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USE OF PREPARATORY SCHOOLS.

By CHARLES SMITH, M.A.,
Author of A Treatise on Algebra," An Elementary Treatise on

Conic Sections,etc.
Revised and adapted to American Schools

By IRVING STRINGHAM, Ph.D.,
Professor of Mathematics and Dean of the College Faculties in the

University of California.
Briefer edition, $1.10. Complete edition, $1.20.

The Complete Edition contains in addition to the material given in the briefer work, chapters on special subjects, a knowledge of which is required for admission to Harvard, Yale, and other colleges of advanced standing. It should be especially valuable to students preparing for Harvard, Cornell, the University of Michigan, of California, Missouri, etc., in which the “ Treatise on Algebra," by the same author, is used.

PRINCIPLES OF ELEMENTARY ALGEBRA,

By N. F. DUPUIS, M.A., F.R.S.C.

Price, $1.10.

“This is one of the most able expositions of algebraic principles that we have yet met with. The book is intended to embrace all the ordinary algebraic subjects, but its real value lies in the reliable guidance it offers to students who, having had an ordinary text-book drilling to the end of quadratics, wish to know what it was all about. The concluding chapter con tains a very practical consideration of that ever increasingly important branch of algebra – deterrninants. Emphatically a book for teachers, we wish this Algebra the wide sale that it merits."

The Schoolmaster. “Professor Dupuis has followed up the success achieved by his ' Elementary Synthetic Geometry' (Macmillan, 1889), and now publishes this “intermediate algebra,' 'a stepping-stone to assist the student in passing from the former stage (of absolute beginners) to the latter (of accomplished algebraists).”. A résumé of the preface will indicate the work attempted, and carried out in an interesting and satisfactory manner. Prominence is given to the formal laws of algebra and to factoring, from which last the theory of the solution of quadratic and other equations is deduced. The inspiration of Chrystal's 'Algebra' is conspicuous throughout and duly acknowledged.” The Academy.

THE MACMILLAN COMPANY,

66 FIFTH AVENUE, NEW YORK.

OF THE

POINT, RAY, AND CIRCLE.

By WILLIAM B. SMITH, Ph.D., Professor of Mathematics in the Tulane University of New Orleans, La.

Cloth. $1.10.

"To the many of my fellow-teachers in America who have questioned me in regard to the Non-Euclidean Geometry, I would now wish to say publicly that Dr. Smith's conception of that profound advance in pure science is entirely sound.

Dr. Smith has given us a book of which our country can be proud. I think it the duty of every teacher of geometry to examine it carefully." — From Prof. GEORGE BRUCE HALSTED, Ph. D. (Johns Hopkins), Professor of Mathematics, University of Texas.

“I cannot see any cogent reason for not introducing the methods of Modern Geometry in text-books intended for first years of a college course. How useful and instructive these methods are, is clearly brought to view in Dr. Smith's admirable treatise. This treatise is in the right direction, and one step in advancing a doctrine which is destined to reconstruct in great measure the whole edifice of Geometry. I shall make provision for it in the advanced class in this school next term.” - From Principal John M. COLAW, A.M., Monterey, Va.

MODERN PLANE GEOMETRY.

Being the Proofs of the Theorems in the Syllabus of Modern Plane Geometry issued by the Association for the

Improvement of Geometrical Teaching.

By G. RICHARDSON, M.A., and A. S. RAMSAY, M.A.

Cloth. $1.00.

"Intended to be an Introduction to the subject of Modern Plane Geometry and to the more advanced books of Cremona and others. It has a twofold object : to serve, in the first place, as a sequel to Euclid ...; and, secondly, as a systematic means of procedure from Euclidean Geometry to the higher descriptive Geometry of Conics and of imaginary points."

THE MACMILLAN COMPANY,

66 FIFTH AVENUE, NEW YORK.

TEXT-BOOK OF EUCLID'S ELEMENTS.

Including Alternative Proofs, together with Additional

Theorems and Exercises, classified and arranged

By H. S. HALL and F. H. STEVENS.

Books I.-VI. and XI. $1.10.

Book I.
Books I. and II.
Books I.-IV.

Also sold separately as follows :
30 cents. | Books III.-VI.

75 cents. 50 cents. Books V., VI., and XI. 70 cents. 75 cents. Book XI.'

30 cents.

