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Rays Arithmetic Curriculum
List of Math Books
 • List of Books Included in Ray's Arithmetic
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List of Books Included in Ray's Arithmetic

There are 38 books, if you include Answer Keys/Teachers Editions. The Teachers Editions are simply the same book as their counterpart, with the answers included next to most of the problems.

If you click on the titles you will be able to view previews of the paperback books available on lulu. You can purchase the books in paperback from lulu, or take the money saving option and purchase all the books for only $59 on CD here.

Basic Math

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”

Ray's Primary Arithmetic
. 95 pages. The first book in the Ray's Series, Primary Arithmetic starts at the very beginning of mathematics by teaching the children to count. The book then slowly progresses with simple problems, first with addition, then subtraction, then multiplication and division. The problems are very simple, so that the child can learn the concepts involved.

Ray's Intellectual Arithmetic. 141 pages. Intellectual Arithmetic begins by reviewing the basic concepts covered in Ray's Primary Arithmetic, adding more problems and raising the difficulty. The book then adds the new concept of Fractions. Finally, it follows fractions with the similar concept of percentages. As these concepts are introduced, applications for the problems are given, showing the child how to solve increasingly complex problems, such as how to divide the rent of a farm between two people considering that one mans livestock eats 1/3 less.

Ray's Elementary Arithmetic192 pages. /Rudimentary Arithmetic. 193 pages. Ray's New Elementary Arithmetic was to a large extent a kind of second version or redesign of Rudimentary Arithmetic, and large portions of Rudimentary Arithmetic are incorporated in the Elementary text.
Ray's New Elementary Arithmetic is designed to lead straight into Practical Arithmetic, by providing an extensive amount of drill work for the student, in order to allow the student ample time and problems to thoroughly master the fundamentals before moving forward.

Ray's Practical Arithmetic. 337 pages. Practical Arithmetic starts by quickly reviewing the basics of addition, subtraction, multiplication and division covered previously in Elementary Arithmetic, and then moves into a study of different types of measurement, followed by factoring, and a more involved study of fractions and percentages. After these mathematical bases have been studied and mastered, real world applications for these mathematics are introduced. These include Transactions, Commissions, Stock values and investments, Interest, Discounts, Monetary exchange, Insurance and Taxes. Practical Arithmetic then concludes by introducing basic geometry. 

Intermediate Math

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.”

This continual grounding in practicality is a peculiar aspect of Ray's Arithmetic, one which is very rare and very valuable. Modern math books have focused so much on the abstract that the student is left to wonder how he will ever be able to use it in his day to day life; a feeling that easily makes mathematics seem like a chore or useless exercise.

Ray's Higher Arithmetic. 409 pages. A very complete study of Arithmetic, this is the last book in the Ray's series before the introduction of Algebra. All of the basic mathematical methods are reviewed thoroughly; and more complicated applications and uses are explored. Finally the book begins the study of Geometry, and the fundamentals of Trigonometry are introduced.

Ray's New Elementary Algebra. 241 pages. “In introducing Algebra to the student with Elementary Algebra, great care has been taken to make the student feel that he is not operating with unmeaning symbols, by means of arbitrary rules; that Algebra is both a rational and practical subject, and that he can rely on 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 which they produce.”

I cannot stress highly enough the importance the above paragraph has to a student embarking on a study of Algebra. From personal experience while studying with Saxon Algebra I know just how frustrating it is to be told what to do, while not given any reasons for why we are doing it or how it works. I didn't want to simply take their word for it but prove it for myself, a thought process most students share. And while I did manage to work these things out eventually, it was a slow and painful process. One of the things that make Ray's Arithmetic such an excellent series is the attention given to the student. Instead of neglecting the reasoning and deducing ability of the students themselves, they are instead encouraged to think on their own. This increases the students interest, his understanding of the material, as well as his recollection of studies later on.

Ray's New Elementary Algebra focuses on the basic forms of Algebra. Algebraic Fractions, Simple Equations, Powers, Roots, Radicals, and finally Quadratic Equations are among the concepts explored. As always, after a concept has been taught, real-world applications for the process are given to the student.

Ray's New Higher Algebra. 407 pages. After reviewing the fundamentals, Higher Algebra then moves on to Theorems, Factoring, Algebraic Fractions, Quadratic Equations, Ratio, Proportion, Binomial Theorem, etc etc. This book is quite lengthy, thoroughly teaching algebraic concepts. While there are relatively few problems for the student to work on and solve, these have been supplied by Test Problems for Ray's New Higher Algebra. 152 pages, as well as A Complete Algebra. 359 pages.


Advanced Math 


Ray's Treatise on Geometry and Trigonometry. 421 pages. Begins by giving definitions for some basic geometrical terms, then begins Geometry, starting with parallel lines, then continuing with Arcs and Radii, the properties of triangles, Parallelograms, measuring area, Polygons, the geometry of space, Pyramids, Prisms, etc. The book then continues on into the subject of Trigonometry, and supplies logarithmic tables. No problems are supplied for the student in this book, which instead gives all it's attention to teaching the concepts. It is suggested that the student use another book to provide problems while learning the mathematical processes from this book.

Ray's Analytic Geometry. 608 pages. Equations to the Right Line, the Plane, Quadrics, The Ellipse, The Hyperbola, and Properties of Conics discussed with great fullness. Abridged Notation is introduced in this book. This book does not supply problems for student work, focusing on teaching the concepts. 

Ray's Differential and Integral Calculus. 442 pages. Begins with definitions. Careful attention has been given to the teaching of the doctrine of limits, which has been made the basis of both the Differential and Integral Calculus. Problems are supplied in the book.


Extra-Curricular Texts


In order to provide students with examples of the interesting fields mathematical studies opens, several books of ranging difficulties have been supplied.


Complete Book Keeping. 161 pages. An often over-looked area of study, book-keeping will always be an important area of expertise for anyone who earns or spends money. As the author states: “Book-keeping... cultivates the judicial powers of the mind... contributes to private and public virtue.. leads to economy and thrift... and it's practice will reduce pauperism and crime.” Beginning with the basic form of double entry book-keeping, Debit, Credit, and all areas of accounting are taught.


Norton's Elements of Physics. 269 pages. This incredibly well-written and intriguing book is so well written that it does not feel so much like a dry text on the mathematics of physics as an exploration of physical laws, thus allowing someone well acquainted with physics or not at all to read this book with great enjoyment. Carefully illustrated, this book begins by introducing the student first to general notions of matter and force, and then introducing new elements one by one. Friction, adhesion, fluids, sound, light, heat, and electricity are all explored, with careful explanations of experiments and studies done by the scientists who explored these properties.


Schuyler's Principles of Logic. 169 pages. Logic is a mathematical pursuit. How can we tell? Through logic. ;-) Because math is based on logical premises (induction), and then followed through in a logical working out of the premises (deduction). The author explains this more thoroughly, but you'll have to read the book.


Ray's Elements of Astronomy. 342 pages. Taking a different approach to astronomy, rather than focusing on the Greek names for constellations this book focuses on the movements of heavenly bodies and the science of astronomy.

Ray's Surveying and Navigation. 492 pages. While this book thoroughly covers the old art of Surveying (the same business George Washington was in for a number of years) this book is especially useful because of it's great attention to the field of Plane and Spherical Trigonometry and Mensuration, and may because of this be used as a textbook for those fields.