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THE

FIRST TWO BOOKS

OF THE

ELEMENTS OF EUCLID,

PRINTED CHIEFLY

ACCORDING TO THE TEXT OF SIMSON :

WITH ADDITIONAL FIGURES, NOTES, EXPLANATIONS, AND

DEDUCTIONS,

BY

NICHOLAS POCOCK, M.A.

LATE MICHEL FELLOW OF QUEEN'S COLLEGE,

AND SEVERAL TIMES ONE OF THE PUBLIC EXAMINERS IN THE

UNIVERSITY OF OXFORD.

[graphic]

LONDON:
LONGMAN, BROWN, GREEN, AND LONGMANS.

1852.

173, d. 14.

LONDON: SPOTTISWOODes and SHAW,

New-street-Square.

PREFACE.

SOME apology seems to be required for sending out another edition of EuclID'S ELEMENTS, in addition to the number which have been already published. And the Editor hopes he may lay claim to some indulgence on the score of his having attempted to make the subject more interesting than hitherto. Any one who has been occupied in teaching this subject, must have observed how difficult it is to keep the learner's attention alive during the whole of a demonstration. It is, indeed, this difficulty of fixing the attention on a subject, which has at first little or nothing that is attractive, that has deterred many from proceeding with this branch of study, and has led to the belief in some, that particular powers of mind, which they do not themselves possess, are required for its comprehension. There cannot be a greater mistake than this: every one who has any power of understanding has powers enough for this subject, provided he has the power of giving his attention to it. And the student who is really anxious to become acquainted with Geometry, may promise himself success if he will only attend to the directions hereafter given, and follow them implicitly.

Attempts have been made to obviate this difficulty by introducing symbolical notation; but this is only remedying one evil by introducing another. This

method dispenses with the necessity of fixed attention, and thus leaves the learner without the advantages which the formation of the habit of attention secures. And accordingly “Symbolical Euclids” are but little used in schools or universities, the chief objection to them appearing to be, that the learner admits the logical consequences of one step from another, without having either premise or conclusion fixed in his memory, and proceeds through the greater part of a proposition without once looking at his figure.

The careful and elaborate edition of Euclid, published by Mr. Potts at Cambridge, seven years ago, seems to obviate much of this difficulty, possessing as it does the advantage of the method of symbolical notation without its disadvantages. One of the principal features of this edition was the arrangement of the distinct statements in a proposition, in separate lines; and, in this respect, the present edition proceeds nearly on the same plan with that. What seemed wanting in that edition, the present attempts to supply, viz. the practice in drawing the figure correctly, and the direction how to do so. It may be thought, perhaps, that the directions are sometimes minute, to the extent of being trifling ; and that it was scarcely necessary to add anything, in this respect, to what the original text contained. The best answer to this would be furnished by testing the powers of any learner, however well he may be thought to understand his subject, in drawing the figures of the XLIVth or XLVth Propositions of the First Book. With regard to other explanations, to which the same remark might seem

applicable, the Editor has only to observe, that it seemed worth while, at the expense of a few additional remarks and figures, to insure, if possible, a greater degree of accuracy. He will only add as a further excuse for such minuteness, that he has been often accustomed, in public examinations, to such definitions as the following:

A straight line is length without breadth.
A circle is a plain figure contained by one straight line, &c.

And most of these faults arise from want of attention to the figures. The great number of additional figures, and the large type in which the work has been printed, for the sake of rendering it more easy for the beginner to follow the arguments, have necessarily increased the expense of the publication ; but it is hoped the advantages to be drawn from this will more than compensate for it. With regard to the few Deductions which have been added, it has been kept in view to interest, and to avoid frightening the learner. Few students, excepting those who have advanced further, can do such Deductions as are usually added to editions of Euclid; and the consequence is, that most become disheartened at finding themselves unequal to what appears to be expected of them. In the present edition, the plan has been followed of giving directions, such as will enable any learner to go through them all if he will take the trouble to refer to the Propositions indicated. Those selected are such as appeared to be most easy and interesting. It only remains to notice that the work is intended for the use of students at Oxford in their first year, and for such as are pre

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