'd mind.' " The right whereof he claims as Author, in conformity with an act of Congress, entitled "An Act to amend the several Acts respecting Copy Rights." CHAS. A. INGERSOLL, Clerk of the District of Connecticut 6-18-31 34424 PREFACE. ABOUT two years since, the author of the following work, undertook the arduous task of composing an Introduction to the Mathematical Sciences, (which he intended should comprise Treatises on Arithmetic and Mensuration, and an Introduction to Algebra,) for the use of the citizens of the United States. Soon after he had determined on the plan of the work, he wrote the following Treatise on Arithmetic, and some other parts of the proposed work, but he was prevented, by ill health and other circumstances, from completing it according to his original design. He has since been advised by several respectable mathematicians to publish the System of Arithmetic, without delay, for the use of schools; and having lately revised the Treatise, and added a copious Appendix, containing much other useful matter, The now presents the work to the public. The work now offered to the public, contains a complete System of common Arithmetic, (including many recent improvements in the science, some of which have never before been published,) and also, some other parts of the Mathematics which are of general utility. In composing this system of Arithmetic, great pains have been taken to express the rules in plain, familiar language, and to adapt the illustrations of them to the capacities of learners. The most important rules are demonstrated, and their practical applications are amply illustrated. Many wrought examples are given, to elucidate the different rules; and these examples are, in general, accompanied by explanations, which will make the numerical operations easy to be understood by learners of the most ordinary capacities. Practical illustrations are also annexed to many of the questions for exercise, where difficulties occur. It is believed that some of the rules in this Treatise are new, and preferable to any other rules of their kind, and that some others are reduced to more commodious forms than they have heretofore been in books on Arithmetic. The author has given a general method of computing simple interest, and a method of extracting the cube roots of |