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TEE 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 ARITMIJETIC, by Induction and Analysis ;

the most complete and interesting intellectual arithmetic extant.

THIRD BOOK. PRACTICAL ARITHMETIC, by Induction and Analysis; a sim

ple and thorough work for schools and private students. KEY TO RAY'S ARITHMETIC, Tord Book. HIGHER ARITHMETIC. Principles of Arithmetic analyzed and

practically applied. For advanced students.

ELEMENTARY ALGEBRA. RAY'S ALGEBRA, First Book, for Common Schools and Acad.

emies; a simple and thorough elementary treatise.

HIGHER ALGEBRA. RAY'S ALGEBRA. Second Book, for advanced students in Acad.

emies, and for Colleges; a lucid and coniprehensive 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 II undred und Fifty. Seven, 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, .

Sept 12, 1925
mino Kinball

PREFACE.

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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 lias 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 2 herefore" of every operation performed, and gain a thorough knowledge of the principles of Arithmetic with its applications, wliile 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.

20. 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 Aritlimetic, has received that attention which its use and importance demand.

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

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5th. Particular attention las 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 witli
decimals, yet it is truly a species of compound numbers, and is
so'regarded in all the ordinary computa!ions of business. llence,
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 mechanical 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. Tiow far this object has been
secured, is submitted to those engaged in the laborious and
responsible work of education.

04 An APPENDIX has been added to this edition, presenting
the Metrical System of Weights and Measures. This has been com.
pilcd chiefly from modern French works on this subject; and was
submitted, in manuscript, to the critical crimination of Pror.
II. A. Newtoy, cf Yale College, to whom we are under great obli-
cations for such corrections, additions, and emendations, as his
intimate lnowledge 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,

reply to his hand, a large number and variety of Drill Exer-
cises for frequent and thorough review.

Two Editions: With Answers,-Without Answers.

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