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EUCLID'S

ELEMENTS OF GEOMETRY,

CHIEFLY FROM THE TEXT OF DR SIMSON,

WITH EXPLANATORY NOTES;

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

EXAMINATION PAPERS;

TO WHICH IS PREFIXED AN INTRODUCTION, CONTAINING
A BRIEF OUTLINE OF THE HISTORY OF

GEOMETRY.

DESIGNED FOR THE USE OF THE HIGHER FORMS IN PUBLIC SCHOOLS

AND STUDENTS IN THE UNIVERSITIES.

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PREFACE.

This new edition of Euclid's Elements of Geometry will be found to differ considerably from those at present in general use in Academical Education. The text is taken from Dr Simson's approved edition, with occasional alterations; but so arranged as to exhibit to the eye of the student the successive steps of the demonstrations, and to facilitate his apprehension of the reasoning. No abbreviations or symbols of any kind are employed in the text. The ancient Geometry had no symbols, nor any notation beyond ordinary language and the specific terms of the science. We may question the propriety of allowing a learner, at the commencement of his Geometrical studies, to exhibit Geometrical demonstrations in Algebraical symbols. Surely it is not too much to apprehend that such a practice may occasion serious confusion of thought. It may be remarked that the practice of exhibiting the demonstrations of Elementary Geometry in an Algebraical form, is now generally discouraged in this University. To each book are appended explanatory notes, in which, especial care has been taken to guard the student against the common mistake of confounding ideas of number with those of magnitude. The work contains a selection of problems and theorems from the Senatehouse and College Examination Papers, for the last forty-five years. These are arranged as Geometrical exercises to the several books of the Elements, and to a few only in each book the solutions are given. An Introduction is prefixed, giving a brief outline of the history and progress of Geometry.

The analysis of language, together with the sciences of number and magnitude, have been long employed as the chief elements of intellectual education. At a very early period, the study of Geometry was regarded as a very important mental discipline, as may be shewn from the seventh book of the Republic of Plato. To his testimony may be added that of the celebrated Pascal, (Euvres, Tom. I. p. 66,) which Mr Hallam has quoted in his History of the Literature of the Middle Ages. “Geometry," Pascal observes, “is almost the only subject as to which we find truths wherein all men agree; and one cause of this is, that geometers alone regard the true laws of demonstration.” These

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