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“The chief peculiarity of Messrs. Hall and Stevens' edition is the extent and variety of the additions. After each important proposition a large number of exercises are given, and at the end of each book additional exercises, theorems, notes, etc., etc., well selected, often ingenious and interesting. There are a great number of minute details about the construction of this edition and its mechanical execution which we have no space to mention, but all showing the care, the patience, and the labor which have been bestowed upon it. On the whole, we think it the most usable edition of Euclid that has yet appeared.” The Nation.

THE ELEMENTS OF SOLID GEOMETRY.

By ROBERT BALDWIN HAYWARD, M.A., F.R.S..

Senior Mathematical Master in Harrow School;
Late President of the Association for the Improvement of

Geometrical Teaching.

16mo. Cloth. 75 cents.

A modification and extension of the first twenty-one propositions of the eleventh book of Euclid, developed out of a Syllabus of solid Geometry submitted by the author to a Committee of the Association for the Improvement of Geometrical Teaching, and reported upon by that Committee with a considerable degree of favor."

THE MACMILLAN COMPANY,

66 FIFTH AVENUE, NEW YORK.

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No stronger commendation of this work is needed than the fact that it is the text used in a large number, if not in the majority, of the leading colleges of the country, among which may be mentioned Harvard University, Cornell University, University of Ohio, of Pennsylvania, of Michigan, of Wisconsin, of Kansas, of California, of Missouri, Stanford University, etc., etc.

“Those acquainted with Mr. Smith's text-books on conic sections and solid geometry will form a high expectation of this work, and we do not think they will be disappointed. Its style is clear and neat, it gives alternative proofs of most of the fundamental theorems, and abounds in practical hints, among which we may notice those on the resolution of expressions into factors and the recognition of a series as a binominal expansion." — Oxford Review.

HIGHER ALGEBRA FOR SCHOOLS.

By H. S. HALL, B.A., and S. R. KNIGHT, B.A.

Cloth. $1,90.

“The ‘Elementary Algebra,' by the same authors, which has already reached a sixth edition, is a work of such exceptional merit that those acquainted with it will form high expectations of the sequel to it now issued. Nor will they be disappointed. Of the authors' 'Higher Algebra,' as of their · Elementary Algebra,' we unhesitatingly assert that it is by far the best work of the kind with which we are acquainted. It supplies a want much felt by teachers.” The Athenæum.

THE MACMILLAN COMPANY,

66 FIFTH AVENUE, NEW YORK.

HALL and KNIGHT. — Elementary Trigonometry. By the

authors of “Algebra for Beginners," “Elementary

Algebra for Schools,” etc. $1.10. HOBSON and JESSOP. – An Elementary Treatise on Plane

Trigonometry. By E. W. Hobson, Sc.D., and C. M.

JESSOP, M.A. $1.25. LEVETT and DAVISON. — The Elements of Trigonometry.

By RAWDON LEVETT and A. F. DAVISON, Masters at King Edward's School, Birmingham. Crown 8vo. $1.60.

This book is intended to be a very easy one for beginners, all difficulties connected with the application of algebraic signs to geometry and with the circular measure of angles being excluded from Part I. Part II. deals with the real algebraical quantity, and gives a fairly complete treatment and theory of the circular and hyperbolic functions considered geometrically. In Part III. complex numbers are dealt with geometrically, and the writers have tried to present much of De Morgan's teaching in as simple a form as possible. LOCK. — Trigonometry for Beginners. As far as the

Solution of Triangles. By the Rev. J. B. Lock. 16mo. 75 cents.

“A very concise and complete little treatise on this somewhat difficult subject for boys; not too childishly simple in its explanations; an incentive to thinking, not a substitute for it. The schoolboy is encouraged, not insulted. The illustrations are clear. Abundant examples are given at every stage, with answers at the end of the book, the general correctness of which we have taken pains to prove. The definitions are good, the arrangement of the work clear and easy, the book itself well printed."'. Journal of Education. Elementary Trigonometry. 6th edition. (In this edition

the chapter on Logarithms has been carefully revised.) 16mo. $1.10.

The work contains a very large collection of good (and not too hard) examples. Mr. Lock is to be congratulated, when so many Trigonometries are in the field, on having produced so good a book; for he has not merely availed himself of the labors of his predecessors, but by the treatment of a well-worn subject has invested the study of it with interest. Nature. LONEY. - Plane Trigonometry. By S. L. LONEY, M.A.

Part I. An Elementary Course, including the Use of
Imaginary Quantities. Cloth. $1.40.

THE MACMILLAN COMPANY,

66 FIFTH AVENUE, NEW YORK.

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