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The School Edition.

EUCLID'S

ELEMENTS OF GEOMETRY,

THE FIRST SIX BOOKS, AND THE PORTIONS OF
THE ELEVENTH AND TWELFTH BOOKS

READ AT CAMBRIDGE,

CHIEFLY FROM THE TEXT OF DR. SIMSON,

WITH EXPLANATORY NOTES ;

A SERIES OF QUESTIONS ON EACH BOOK ;

AND A SELECTION OF GEOMETRICAL EXERCISES FROM
THE SENATE-HOUSE AND COLLEGE EXAMINATION

PAPERS; WITH HINTS, &c.

DESIGNED FOR THE USE OF THE JUNIOR CLASSES IN PUBLIC AND

PRIVATE SCHOOLS.

BY

ROBERT POTTS, M.A.,

TRINITY COLLEGE.

CORRECTED AND IMPROVED.

LONDON:
LONGMAN, GREEN, LONGMAN, ROBERTS, AND GREEN.

M.DCCC.LXIV.

INTERNATIONAL EXHIBITION,

1862.

A Medal has been awarded to R. Potts, ,“For the excellence of his works on Geometry.”

Jury Awards, Class XXIX, p. 313.

GA:B

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SOME time after the publication of an Octavo Edition of Euclid's Elements with Geometrical Exercises, &c., designed for the use of Academical Students ; at the request of some schoolmasters of eminence, a duodecimo Edition of the Six Books was put forth on the same plan for the use of Schools. Soon after its appearance, Professor Christie, the Secretary of the Royal Society, in the Preface to his Treatise on Descriptive Geometry for the use of the Royal Military Academy, was pleased to notice these works in the following terms :“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."

For the very favourable reception which both Editions have met with, the Editor's grateful acknowledgements are due. It has been his desire in putting forth a revised Edition of the School Euclid, to render the work in some degree more worthy of the favour which the former editions have received. In the present Edition several errors and oversights have been corrected and some additions made to the notes: the questions on each book have been considerably augmented and a better arrangement of the Geometrical Exercises has been attempted : and lastly, some hints and remarks on them have been given to assist the learner. The additions made to the present Edition amount to more than fifty pages, and, it is hoped, that they will render the work more useful to the learner.

And here an occasion may be taken to quote the opinions of some able men respecting the use and importance of the Mathematical Sciences.

On the subject of Education in its most extensive sense, an ancient writer “directs the aspirant after excellence to commence with the Science of Moral Culture; to proceed next to Logic; next to Mathematics; next to Physics; and lastly, to Theology." Another writer on Education would place Mathematics before Logic, which (he remarks) “seems the preferable course: for by practising itself in the

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