Suggested Grade Level	Books
Grade 8 or Grade 9 or Grade 10	Ray's Elementary Algebra Key to Ray's Elementary Algebra
Grade 9 or Grade 10 or Grade 11	Ray's Higher Algebra  Key to Ray's Higher Algebra  Test Problems in Higher Algebra
Grade 10 or Grade 11 or Grade 12	Ray's Plane and Solid Geometry
Grade 11 or Grade 12	Ray's Geometry and Trigonometry

Ray's Elementary Algebra - This 240-page book is a great algebra textbook. It goes over simple equations, powers, roots, radicals, quadratic equations, progressions, and algebraic proportions. It contains a 49-page key. Read from the Introduction to Ray's Elementary Algebra.

Ray's Higher Algebra - This is the second algebra book in the Ray's series. It is 406 pages. It says it is for "colleges, schools, and private students." This book makes a great Algebra II book for high schools. It is of course more rigorous than most Algebra II books. It reviews the first Algebra book, and then goes into theorems, factoring, algebraic fractions, permutations, binomial theorem, indeterminate coefficients, and logarithms. It includes a 175-page key. It also comes with a "Test Problems" book which is extremely rare and had to be photocopied at the Library of Congress. It is 153 pages of problems keyed for Ray's Higher Algebra. It was published in 1882. It does not have an answer key. I seriously doubt one even exists. It was written by three Cincinnati high school teachers and published by the publishers of the Ray's Series.  Read from the Introduction to Ray's Higher Algebra.

Ray's Plane and Solid Geometry - This is the introductory Geometry text for Ray's Arithmetic. It contains 250 pages. No key was ever published.

Ray's Geometry and Trigonometry - This book was designed to follow Plane and Solid Geometry. It begins with a review of that text, then launches into advanced geometry, then into Trigonometry. It contains 420 pages. No key was ever published.

Some Important Notes:

The Ray's books never mention grade level - the grade levels listed above are only suggestions.

Some of the books have Keys, which are included on the CD-ROM.  The Keys are all keyed to (excuse the pun) the "Article Numbers" in the main textbooks. "Articles" in Ray's Arithmetic are the same as "Lessons" to us. The Keys contain answers to the more difficult problems in the books. It also shows HOW to work the problems which is an added help. It is suggested that students use these to check their work. Students should move from section to section as they master the problems in that section. Generally, a section takes a day to do, however, some only take a few minutes and some have many problems to work. They are not of uniform difficulty.

THE object of the study of Mathematics is two fold—the acquisition of useful knowledge, and the cultivation and discipline of the mental powers. A parent often inquires, "Why should my son study Mathematics? I do not expect him to be a surveyor, an engineer, or an astronomer." Yet, the parent is very desirous that he should be able: to reason correctly, and to exercise, in all his relations in life, the energies of a cultivated and disciplined mind. This is, indeed, of more value than the mere attainment of any branch of knowledge.

 

The science of Algebra, properly taught, stands among the first of those studies essential to both the great objects of education. In a course of instruction properly arranged, it naturally follows Arithmetic, and should be taught immediately after it.

 

In the following work, the object has been to furnish an elementary treatise, commencing with the first principles, and leading the pupil, by gradual and easy steps, to knowledge of the elements of the science. The design has been, to present these in a brief, clear, and scientific manner, so that the pupil should not be taught merely to perform a certain routine of exercises mechanically, but to understand the why and the wherefore of every step. For this purpose, every rule is demonstrated, and every principle analyzed, in order that the mind of the pupil may be disciplined and strengthened so as to prepare him, either for pursuing the study of Mathematics intelligently, or more successfully attending to any pursuit in life.

 

Some teachers may object, that this work is too simple, and too easily understood. A leading object has been, to make the pupil feel, that he is not operating on unmeaning symbols, by means of arbitrary rules; that Algebra is both a rational and a practical subject, and that he can rely upon his reasoning, and the results of his operations, with the same confidence as in arithmetic. For this purpose, he is furnished, at almost every step, with the means of testing the accuracy of the principles on which the rules are founded, and of the results that they produce.

