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ROBERT POTTS, M.A., TRINITY COLLEGE, CAMBRIDGE,

HON. LL.D., WILLIAM AND MARY COLLEGE, VA., U.S.

EUCLID'S ELEMENTS OF GEOMETRY.

1. Euclid's Elements of Geometry, the University Edition, with Notes, Questions, and Geometrical Exercises, selected from the Cambridge Senate House and College Examination Papers, with Hints for Solution of the Exercises. Demy 8vo., pp. 520, 10s.

2. The School Edition, with Notes, Geometrical Exercises, &c. 12mo., pp. 418, 4s. 6d.

The School Edition has also been published in the following portions, with the Notes, &c., to each book:

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The University Edition of Euclid's Elements was first published in 1845, and the first School Edition in 1846. Both Editions have been enlarged and improved from time to time, and the total sales of copies of the work up to the present year amount to a number very considerably above half-a-million.

In the year 1853, the Council of Education at Calcutta were pleased to order the introduction of these Editions of Euclid's Elements into the Schools and Colleges under their control in Bengal.

In the year 1860, a Translation of the Geometrical Exercises was made into the German Language, by Hans H. Von Aller, with a Preface by Dr. Wittstein, and published at Hanover.

At the International Exhibition of 1862, in London, a Medal was awarded to R. Potts, "For the Excellence of his Works on Geometry." Jury Awards, Class xxix., p. 313.

Critical Remarks on the Editions of Euclid.

"In my opinion Mr. Potts has made a valuable addition to Geometrical literature by his Editions of Euclid's Elements."-W. Whewell, D.D., Master of Trinity College, Cambridge. (1848.)

Mr. Potts has done great service by his published works in promoting the study of Geometrical Science."-H. Philpott, DD., Master of St. Catharine's College. (1848.)

"Mr. Potts' Editions of Euclid's Geometry are characterized by a due appreciation of the spirit and exactness of the Greek Geometry, and an acquaintance with its history, as well as by a knowledge of the modern extensions of the Science. The Elements are given in such a form as to preserve entirely the spirit of the ancient reasoning, and having been extensively used in Colleges and Public Schools, cannot fail to have the effect of keeping up the study of Geometry in its original purity."-J, Challis, M.A., Plumian Professor of Astronomy and Experimental Philosophy in the University of Cambridge. (1848.)

"Mr. Potts' Edition of Euclid is very generally used in both our Universities and in our Public Schools; the notes which are appended to it shew great research, and are admirably calculated to introduce a student to a thorough knowledge of Geometrical principles and methods."-George Peacock, D.D., Lowndean Professor of Mathematics in the University of Cambridge, and Dean of Ely. (1848)

"By the publication of these works, Mr. Potts has done very great service to the cause of Geometrical Science. I have adopted Mr. Potts' work as the text-book for my own Lectures in Geometry, and I believe that it is recommended by all the Mathematical Tutors and Professors in this University."-R. Walker, M.A., F.K.S., Reader in Experimental Philosophy in the University, and Tutor of Wadham College, Oxford. (1848.)

"When the greater Portion of this Part of the Course was printed, and had for some time been in use in the Academy, a new Edition of Euclid's Elements, by Mr. Robert Potts, M.A, of Trinity College, Cambridge, which is likely to supersede most others, to

the extent, at least, of the Six Books, was published. From the manner of arranging the Demonstrations, this edition has the advantages of the symbolical form, and it is at the same time free from the manifold objections to which that form is open. The duodecimo edition of this Work, comprising only the first Six Books of Euclid, with Deductions from them, having been introduced at this Institution as a text book, now renders any other Treatise on Plane Geometry unnecessary in our course of Mathematics."-Preface to Descriptive Geometry, &c. for the Use of the Royal Military Academy, by S. Hunter Christie, M.A., of Trinity College, Cambridge, late Secretary of the Royal Society, &c., Professor of Mathematics in the Royal Military Academy, Woolwich. (1817.)

"Mr. Potts, by the publication of his Edition of Euclid, with its most valuable notes and problems, and the solutions and commentaries, has recalled the attention of Englishmen to the subject:-first in his own and the Sister Universities, then in the public schools, and, finally, in most Scholastic Establishments in the Country.-His Euclid is one of our own text-books in the Royal Military Academy, and we find its arrangements and additions exceedingly conducive to the acquisition of a thorough understanding of the subject by the Gentlemen Cadets."-T. S. Davies, Professor of Mathematics in the Royal Military Academy, Woolwich. (1848.)

"The Edition of the Elements of Euclid which Mr. Potts has published, is confessedly the best which has yet appeared."-John Phillips Higman, M.A., F.R.S., late Fellow and Tutor of Trinity College, Cambridge. (1848)

"Mr. Potts has lately published an Edition of Euclid's Elements of Geometry, which he has illustrated with a collection of Examples. I consider that he has performed his task with great care and judgment, and that the work seems to bid fair to possess a larger share of popular favour than any edition of Euclid yet published."-R. Buston, B.D., Fellow and Tutor of Emmanuel College. (1848.)

"I consider Mr. Potts' Edition of Euclid to be a most valuable addition to our Cambridge Mathematical literature, and especially to the department of Geometry; and look to it as a great help towards keeping up, and indeed reviving, the true spirit and feeling for Geometry, which of late years had been too much neglected among us.”—W. Williamson, B.D., Fellow and Tutor of Clare College. (1848.)

