THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. MATHEMATICS. DAVIES'S COMPLETE SERIES. ARITHMETIC. Davies' Primary Arithmetic. 'Davies' Intellectual Arithmetic. Davies' Elements of Written Arithmetic. Davies' Practical Arithmetic. Davies' University Arithmetic. TWO-BOOK SERIES. First Book in Arithmetic, Primary and Mental. ALGEBRA. Davies' New Elementary Algebra. Davies' University Algebra. Davies' New Bourdon's Algebra. GEOMETRY. Davies' Elementary Geometry and Trigonometry. Davies' Legendre's Geometry. Davies' Analytical Geometry and Calculus. Davies' New Calculus. MENSURATION. Davies' Practical Mathematics and Mensuration, Davies' Elements of Surveying. Davies' Shades, Shadows, and Perspective. MATHEMATICAL SCIENCE. Davies' Grammar of Arithmetic. Davies' Outlines of Mathematical Science. Davies & Peck's Dictionary of Mathematics. THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. DAVIES' SERIES-Continued. THE NEW SURVEYING. Van Amringe's Davies' Surveying. By Charles Davies, LL.D., author of a Full Course of Mathematics. Revised by 3 Howard Van Amringe, A.M., Ph.D., Professor of Mathematics in Columbia College 566 pages. 8vo. Full sheep. Davies' Surveying originally appeared as a text-book for the use of the United States Military Academy at West Point. It proved acceptable to a much wider field, and underwent changes and improvements, until the author's final revision, and has remained the standard work on the subject for many years. In the present edition, 1883, while the admirable features which have hitherto commended the work so highly to institutions of learning and to practical surveyors have been retained, some of the topics have been abridged in treatment, and some enlarged. Others have been added, and the whole has been arranged in the order of progressive development. A change which must prove particularly acceptable is the transformation of the article on mining-surveying into a complete treatise, in which the location of claims on the surface, the latest and best methods of underground traversing, &c., the calculation of ore-reserves, and all that pertains to the work of the mining-surveyor, are fully explained and illustrated by practical examples. Immediately on the publication of this edition it was loudly welcomed in all quarters. A letter received as we write, from Prof. R. C. Carpenter, of the Michigan State Agricultural College, says: "I am delighted with it. I do not know of a more complete work on the subject, and I am pleased to state that it is filled with examples of the best methods of modern practice. We shall introduce it as a text-book in the college course.' This is a tair specimen of the general reception. Van Amringe's Davies' LEGENDRE. Legendre. Elements of Geometry and Trigonometry. By Charles Davies, LL. D. Revised (1885) by Prof. J. H. Van Amring of Columbia College. New pages. Svo. Full leather. The present edition of the Legendre is the result of a careful re-examination of the work, into which have been incorporated such emendations in the way of greater clearness of expression or of proof as could be made without altering it in form or substance. Practical exercises are placed at the end of the several books, and comprise additional theorems, problems, and numerical exercises upon the principles of the Book or Books preceding. They will be found of great service in accustoming students, early in and throughout their course, to make for themselves practical application of geometric principles, and constitute, in addition, a large and excellent body of review and test questions for the convenience of teachers. The Trigonometry and mensuration have been carefully revised throughout; the deduction of principles and rules has been sim. plified; the discussion of the several cases which arise in the solution of triangles plane and spherical, has been made more full and clear; and the whole has, in definition. demonstration, illustration, &c., been made to conform to the latest and best methods. It is believed that in clearness and precision of definition, in general simplicity and rigor of demonstration, in the judicious arrangement of practical exercises, in orderly and logical development of the subject, and in compactness of form, Davies' Legendre is superior to any work of its grade for the general training of the logical powers of pupils, and for their instruction in the great body of elementary geometric truth. The work has been printed from entirely new plates, and no care has been spared to make it a model of typographical excellence. THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. DAVIES'S NATIONAL COURSE OF MATHEMATICS. ITS RECORD. In claiming for this series the first place among American text-books, of whatever class, the publishers appeal to the magnificent record which its volumes have earned during the thirty-five years of Dr. Charles Davies's mathematical labors. The unremitting exertions of a life-time have placed the modern series on the same proud eminence among competitors that each of its predecessors had successively enjoyed in a course of constantly improved editions, now rounded to their perfect fruition, - for it seems almost that this science is susceptible of no further demonstration. During the period alluded to, many authors and editors in this department have started into public notice, and, by borrowing ideas and processes original with Dr. Davies, have enjoyed a brief popularity, but are now almost unknown. Many of the series of to-day, built upon a similar basis, and described as "modern books," are destined to a similar fate; while the most far-seeing eye will find it