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OPINIONS ON THE SCHOOL EUCLID.

“The plan of extreme subdivision, and the differences of type, are undoubtedly calculated to give help to the beginner.'

PROFESSOR DE MORGAN. "I should think that the mode in which it is printed will be a great assistance to beginners ; indeed, they can hardly fail to follow the demonstrations in it, if they can catch the syllogistic process at all. Professor G. D. LIVEING, late Secretary to the Syndicate for conducting the Cambridge Local Examinations, and Examiner in Experimental Philosophy in the University of London.

• It seems to me to be a very useful book, and exactly adapted for the boys who come up for our examinations. I trust the teachers too will learn something from it.' Rev. T. J. POTTER, M.A., Trinity College, Cambridge, Examiner in Mathematics to the College of Preceptors.

The School Euclid, comprising the first Four Books, will bear comparison with any that has yet been produced.' Dr. RUTHERFORD, Royal Military Academy, Woolwich.

* As far as it goes, this is an excellent School-book.' The Diary, edited by W. S. WOOLHOUSE, F.R.A.S.

• Mr. IsBISTER believes that much of the difficulty of teaching Euclid to young people arises from the absence in the ordinary editions of the Elements of those aids to the learner which are so plentifully supplied in every other department of instruction. The belief is well founded ; and the expedients he has adopted are well calculated to remove the difficulty in question.' MUSEUM.

'An attempt is made in this edition of the first four books of Simson's Euclid to make the members of each proposition clear to the eye by the adoption of different species of type. In the figures, the parts which are given in the enunci. ation are represented by dark lines, and those which are added in the course of the demonstration, by dotted lines. These are decidedly improvements, and will probably tend to smooth the course of learners.'

PARTHENON. “We have much pleasure in strongly recommending this book to all our readers. It will be found most serviceable to all who are teaching or learning Euclid. Mr. IsBISTER has availed himself of the labours of those who have striven to render the demonstrations clear to the learner, and he has neither spoken slightingly of those labours nor ignored his obligations to them. We cannot better describe Mr. IsBISTER's Euclid than by saying that to us it appears like Mr. Potts's Euclid improved. Without wishing to detract in the slightest from the merit to which Mr. IsBISTER is entitled for precision of language, we candidly state our belief that the chief point of superiority of his edition of Euclid over others of recent date, consists in the technical arrangement. The engraver and the printer bave proved invaluable auxiliaries to Mr. ISBISTER, who has evidently endeavoured to improve upon improvements.' PUPIL TEACHER. “The changes introduced are undoubted improvements.'

PAPERS FOR THE SCHOOLMASTER.

THE COLLEGE EUCLID:

COMPRISING

THE FIRST SIX AND THE PARTS OF THE
ELEVENTH AND TWELFTH BOOKS READ AT THE UNIVERSITIES ;

CHIEFLY FROM THE TEXT OF DR. SIMSON.

WITH A NEW ARRANGEMENT OF THE FIGURES AND
DEMONSTRATIONS; THE ENUNCIATIONS OF THE PROPOSITIONS
SEPARATELY; QUESTIONS ON THE DEFINITIONS; ARITHMETICAL AND

ALGEBRAICAL DEMONSTRATIONS OF BOOKS II. AND V.; AND A

SELECTION OF GEOMETRICAL PROBLEMS FOR SOLUTION.

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LONDON:
LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN.

1865.
183.9.6

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PREFACE.

The present edition of Euclid's Elements of Geometry, designed chiefly for the higher classes in schools and colleges, contains the parts usually read in the Universities, and is arranged on the same general plan which has proved so successful in the edition of the Four Books published, for the use of younger students, under the name of The School Euclid. Like many of its predecessors, it is based on the work of Dr. Simson, whose valuable edition has been generally followed. The alterations introduced have been chiefly confined to the arrangement, in which, however, considerable changes and, it is hoped, improvements have been made. Among these the following may be noticed :

1. The references to previous propositions and definitions, generally given in the common editions in the margin, are here collected immediately after the enunciations. An opportunity is thus afforded to the student of revising and making himself thoroughly master, before he begins the demonstration, of the references of which he is about to make use, so that, when they occur in their proper place in the text, their application may be at once perceived, without necessitating any pause in the reasoning in order to make sure of the reference before advancing to the next step in the proof.

2. In describing the figures, the parts which are given in the enunciation are represented by dark lines, and those which are added in the course of the demonstration by dotted lines. The process of the construction is thus exhibited to the eye, and the data and the quæsita of the problem can always be distinguished at a glance.

3. In the demonstrations, the several steps of the proof are arranged in a logical form, by giving the premisses and the conclusion always in separate lines, and in a different type ; the construction and the demonstration' are distinguished by separate headings; and, as a further aid to the student, the enunciations are broken into paragraphs, and the demonstrations into corresponding divisions, wherever the proposition consists of more than one case.

In this way the constituent parts of a proposition are presented separately, part by part; and the learner, knowing exactly where one begins and the other ends, is enabled to make himself master of the one before he proceeds to the other.

The editions of Hill, Blakelock, and Williams were among the earliest to show the advantages of printing separately the parts of a proposition and its demonstration ; and they have been followed with great success by several modern editors. The plan adopted by them, of printing every sentence, or part of a sentence, which contains a new step in the reasoning, in a separate line, * has been followed in the

# The method of exhibiting the propositions in separate lines, now so extensively adopted, was first introduced in an edition of the • Elements’ published, in 1726, by the Rev. Henry Hill, who thus refers to it in his Preface :

• The Method I have taken in writing is entirely new; wholly different from any that has hitherto been made choice of by any of the interpreters of Euclid, and such as does not so much require intent and severe thinking as a bare and easie inspection.

“The better to avoid obscurity and confusion, and that painful attention which we have a general aversion to, and which disturbs and distracts the mind, I have set each and every demonstration out in lines or steps ; so that the several mediums that are necessary in order to investigate the truth of many propositions, might no ways puzzle or perplex the young geometrician ; but that he may have a clear and perfect notion and idea of the most intricate Demonstrations in the Elements of Geometry.'- The First Six, together with the Eleventh and Twelfth Books of Euclid's Elements, demonstrated after a new, plain, and easie Method, by Henry Hill, A.M. London: 1726.

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