Todhunter (I.)—continued.

in elementary treatises on the theory of Equations, together with Examples for exercise. These have been selected from the College and University Examination Papers, and the results have been given when it appeared necessary. In order to exhibit a comprehensive view of the subject, the treatise includes investigations which are not found in all the preceding elementary treatises, and also some investigations which are not to be found in any of them. For the Second Edition the work has been revised and some additions have been made, the most important being an account of the researches of Professor Sylvester respecting Newton's Rule. A thoroughly trustworthy, complete, and yet not too elaborate treatise." PHILOSOPHICAL MAGAZINE.

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PLANE TRIGONOMETRY. For Schools and Colleges. Fourth Edition. Crown 8vo. cloth. 5s.

The design of this work has been to render the subject intelligible to beginners, and at the same time to afford the student the opportunity of obtaining all the information which he will require on this branch of Mathematics. Each chapter is followed by a set of Examples: those which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously reserved by the student for exercise after he has made some progress in the subject. In the Second Edition the hints for the solution of the Examples have been considerably increased. A TREATISE ON SPHERICAL TRIGONOMETRY. Edition, enlarged. Crown 8vo. cloth. 4s. 6d.

New

The present work is constructed on the same plan as the treatise on Plane Trigonometry, to which it is intended as a sequel. In the account of Napier's Rules of Circular Parts, an explanation has been given of a method of proof devised by Napier, which seems to have been overlooked by most modern writers on the subject. Considerable labour has been bestowed on the text in order to render it comprehensive and accurate, and the Examples (selected chiefly from College Examination Papers) have all been carefully verified. "For educational purposes this work seems to be superior to any others on the subject."-CRITIC,

Todhunter (I.)-continued.

PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples. Fourth Edition, revised and enlarged. Crown 8vo. cloth. 7s. 6d.

The author has here endeavoured to exhibit the subject in a simple manner for the benefit of beginners, and at the same time to include in one volume all that students usually require. In addition, therefore, to the propositions which have always appeared in such treatises, he has introduced the methods of abridged notation, which are of more recent origin; these methods, which are of a less elementary character than the rest of the work, are placed in separate chapters, and may be omitted by the student at first.

A TREATISE ON THE DIFFERENTIAL CALCULUS.

With

numerous Examples. Fifth Edition. Crown 8vo. cloth. 10s. 6d. The author has endeavoured in the present work to exhibit a comprehensive view of the Differential Calculus on the method of limits. In the more elementary portions he has entered into considerable detail in the explanations, with the hope that a reader who is without the assistance of a tutor may be enabled to acquire a competent acquaintance with the subject. The method adopted is that of Differential Coefficients. To the different chapters are appended examples sufficiently numerous to render another book unnecessary; these examples being mostly selected from College Examination Papers. "It has already taken its place as the text-book on that subject."-PHILOSOPHICAL MAGAZINE.

A TREATISE ON THE INTEGRAL CALCULUS AND ITS APPLICATIONS. With numerous Examples. Third Edition, revised and enlarged. Crown 8vo. cloth.

IOS. 6d.

This is designed as a work at once elementary and complete, adapted for the use of beginners, and sufficient for the wants of advanced students. In the selection of the propositions, and in the mode of establishing them, it has been sought to exhibit the principles clearly, and to illustrate all their most important results. The process of summation has been repeatedly brought forward, with the view of securing the attention of the student to the notions which form the true foundation of the Calculus

Todhunter (I.)-continued.

itself, as well as of its most valuable applications. Every attempt has been made to explain those difficulties which usually perplex beginners, especially with reference to the limits of integrations. A new method has been adopted in regard to the transformation of multiple integrals. The last chapter deals with the Calculus of Variations. A large collection of exercises, selected from College Examination Papers, has been appended to the several chapters.

EXAMPLES OF ANALYTICAL GEOMETRY OF THREE DIMENSIONS. Second Edition, revised. Crown 8vo. cloth 45. A TREATISE ON ANALYTICAL STATICS. With numerous Examples. Third Edition, revised and enlarged. Crown 8vo. cloth. IOS. 6d.

In this work on statics (treating of the laws of the equilibrium of bodies) will be found all the propositions which usually appear in treatises on Theoretical Statics. To the different chapters examples are appended, which have been principally selected from University Examination Papers. In the Third Edition many additions have been made, in order to illus trate the application of the principles of the subject to the solution of problems.

A HISTORY OF THE MATHEMATICAL THEORY OF PROBABILITY, from the time of Pascal to that of Laplace.

