Series of Mathematics, The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of MATHEMATICAL TEXT-BOOKS Cver issued in this country. 57040 Robinson's Progressive Table Book, Robinson's Progressive Primary Arithmetic, - Robinson's Arithmetical Examples, Robinson's New Elementary Algebra, Robinson's Key to Elementary Algebra, · Robinson's University Algebra, Robinson's Key to University Algebra, Robinson's New University Algebra, Kiddle's New Elementary Astronomy, Robinson's University Astronomy, Robinson's Mathematical Operations, Robinson's Key to Geometry and Trigonometry, Conic Entered, according to Act of Congress, in the year 1864, by DANIEL W. FISH, A.M., In the Clerk's Office of the District Court of the United States, for the Northern District of New York. PREFACE. In the preparation of this work, it was not designed to make a book to take the place of any other, nor one to constitute a necessary part of the series to which it belongs, nor to adapt it to the use of beginners, or those commencing the study of Arithmetic; but it was prepared to meet a demand in graded and advanced schools for a larger number of carefully prepared and practical examples for review and drill exercises than are furnished from ordinary text-books; and it may be used in connection with any other series of Arithmetics. Of course, it is no substitute for a systematic treatise. On the contrary, its leading aim is to bring together promiscuously a large number of practical examples, involving nearly all the principles and ordinary processes of common Arithmetic, and designed thoroughly to test the pupil's judgment; to bring into use his knowledge of the theory and applications of numbers; to cultivate a habit of patient investigation and self-reliance; to test the truth and accuracy of his own processes by proof-the only test he will have to depend upon in all the computations in real business transactions in after life; in a word, to make him independent of the text-book, and of written rules and analysis. Although the examples are promiscuous, yet there is a general classification of them, the work being divided into six chapters. The first chapter presents the Standards and Tables of Weights and Measures; the second involves the applications of the Simple Rules of Arithmetic; the third embraces Common and Decimal Fractions; the fourth takes in Compound and Denominate Numbers; the fifth involves Percentage, in all its varied applications; and the sixth comprehends all other subjects properly belonging to this science. The examples in each chapter involve the combination and application of the principles and processes contained in the preceding ones, but not to any extent those of the following chapters. Classes, therefore, that, in regular course, have gone over the Simple Rules of Arithmetic only, will find in the second chapter of this book all they need in the way of supplementary examples for drill and review. Those who have finished, in any systematic treatise, the study of Fractions, will here have in chapter third proper exercises to try their skill in this part of the science; and so they may proceed by successive reviews, till the same searching test comes to be applied to every part of the subject. Two editions are printed; one with answers at the close of the book, for the use of teachers, so that when different members of the same class obtain different results to the same example, he may decide which is correct, without being obliged to take the time nece ary to solve or verify it himself. The other edition is without answers, and designed for the use of classes. NEW YORK, July, 1864. D. W. F. MEASURES. CHAPTER I. 1. Measure is that by which extent, dimension, capacity, or amount is ascertained, determined according to some fixed standard. NOTE. The process by which the extent, dimension, capacity, or amount is ascertained, is called Measuring; and consists in comparing the thing to be measured with some conventional standard. Measures are of seven kinds: 1. Length. 2. Surface or Area. 3. Solidity or Capacity. 4. Weight, or Force of Gravity. 5. Time. 6. Angles. 7. Money or Value. The first three kinds may be properly divided into two classes-Measures of Extension and Measures of Capacity. MEASURES OF EXTENSION. 2. Extension has three dimensions-length, breadth, and thickness. A Line has only one dimension-length. A Surface or Area has two dimensions-length and breadth. I. LINEAR MEASURE. 3. Linear Measure, also called Long Measure, is used in measuring lines or distances. |