Excerpt from Secondary-School Mathematics, Vol. 1 This text differs widely from that marked out by custom and tradition. It treats the various branches of mathematics more with reference to their unities and less as isolated entities (sciences). It seeks to give pupils usable knowledge of the principles underlying mathematics and ready control of them. These texts are not an experiment; they were thoroughly tried out in mimeograph form on hundreds of high school pupils before being put into book form. The scope of Books I and II does not vary greatly from that covered in algebras and geometries of the usual type. However, Book I is different in that arithmetic, algebra, and geometry are treated side by side. The effect of this arrangement is increased interest and power of analysis on the part of the learner, and greater accuracy in results. Some pupils like arithmetic, others like algebra, still others like geometry; the change is helpful in keeping up interest. The study of geometry forces analysis at every step and stage; consequently written problems and problems to be stated have no terrors for those who are taught in this way. For several years mathematical associations have urged that all work should be based upon the equation. In accordance with this view we have made the demonstrations in this book largely algebraic, thus making the demonstration essentially a study in simultaneous equations. In this method of treatment, we have found it advantageous not to hurry the work. Pupils gain power, not in solving many problems, but in analyzing and thoroughly understanding the principles of a few. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Secondary-School Mathematics, Vol. 2 This volume continues the work of Book I and completes the required work in most four-year high schools; namely, algebra through quadratic equations, and all of plane geometry. In addition it trains the pupil in the use of logarithms and trigonometry of the right triangle. These last two topics are taught as a direct consequence of the theory of exponents and of ratios in similar right triangles. With algebra through proportion and most of straight line geometry at the student's command, this book offers from the very beginning the greatest opportunities for the introduction of interesting problems which are impossible in the old plan of keeping algebra and geometry separate. The applied problems, involving a knowledge of technical terms in shop or in the work of household arts, are so arranged that their introduction is at the discretion of the teacher, this of course depending largely on the type of school in which the text is being used. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Secondary Mathematics, Vol. 1 The authors have been aware of the popular demand for a closer union of algebra and geometry, but have recognized that demand only when the union came about naturally and would assist the mathematical sequence desired. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Junior High School Mathematics, Vol. 1 Impress the class with the importance of checking all work and insist throughout the course that all computation be thor oughly checked and 'one hundred per cent accurate when handed in as classroom work. Show them that this is just what a clerk or an accountant has to do in life if he is to hold his position. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from The High School Algebra, Vol. 1 IN issuing a new edition of the high school algebra, part I., the Authors desire to express their appreciation of the favor with which their work has been received, and which has rendered a reprint a necessity. For the convenience of both teachers and students the new edition retains not only the matter of the first edition, but also the numbering of the Articles and Exercises unchanged and the pages unbroken. A few additions have been made to the text, a few examples have been changed, and a considerable number of new examples have been inserted at the end of the book. These new examples will be found to require a moderate amount of intelligent thought for their solution, but difficult or complicated work has not been introduced. They are chiefly applications Of algebraical princi ples rather than mere symbolical transformations. Experience has shown that the most valuable exercises are those in which the student is required to translate statements of fact, expressed in ordinary language, into the language of symbols, to perform the necessary Operations, and finally to interpret the result. Such work can be performed only by students to whom the symbols both of quantity and operation have a definite meaning. In pursuance of this idea many of the examples are of a geometrical character, but are well within the powers of the average intelligent student. The order in which they are placed is frequently worthy of attention. Sometimes one or more simple examples lead to the solution of a more difficult one of the same character. Sometimes a succession of values is given to an element Of a problem for the purpose of exhibiting a contrast in the results. The careful study of such groups will be found instructive and profitable. The answers have been designedly omitted. Many of the examples are of such a character that their chief value would be lost by the student seeing the result. In other cases the verification of the result Obtained is easily made, and is a valuable additional exercise. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from A High School Algebra, Vol. 1 In a product it is customary to put the numerical factor (if any) first, and the literal factors in alphabetical order. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Algebra, Vol. 1: An Elementary d104-Book for the Higher Classes of Secondary Schools and for Colleges IN this Edition considerable alterations have been made in chapter xii. In particular, the proof of the theorem that every integral equation has a root has been amplified, and also illustrated by graphical considerations. An Appendix has been added dealing with the general algebraic solution of Cubic and Biquadratic Equations; with the reducibility of equations generally; and with the possibility of solution by means of square roots. As the theorems established have interesting applications in Ele mentary Geometry, it is believed that they may find an appropriate place in an Elementary work on Algebra. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.