difficult to fix the time, on the basis of any data afforded by their past history, when these books will cease to increase and prosper, and fix a still firmer hold on the affection of every educated American. One cause of this unparalleled popularity is found in the fact that the enterprise of the author did not cease with the original completion of his books. Always a practical teacher, he has incorporated in his text-books from time to time the advantages of every improvement in methods of teaching, and every advance in science. During all the years in which he has been laboring he constantly submitted his own theories and those of others to the practical test of the class-room, approving, rejecting, or modifying them as the experience thus obtained might suggest. In this way he has been able to produce an almost perfect series of class-books, in which every department of mathematics has received minute and exhaustive attention. Upon the death of Dr. Davies, which took place in 1876, his work was immediately taken up by his former pupil and mathematical associate of many years, Prof. W. G. Peck, LL.D., of Columbia College. By him, with Prof. J. H. Van Amringe, of Columbia College, the original series is kept carefully revised and up to the times. DAVIES'S SYSTEM IS THE ACKNOWLEDGED NATIONAL STANDARD FOR THE UNITED STATES, for the following reasons: 1st. It is the basis of instruction in the great national schools at West Point and Annapolis. 2d. It has received the quasi indorsement of the National Congress. 3d. It is exclusively used in the public schools of the National Capital. 4th. The officials of the Government use it as authority in all cases involving mathematical questions. 5th. Our great soldiers and sailors commanding the national armies and navies were educated in this system. So have been a majority of eminent scientists in this country All these refer to "Davies " as authority. 6th. A larger number of American citizens have received their education from this than from any other series. 7th. The series has a larger circulation throughout the whole country than any other, being extensively used in every State in the Union. THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. DAVIES AND PECK'S ARITHMETICS. OPTIONAL OR CONSECUTIVE. The best thoughts of these two illustrious mathematicians are combined in the following beautiful works, which are the natural successors of Davies's Arithmetics, sumptuously printed, and bound in crimson, green, and gold: — Davies and Peck's Brief Arithmetic. Also called the "Elementary Arithmetic." It is the shortest presentation of the subject, and is adequate for all grades in common schools, being a thorough introduction to practical life, except for the specialist. At first the authors play with the little learner for a few lessons, by object-teaching and kindred allurements; but he soon begins to realize that study is earnest, as he becomes familiar with the simpler operations, and is delighted to find himself master of important results. The second part reviews the Fundamental Operations on a scale proportioned to the enlarged intelligence of the learner. It establishes the General Principles and Properties of Numbers, and then proceeds to Fractions. Currency and the Metric System are fully treated in connection with Decimals. Compound Numbers and Reduction follow, and finally Percentage with all its varied applications. An Index of words and principles concludes the book, for which every scholar and most teachers will be grateful. How much time has been spent in searching for a halfforgotten definition or principle in a former lesson! Davies and Peck's Complete Arithmetic. This work certainly deserves its name in the best sense. Though complete, it is not, like most others which bear the same title, cumbersome. These authors excel in clear, lucid demonstrations, teaching the science pure and simple, yet not ignoring convenient methods and practical applications. For turning out a thorough business man no other work is so well adapted. He will have a clear comprehension of the science as a whole, and a working acquaintance with details which must serve him well in al1 emergencies. Distinguishing features of the book are the logical progression of the subjects and the great variety of practical problems, not puzzles, which are beneath the dignity of educational science. A clearminded critic has said o. Dr. Peck's work that it is free from that juggling with numbers which some authors falsely call "Analysis." A series of Tables for converting ordinary weights and measures into the Metric System appear in the later editions. PECK'S ARITHMETICS. Peck's First Lessons in Numbers. This book begins with pictorial illustrations, and unfolds gradually the science of numbers. It noticeably simplifies the subject by developing the principles of addition and subtraction simultaneously; as it does, also, those of multiplication and division. Peck's Manual of Arithmetic. This book is designed especially for those who seek sufficient instruction to carry them successfully through practical life, but have not time for extended study. Peck's Complete Arithmetic. This completes the series but is a much briefer book than most of the complete arithmetics, and is recommended not only for what it contains, but also for what is omitted. It may be said of Dr. Peck's books more truly than of any other series published, that they are clear and simple in definition and rule, and that superfluous matter of every kind has been faithfully eliminated, thus magnifying the working value of the book and saving unnecessary expense of time and labor. |