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Todhunter (1.)continued. difficulties, and methodical treatment, characterise Mr. Todhunter's works.”_CIVIL ENGINEER.

THE ELEMENTS OF EUCLID. For the Use of Colleges and

Schools. New Edition. 18mo. cloth. 35. 6d. As the elements of Euclid are usually placed in the hands of young students, it is important to exhibit the work in such a form as will assist them in overcoming the difficulties which they experience on their first introduction to processes of continuous argument. No method appears to be so useful as that of breaking up the demonstrations into their constituent parts; a plan strongly recommended by Professor De Morgan. In the present Edition each distinct assertion in the argument begins a new line : and at the ends of the lines are placed the necessary references to the preceding principles on which the assertions depend. The longer propositions are distributed into subordinate parts, which are distinguished by breaks at the beginning of the lines. Notes, appendix, and a collection of exercises are added.

MENSURATION FOR BEGINNERS. With Numerous Examples...

25. 6d.

18mo. cloth. The subjects included in the present work are those which have usually found a place in Elementary Treatises on Mensuration. The mode of treatment has been determined by the fact that the work is intended for the use of beginners. Accordingly it is divided into short independent chapters, which are followed by appropriate examples. A knowledge of the elements of Arithmetic is all that is assumed; and in connexion with most of the Rules of Mensuration it has been found practicable to give such explanations and illustrations as will supply the place of formal mathematical demonstrations, which would have been unsuitable to the character of the work. For simplicity and clearness of arrangement it is unsurpassed by any text-book on the subject which has come under our notice.". EDUCATIONAL TIMES.

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25. 6d.

Todhunter (I.)continued.
ALGEBRA FOR BEGINNERS. With numerous Examples. New

Edition. 18mo. cloth.
Great pains have been taken to render this work intelligible to young
students, by the use of simple language and by copious explanations. In
determining the subjects to be included and the space to be assigned to each,
the Author has been guided by the papers given at the various examinations
in elementary Algebra which are now carried on in this country. The
book may be said to consist of three parts. The first part contains the
elementary operations in integral and practional expressions ; the second
the solution of equations and problems; the third treats of various subjects
which are introduced but rarely into examination papers, and are more
briefly discussed. Provision has at the same time been made for the
introduction of easy equations and problems at an early stage--for those
who prefer such a course.
KEY TO ALGEBRA FOR BEGINNERS. Crown 8vo. cloth.

6s. 68. TRIGONOMETRY FOR BEGINNERS. With numerous Examples.

New Edition. 18mo, cloth. Intended to serve as an introduction to the larger treatise on Plane Trigonometry, published by the Author. The same plan has been adopted as in the Algebra for Beginners : the subject is discussed in short chapters, and a collection of examples is attached to each chapter. The first fourteen chapters present the geometrical part of Plane Trigonometry; and contain all that is necessary for practical purposes. The range of matter included is such as seems required by the various examinations in elementary Trigonometry which are now carried on in the country. Answers are appended. MECHANICS FOR BEGINNERS. With numerous Examples.

Second Edition. 18mo, cloth. 45. 6d. Intended as a companion to the two preceding books. The work forms an elementary treatise on demonstrative mechanics. It may be true that this part of mixed mathematics has been sometimes made too abstract and speculative; but it can hardly be doubted that a knowledge of the elements

25. 6.

MATHEMATICS.

39

Todhunter (I.)-continued.

at least of the theory of the subject is extremely valuable even for thos who are mainly concerned with practical results. The Author has accord. ingly endeavoured to provide a suitable introduction to the study of applica as well as of theoretical mechanics. The work consists of two parts, namely, Statics and Dynamics. It will be found to contain all that is usually comprised in elementary treatises on Mechanics, together with some additions.

ALGEBRA. For the Use of Colleges and Schools. Fifth Edition.

Crown 8vo. cloth. 75. 6d. This work contains all the propositions which are usually included in elementary treatises on Algebra, and a large number of Examples for Exercise. The author has sought to render the work easily intelligible to students, without impairing the accuracy of the demonstrations, or contracting the limits of the subject. The Examples, about Sixteen hundred and fifty in number, have been selected with a view to illustrate every part of the subject. Each chapter is complete in itself; and the work will be found peculiarly adapted to the wants of students who are without the aid of a teacher. The Answers to the examples, with hints for the solution of some in which assistance may be needed, are given at the end of the book. In the present edition two New Chapters and Three hundred miscellaneous Examples have been added. The latter are arranged in sets, each set containing ten examples. It has merits which unquestionably places it first in the class to which it belongs.—EDUCATOR.

KEY TO ALGEBRA FOR THE USE OF COLLEGES AND

SCHOOLS. Crown 8vo.

IOS. 6d.

AN ELEMENTARY TREATISE ON THE THEORY OF

EQUATIONS. Second Edition, revised. Crown 8vo. cloth.

75. 6d.

This treatise contains all the propositions which are usually included in elementary treatises on the theory of Equations, together with Examples for exercise. These have been selected from the College and University

40

EDUCATIONAL BOOKS.

Todhunter (I.)-continued.
Examination Papers, and the results have been given when it appeared
necessary. In order to exhibit a comprehensive view of the subject, the
treatise in investigations which are not found 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. Fourtk

Edition. Crown 8vo. cloth. 55. 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.

1

A TREATISE ON SPHERICAL TRIGONOMETRY. Second

Edition, enlarged. Crown 8vo. cloth. 45. 6d. 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.

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Todhunter (1.)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. 75. 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.

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A TREATISE ON THE DIFFERENTIAL CALCULUS. With

numerous Examples. Fisth Edition. Crown 8vo. cloth. 1os. 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 IT

APPLICATIONS. With numerous Examples. Third Editio 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 establishingihe on, it has been sought to exhibit the principles clearly, and to illustrate all their most important results. The process of summation has been

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