Isaac Todhunter: Euclid Preface

In 1905 the London publisher Joseph Malaby Dent had the idea of producing the Everyman's Library, a cheap series of reprints of classical texts. His original aim was to produce 1000 volumes, creating a library of world literature, which would sell at one shilling per volume. Dent wanted the series:-

... to appeal to every kind of reader: the worker, the student, the cultured man, the child, the man and the woman [so that] for a few shillings the reader may have a whole bookshelf of the immortals; for five pounds (which will procure him with a hundred volumes) a man may be intellectually rich for life.

In 1932 Euclid's Elements was published as No 891 in the Everyman's Library. Todhunter's Euclid, published in 1962, was chosen to be the edition reprinted and an Introduction to the Everyman's Library book was written by Sir Thomas L Heath.

Below we reproduce an extract from Todhunter's Preface to his edition of Euclid written in October 1862. This extract is as given in the Everyman's Library edition.

EXTRACT FROM TODHUNTER'S ORIGINAL PREFACE

In offering to students and teachers a new edition of the Elements of Euclid, it will be proper to give some account of the plan on which it has been arranged, and of the advantages which it hopes to present.

Geometry may be considered to form the real foundation of mathematical instruction. It is true that some acquaintance with Arithmetic and Algebra usually precedes the study of Geometry; but in the former subjects a beginner spends much of his time in gaining a practical facility in the application of rules to examples, while in the latter subject he is wholly occupied in exercising his reasoning faculties.

In England the text-book of Geometry consists of the Elements of Euclid; for nearly every official programme of instruction or examination explicitly includes some portion of this work. Numerous attempts have been made to find an appropriate substitute for the Elements of Euclid; but such attempts, fortunately, have hitherto been made in vain. The advantages attending a common standard of reference in such an important subject, can hardly be overestimated; and it is extremely improbable, if Euclid were once abandoned, that any agreement would exist as to the author who should replace him. It cannot be denied that defects and difficulties occur in the Elements of Euclid, and that these become more obvious as we examine the work more closely; but probably during such examination the conviction will grow deeper that these defects and difficulties are due in a great measure to the nature of the subject itself, and to the place which it occupies in a course of education; and it may be readily believed that an equally minute criticism of any other work on Geometry would reveal more and graver blemishes.

Of all the editions of Euclid that of Robert Simson has been the most extensively used in England, and the present edition substantially reproduces Simson's; but his translation has been carefully compared with the original, and some alterations have been made, which it is hoped will be found to be improvements. These alterations, however, are of no great importance; most of them have been introduced with the view of rendering the language more uniform, by constantly using the same words when the same meaning is to be expressed.

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; this was strongly recommended by Professor De Morgan more than thirty years ago as a suitable exercise for students, and the plan has been adopted more or less closely in some modern editions. An excellent example of this method of exhibiting the Elements of Euclid will be found in an edition in quarto, published at the Hague, in the French language, in 1762. Two persons are named in the title-page as concerned in the work, Koenig and Blassiere. This edition has served as the model for that which is now offered to the student: some slight modifications have necessarily been made, owing to the difference in the size of the pages.

It will be perceived then, that 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. Moreover, the longer propositions are distributed into subordinate parts, which are distinguished by breaks at the beginning of the lines.

This edition contains all the propositions which are usually read in the Universities. After the text will be found a selection of notes; these are intended to indicate and explain the principal difficulties which have been noticed in the Elements of Euclid, and to supply the most important inferences which can be drawn from the propositions. The notes relate to Geometry exclusively; they do not introduce developments involving Arithmetic and Algebra, because these latter subjects are always studied in special works, and because Geometry alone presents sufficient matter to occupy the attention of early students. After some hesitation on the point, all remarks relating to Logic have also been excluded. Although the study of Logic appears to be reviving in this country, and may eventually obtain a more assured position than it now holds in a course of liberal education, yet at present few persons take up Logic before Geometry; and it seems therefore premature to devote space to a subject which will be altogether unsuitable to the majority of those who use a work like the present.

I TODHUNTER.

ST JOHN'S COLLEGE, October 1862.


JOC/EFR August 2007

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