 

Throughout the work, the aim has been to combine the clear explanatory methods of the French mathematicians with the practical exercises of the English and German, so that the pupil should acquire both a practical and theoretical knowledge of the subject While every page is the result of the author's own reflection, and the experience of many years in the school-room, it is also proper to state, that a large number of the best treatises in the same subject, both English and French, have been carefully consulted, so that the present work might embrace the modern and most approved methods of treating the various subjects presented.

 

With these remarks, the work is submitted to the judgment of fellow laborers in the field of education.

 

WOODWARD COLLEGE, August 1848.

 

In this NEW ELECTROTYPE EDITION, the whole volume has been subjected to a careful and thorough revision. The oral problems, at the beginning, have been omitted; the number of examples reduced, where they were thought to be needlessly multiplied; the rules and demonstrations abridged; other methods of proof, in a few instances, substituted; and questions for GENERAL REVIEW introduced at intervals, and at the conclusion. It is confidently believed that these modifications, while they do not impair the integrity or change the essential features of the book, will materially enhance its value, and secure, the approbation of all intelligent teachers.

March, 1866.

ALGEBRA is justly regarded one of the most interesting and useful branches of education, and an acquaintance with it is now sought by all who advance beyond the more common elements. To those who would know Mathematics, a knowledge not merely of its elementary principles, but also of its higher parts, is essential; while no one can lay claim to that discipline of mind which education confers, who is not familiar with the logic of Algebra.

 

It is both a demonstrative and a practical science—a system of truths and reasoning, from which is derived a collection of Rules that may be used in the solution of an endless variety of problems, not only interesting to the student, but many of which are of the highest possible utility in the arts of life.

 

The object of the "present treatise is to present an outline of this science in a brief, clear, and practical form. The aim throughout has been to demonstrate every principle, and to furnish the student the means of understanding clearly the rationale of every process he is required to perform. No effort has been made to simplify subjects by omitting that which is difficult, but rather to present them in such a light as to render their acquisition within the reach of all who will take the pains to study.

 

To fix the principles in the mind of the student, and to show their bearing and utility, great attention has been paid to the preparation of practical exercises. These are intended rather to illustrate the principles of the science, than as difficult problems to torture the ingenuity of the learner, or amuse the already skillful Algebraist,

 

An effort has been made throughout the work to observe a natural and strictly logical connection between the different parts, so that the learner may not be required to rely on a principle, or employ a process, with the rationale of which he is not already acquainted. The reference by Articles will always enable him to trace any subject back to its first principles.

 

The limits of a preface will not permit a statement of the peculiarities of the work, nor is it necessary, as those who are interested to know will examine it for themselves. It is, however, proper to remark that Quadratic Equations have received more than usual attention. The same may be said of Radicals, of the Binomial Theorem, and of Logarithms, all of which are so useful in other branches of Mathematics.

 

On some subjects it was necessary to be brief, to bring the work within suitable limits. For example, what is here given of the Theory of Equations, is to be regarded merely as an outline of the more practical and interesting parts of the subject, which alone is sufficient for a distinct treatise, as may be seen by reference to the works of Young or Hymers in English, or of DeFourcy or Reynaud in French.

 

Some topics and exercises, deemed both useful and interesting, will be found here, not hitherto presented to the notice of students. But these, as well as-the general manner of treating the subject, are submitted, with deference, to the intelligent educational public, to whom the author is already greatly indebted for the favor with which his previous works have been received.

 

WOODWARD COLLEGE, May 1852.

 

In preparing the present edition, only such changes have been made as were demanded by recent progress in algebraic science, and the need of which was indicated by long use of the book in the classroom.

 

These alterations, while not impairing the integrity of this favorite algebra, will, it is confidently hoped, commend it still more to public approval.

 

HAMPDEN SIDNEY COLLEGE,

Virginia, May 1875.