THE BEST AND CHEAPEST

MATHEMATICAL WORKS.

BY PROFESSOR JOSEPH RAY.

TYPE ENLARGED-NEW STEREOTYPE PLATES.

Each Book of Ray's Arithmetical Course, also of the Algebraic, is a complete work in itself, and is sold separately.

FIRST BOOK.

PRIMARY LESSONS: simple and progressive Mental Lessons and Tables for little learners.

SECOND BOOK.

INTELLECTUAL ARITHMETIC, by Induction and Analysis; the most complete and interesting intellectual arithmetic extant.

THIRD BOOK.

PRACTICAL ARITHMETIC, by Induction and Analysis; a simple and thorough work for schools and private students. KEY TO RAY'S ARITHMETIC, THIRD BOOK.

HIGHER ARITHMETIC, Principles of Arithmetic analyzed and practically applied. For advanced students.

ELEMENTARY ALGEBRA.

RAY'S ALGEBRA, FIRST BOOK, for Common Schools and Academies; a simple and thorough elementary treatise.

HIGHER ALGEBRA.

RAY'S ALGEBRA. SECOND Book, for advanced students in Academies, and for Colleges; a lucid and comprehensive work. KEY TO RAY'S ALGEBRA, FIRST AND SECOND BOOKS, complete in one volume, 12mo.

Entered according to Act of Congress, in the year Eighteen Hundred and FiftySeven, by WINTHROP B. SMITH, in the Clerk's Office of the District Court of the United States, for the Southern District of Ohio.

ELECTROTYPED at Franklin Type FOUNDERY, CINCINNATI, 0.

Sept 12, 1925

FEw, it any works on Arithmetic, have received the approbation which has been bestowed upon "Ray's Arithmetic, Part Third;" and the constantly increasing demand for it having rendered another renewal of the stereotype plates necessary. it has been made the occasion for remodeling and greatly improving the volume in all its parts.

The Inductive and Analytic methods here adopted, lead the learner to an understanding of the principles from which the rules are derived, and teach him to regard rules as results rather than reasons: he will understand the "why and wherefore" of every operation performed, and gain a thorough knowledge of the principles of Arithmetic with its applications, while the faculties of the mind are strengthened and disciplined.

The leading features of the work are:

1st. Every principle is clearly explained by an analysis or solution of simple examples, from which a Rule is derived. This is followed by graduated exercises designed to render the pupil familiar with its application.

2d. The arrangement is strictly philosophical; no principle is anticipated: the pupil is never required to perform any operation until the principle on which it is founded has first been explained. For this reason, those processes of reduction that require the use of fractions, are introduced after fractions.

3d. The subject of Fractions, a thorough understanding of which is almost a knowledge of Arithmetic, has received that attention which its use and importance demand.

4th. The subject of Proportion is introduced immediately after Decimals; this enables the instructor to treat Percentage and its various applications, either by proportion, or by analysis, as he may prefer.

EducT 118.68.73%

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THE BEST AND CHE

MATHEMATICAL

BY PROFESSOR JOSEPI

TYPE ENLARGED-NEW STEREOTY

Each Book of Ray's Arithmetical Course,
is a complete work in itself, and is s

FIRST BOOK.

PRIMARY LESSONS: simple and progress: and Tables for little learners.

5th. Particular attention has been given to render the work
practical; the weights and measures are referred to, and con-
form to the legal standards; while pounds, shillings, and pence,
being no longer used in actual business, are only introduced
under Exchange.

While Federal Money may be considered in connection with
decimals, yet it is truly a species of compound numbers, and is
so regarded in all the ordinary computations of business. Ilence,
the propriety of assigning it the place which it occupies in this
work.

While cancellation is introduced, it is not made a hobby, or an
arithmetical machine, by which results can be obtained merely
in a mechi nical manner.

The objec: throughout has been to combine practical utility with
scientific accuracy; to present a work embracing the best methods,
with all real improvements. How far this object has been
secured, is submitted to those engaged in the laborious and
responsible work of education.

An APPENDIX has been added to this edition, presenting
the Metrical System of Weights and Measures. This has been com-
piled chiefly from modern French works on this subject; and was
submitted, in manuscript, to the critical examination of PROF.
II. A. NEWTON, of Yale College, to whom we are under great obli-
gations for such corrections, additions, and emendations, as his
intimate knowledge of the subject suggested.

A NEW BOOK.-RAY'S TEST EXAMPLES.

Three Thousand Test Examples in Arithmetic; Prac-
tical Problems for the Slate or Blackboard, for Drill
exercises and Review.

Designed to save the teacher much time and labor by furnishing,
ready to his hand, a large number and variety of Drill Exer-
cises for frequent and thorough review.

Two Editions: With Answers,-Without Answers.