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.

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 all 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 of 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 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.

THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS.

Algebra. The student's progress in Algebra depends very largely upon the proper treatment of the four Fundamental Operations. The terms Addition, Subtraction, Multiplication, and Division in Algebra have a wider meaning than in Arithmetic, and these operations have been so defined as to include their arithmetical meaning; so that the beginner is simply called upon to enlarge his views of those fundamental operations. Much attention has been given to the explanation of the negative sign, in order to remove the well-known difficulties in the use and interpretation of that sign. Special attention is here called to "A Short Method of Removing Symbols of Aggregation," Art. 76. On account of their importance, the subjects of Factoring, Greatest Common Divisor, and Least Common Multiple have been treated at greater length than is usual in elementary works. In the treatment of Fractions, a method is used which is quite simple, and, at the same time, more general than that usually employed. In connection with Radical Quantities the roots are expressed by fractional exponents, for the principles and rules applicable to integral exponents may then be used without modification. The Equation is made the chief subject of thought in this work. It is defined near the beginning, and used extensively in every chapter. In addition to this, four chapters are devoted exclusively to the subject of Equations. All Proportions are equations, and in their treatment as such all the difficulty commonly connected with the subject of Proportion disappears. The chapter on Logarithms will doubtless be acceptable to many teachers who do not require the student to master Higher Algebra before entering upon the study of Trigonometry.

HIGHER MATHEMATICS.

Peck's Manual of Algebra.

Bringing the methods of Bourdon within the range of the Academic Course.

Peck's Manual of Geometry.

By a method purely practical, and unembarrassed by the details which rather confuse than simplify science.

Peck's Practical Calculus.

Peck's Analytical Geometry.

Peck's Elementary Mechanics.

Peck's Mechanics, with Calculus.

The briefest treatises on these subjects now published. Adopted by the great Universities: Yale, Harvard, Columbia, Princeton, Cornell, &c.

Macnie's Algebraical Equations.

Serving as a complement to the more advanced treatises on Algebra, giving special attention to the analysis and solution of equations with numerical coefficients.

Church's Elements of Calculus.

Church's Analytical Geometry.

Church's Descriptive Geometry. With plates. 2 vois. These volumes constitute the "West Point Course" in their several departments. Prof. Church was long the eminent professor of mathematics at West Point Military Academy, and his works are standard in all the leading colleges.

Courtenay's Elements of Calculus.

A standard work of the very highest grade, presenting the most elaborate attainable survey of the subject.

Hackley's Trigonometry.

With applications to Navigation and Surveying, Nautical and Practical Geometry, and Geodesy.

GENERAL HISTORY.

Monteith's Youth's History of the United States.

A History of the United States for beginners. It is arranged upon the catechetical plan, with illustrative maps and engravings, review questions, dates in parentheses (that their study may be optional with the younger class of learners), and interesting biographical sketches of all persons who have been prominently identified with the history of our country.

Willard's United States. School and University Editions. The plan of this standard work is chronologically exhibited in front of the titlepage. The maps and sketches are found useful assistants to the memory; and dates, usually so difficult to remember, are so systematically arranged as in a great degree to obviate the difficulty. Candor, impartiality, and accuracy are the distinguishing features of the narrative portion.

Willard's Universal History. New Edition.

The most valuable features of the United States" are reproduced in this. The peculiarities of the work are its great conciseness and the prominence given to the chronological order of events. The margin marks each successive era with great distinctness, so that the pupil retains not only the event but its time, and thus fixes the order of history firmly and usefully in his inind. Mrs. Willard's books are constantly revised, and at all times written up to embrace important historical events of recent date. Professor Arthur Gilman has edited the last twenty-five years to 1882.

Lancaster's English History.

By the Master of the Stoughton Grammar School, Boston. The most practical of the "brief books." Though short, it is not a bare and uninteresting outline, but contains enough of explanation and detail to make intelligible the cause and effect of events. Their relations to the history and development of the American people is made specially prominent.

Willis's Historical Reader.

Being Collier's Great Events of History adapted to American schools. This rare epitome of general history, rem arkable for its charming style and judicious selection of events on which the destinies of nations have turned, has been skilfully manipulated by Professor Willis, with as few changes as would bring the United States into its proper position in the historical perspective. As reader or text-book it has few equals and no superior.

Berard's History of England.

By an authoress well known for the success of her History of the United States. The social life of the English people is felicitously interwoven, as in fact, with the civil and military transactions of the realm.

Possesses the charm of an attractive romance. The fables with which this history abounds are introduced in such a way as not to deceive the inexperienced, while adding materially to the value of the work as a reliable index to the character and institutions, as well as the history of the Roman people.

THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS.

A BRIEF HISTORY OF
ANCIENT PEOPLES
INTRODUCTION

A Brief History of Ancient Peoples.

With an account of their monuments, literature, and manners. 340 pages. 12mo. Profusely illustrated.

In this work the political history, which occupies nearly, if not all, the ordinary school text, is condensed to the salient and essential facts, in order to give room for a clear outline of the literature, religion, architecture, character, habits, &c., of each nation. Surely it is as important to know something about Plato as all about Cæsar, and to learn how the ancients wrote their books as how they fought their battles.

The chapters on Manners and Customs and the Scenes in Real Life represent the people of history as men and women subject to the same wants, hopes

and fears as ourselves, and so bring the distant past near to us. The Scenes, which are intended only for reading, are the result of a careful study of the unequalled collections of monuments in the London and Berlin Museums, of the ruins in Rome and Pompeii, and of the latest authorities on the domestic life of ancient peoples. Though intentionally written in a semi-romantic style, they are accurate pictures of what might have occurred, and some of them are simple transcriptions of the details sculptured in Assyrian alabaster or painted on Egyptian walls.