The subject of this volume has high claims to consideration on account of the subtle problems which it involves, the valuable contributions to analysis which it has produced, its important practical applications, and the eminence of those who have cultivated it. The subject claims all the interest which illustrious names can confer: nearly every great mathematician within the range of a century and a half comes up in the course of the history. The present work, though principally a history, may claim the title of a comprehensive treatise on the Theory of Probability, for it assumes in the reader only so much knowledge as can be gained from an elementary book on Algebra, and introduces him to almost every process and every species of problem which the literature of the subject can furnish. author has been careful to reproduce the essential elements of the original

The

Todhunter (I.)-continued.

works which he has analysed, and to corroborate his statements by exact quotations from the originals, in the languages in which they were published.

RESEARCHES IN THE CALCULUS OF VARIATIONS,

principally on the Theory of Discontinuous Solutions: an Essay to which the Adams Prize was awarded in the University of Cambridge in 1871. 8vo. 6s.

The subject of this Essay was prescribed in the following terms by the Examiners:-"A determination of the circumstances under which discontinuity of any kind presents itself in the solution of a problem of maximum or minimum in the Calculus of Variations, and applications to particular instances. It is expected that the discussion of the instances should be exemplified as far as possible geometrically, and that attention be especially directed to cases of real or supposed failure of the Calculus." The Essay, then, is mainly devoted to the consideration of discontinuous solutions; but incidentally various other questions in the Calculus of Variations are examined and elucidated. The author hopes that he has definitely contributed to the extension and improvement of our knowledge of this refined department of analysis.

Wilson (J. M.)-ELEMENTARY GEOMETRY. Angles, Parallels, Triangles, Equivalent Figures, the Circle, and Proportion. By J. M. WILSON, M.A., late Fellow of St. John's College, Cambridge, and Mathematical Master of Rugby School. Second Edition. Extra fcap. 8vo. 3s. 6d.

The distinctive features of this work are intended to be the following. The classification of Theorems according to their subjects; the separation of Theorems and Problems; the use of hypothetical constructions; the adoption of independent proofs where they are possible and simple; the introduction of the terms locus, projection, &c. ; the importance given to the notion of direction as the property of a straight line; the intermixing of exercises, classified according to the methods adopted for their solution; the diminution of the number of Theorems; the compression of proofs, especially in the later parts of the book; the tacit, instead of the explicit,

Wilson (J. M.)-continued.

"The methods em

reference to axioms; and the treatment of parallels. ployed have the great merit of suggesting a ready application to the solution of fresh problems."—GUARDIAN.

ELEMENTARY GEOMETRY. PART II. (separately). The Circle and Proportion. By J. M. WILSON, M.A. Extra fcap. 8vo. 2s. 6d. - A TREATISE ON DYNAMICS. By

Wilson (W. P.)

W. P. WILSON, M.A., Fellow of St. John's College, Cambridge, and Professor of Mathematics in Queen's College, Belfast. 8vo. 9s. 6d. SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the use of Schools. By J. M. WILSON, M.A. Extra fcap. 8vo. 3s. 6d. This work is an endeavour to introduce into schools some portions of Solid Geometry which are now very little read in England. The first twenty-one Propositions of Euclid's Eleventh Book are usually all the Solid Geometry that a boy reads till he meets with the subject again in the course of his analytical studies. And this is a matter of regret, because this part of Geometry is specially valuable and attractive. In it the attention of the student is strongly called to the subject matter of the reasoning; the geometrical imagination is exercised; the methods employed in it are more ingenious than those in Plane Geometry, and have greater diffi culties to meet; and the applications of it in practice are more varied Wolstenholme.. A BOOK OF MATHEMATICAL PROBLEMS, on Subjects included in the Cambridge Course. By JOSEPH WOLSTENHOLME, Fellow of Christ's College, sometime Fellow of St. John's College, and lately Lecturer in Mathematics at Christ's College. Crown 8vo. cloth. 8s. 6d. CONTENTS:-Geometry (Euclid)—Algebra-Plane Trigonometry— Geometrical Conic Sections-Analytical Conic Sections-Theory of Equa tions-Differential Calculus-Integral Calculus-Solid Geometry-Statics -Elementary Dynamics-Newton-Dynamics of a Point-Dynamics of a Rigid Body-Hydrostatics-Geometrical Optics-Spherical Trigonometry and Plane Astronomy. Judicious, symmetrical, and weli arranged.”

GUARDIAN.

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