"I believe there is a general opinion in this University that the Principles of Euclid and Elementary Geometry cannot possibly be presented to the mind of a commencing student in a better form, nor be accompanied by a more judicious selection of problems, with hints for their solution, than occurs in the pages of Mr. Potts' publications. By combining symmetry of arrangement with simplicity of language, and by restoring the syllogism to its plain and simple form, so as to make an introduction to Geometry serve at the same time as an exercise in logic (an advantage which has been quite lost sight of in many of the abbreviated editions with which this University had previously been deluged), I consider that Mr. Potts has done good service to the cause of education."-J. Power, M.A., Fellow of Clare College, and University Librarian. (1848.)

"Mr. Potts has maintained the text of Simson, and secured the very spirit of Euclid's Geometry, by means which are simply mechanical. It consists in printing the syllogism in a separate paragraph, and the members of it in separate subdivisions, each, for the most part, occupying a single line. The divisions of a proposition are therefore seen at once without requiring an instant's thought. Were this the only advantage of Mr. Potts' Edition, the great convenience which it affords in tuition would give it a claim to become the Geometrical text-book of England. This, however, is not its only merit."-Philosophical Magazine, January, 1848.

"If we may judge from the solutions we have sketched of a few of them [the Geometrical Exercises], we should be led to consider them admirably adapted to improve the taste as well as the skill of the Student. As a series of judicious exercises, indeed, we do not think there exists one at all comparable to it in our language-viewed either in reference to the student or teacher.-Mechanics' Magazine, No. 1175.

"The 'Hints' are not to be understood as propositions worked out at length, in the manner of Bland's Problems, or like those worthless things called 'Keys,' as generally 'forged and filed,'-mere books for the dull and the lazy. In some cases references only are made to the Propositions on which a solution depends; in others, we have a step or two of the process indicated; in one case the analysis is briefly given to find the construction or demonstration; in another case the reverse of this. Occasionally, though seldom, the entire process is given as a model; but most commonly, just so much is suggested as will enable a student of average ability to complete the whole solution-in short, just so much (and no more) assistance is afforded as would, and must be, afforded by a tutor to his pupil. Mr. Potts appears to us to have hit the 'golden mean' of Geometrical tutorship."-Mechanics' Magazine, No. 1270.

"We can most conscientiously recommend it [The School Edition] to our own younger readers, as the best edition of the best book on Geometry with which we are acquainted."— Mechanics' Magazine, No. 1227.

LONDON: LONGMANS & CO., PATERNOSTER ROW.

ROBERT POTTS, M.A., TRINITY COLLEGE, CAMBRIDGE.

HON. LL.D. WILLIAM AND MARY COLLEGE, VA., U.S.

PALEY'S EVIDENCES OF CHRISTIANITY

and the Horæ Paulinæ, edited with Notes; with an Analysis and a selection of Examination Questions from the Cambridge Papers. 8vo., pp. 588, 10s. 6d., cloth.

"Mr. Potts' is the most complete and useful edition yet published."-Eclectic Review.

"We feel that this ought to be henceforth the Standard Edition of the Evidences and the Hora."-Biblical Review.

"The scope and contents of this new edition of Paley are pretty well expressed in the title. The Analysis is intended as a guide to Students not accustomed to abstract their reading, as well as an assistance to the mastery of Paley; the Notes_consist of original passages referred to in the text, with illustrative observations by the Editor the questions have been selected from the examinations for the last thirty years."-Spectator.

A BRIEF ACCOUNT OF THE
SCHOLARSHIPS AND EXHIBITIONS

Open to competition in the University of Cambridge, with Specimens of the Examination Papers. Fcap. 8vo., pp. 157, cloth, 18. 6d.

LIBER CANTABRIGIENSIS,

An account of the Aids, Encouragements, and Rewards open to Students in the University of Cambridge. Fcap. 8vo., pp. 570, bds., 48. 6d.

MAXIMS, APHORISMS, &c., FOR LEARNERS. Double crown, bds., pp. 192, 1s. 6d.

LONDON: LONGMANS & CO., PATERNOSTER ROW.

KING EDWARD VI. ON THE SUPREMACY, With an English Translation, and a few brief notices of his Life, Education, and Death. Double crown, cloth bds., gilt edges, 2s. 6d.

This short treatise is printed from the autograph copy of King Edward VI., preserved in the Cambridge University Library, and is really a literary curiosity, whether it be regarded in reference to the author or the subject.

CAMBRIDGE: W. METCALFE & SON. LONDON: N. S. DEPOSITORY.

A CHAPTER OF ENGLISH HISTORY ON THE SUPREMACY OF THE CROWN, With an Appendix of Public Documents. 8vo.

CAMBRIDGE: W. METCALFE & SON.

ELEMENTARY ARITHMETIC,

WITH BRIEF NOTICES OF ITS HISTORY.

SECTION VII.

INTEGERS, CONCRETE.

BY ROBERT POTTS, M.A.,

TRINITY COLLEGE, CAMBRIDGE,

HON. LL.D. WILLIAM AND MARY COLLEGE, VA., U.S.

CAMBRIDGE:

PUBLISHED BY W. METCALFE AND SON, TRINITY STREET.

LONDON:

SOLD AT THE NATIONAL SOCIETY'S DEPOSITORY, WESTMINSTER.

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W. METCALFE AND SON, TRINITY STREET, CAMBRIDGE.

6d.

NOTICE.

As the Book-post affords great convenience for the prompt transmission of Books to persons living at a distance from towns, copies of Mr. Potts' publications can be supplied by Messrs. W. Metcalfe and Son, through the Book-post, within the United Kingdom, on receiving orders with prepayment in postage stamps, post office orders, or otherwise.

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