THE SCHOOL EUCLID.

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 Exammations, 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.

'Mr. ISBISTER believes that much of the difficulty of teaching Euclid to young people arises from the absence in the ordinary edition 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 enunciation 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 have 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 SCHOOL EUCLID:

COMPRISING

THE FIRST FOUR BOOKS.

CHIEFLY

FROM THE TEXT OF DR. SIMSON.

WITH A

New Arrangement of the Figures and Demonstrations;

THE ENUNCIATIONS OF THE PROPOSITIONS

OF EACH BOOK SEPARATELY FROM THE TEXT; AND A SELECTION OF EASY
GEOMETRICAL PROBLEMS FOR SOLUTION.

Designed as a Help to Beginners and Candidates preparing for Examinations.

LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN.

1863.

1831. 2.

PREFACE.

THE

HERE are few persons engaged in tuition who have not experienced the difficulty of teaching Euclid to young pupils, more especially to those who have not acquired habits of close application, or who have no natural aptitude for mathematical studies. One reason for this arises probably from the nature of the subject itself, which requires a more sustained attention, and a greater concentration of thought and power of abstraction, than beginners can ordinarily be induced to apply to any subject at the age when the study of Euclid is commonly begun in schools. But another, and undoubtedly the chief cause of the difficulty, is 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.

Such assistance it is the special design of the present edition to afford, partly by the use of a peculiar type in those parts of a proposition which require to be distinguished from each other, and partly by a new arrangement of the figures and demonstrations, which it is hoped will be found to embody some important improvements on the ordinary method of pre senting the subject to beginners. The chief features of this arrangement may be summed up as follows:

1. Immediately following the enunciation are given, in each case, the 'references,' or elements, of the proposition - the definitions, axioms, and previous propositions on which the successive steps of the reasoning depend. These must be thoroughly mastered by the pupil; and they should in all cases be required to be written out, or repeated aloud, before either