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RAY'S ARITHMETIC, THIRD BOOK.
INDUCTION AND ANALYSIS.
BY JOSEPH RAY, M.D.
LATE PROFESSOR OF MATHEMATICS IN WOODWARD COLLEGR.
ONE THOUSANDTH EDITION-IMPROVED.
NEW YORK: CLARK & MAYNARD,
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 arithmetio 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, THIRD BOOK. HIGUER 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 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 Fifty• Beven, 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, O.
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 ihan 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 lise 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. MESO085