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OF

PLANE TRIGONOMETRY

FOR THE USE OF THE JUNIOR CLASS OF

MATHEMATICS IN THE UNIVERSITY

OF GLASGOW.

BY

HUGH BLACKBURN, M.A.

PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW,

LATE FELLOV OF TRINITY COLLEGE, CAMBRIDGE.

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Cambridge : PRINTED BY C. J. CLAY, M. A.

AT THE UNIVERSITY PRESS.

PREFACE,

SOME apology is required for adding another to the long list of books on Trigonometry. My excuse is that during twenty years' experience I have not found any published book exactly suiting the wants of my Students. In conducting a Junior Class by regular progressive steps from Euclid and Elementary Algebra to Trigonometry, I have had to fill up by oral instruction the gap between the Sixth Book of Euclid and the circular measurement of Angles ; which is not satisfactorily bridged by the propositions of Euclid's Tenth and Twelfth Books usually supposed to be learned; nor yet by demonstrations in the modern books on Trigonometry, which mostly follow Woodhouse; while the Appendices to Professor Robert Simson's Euclid in the editions of Professors Playfair and Wallace of Edinburgh, and of Professor James Thomson of Glasgow, seemed to me defective for modern requirements, as not sufficiently connected with Analytical Trigonometry.

What I felt the want of was a short Treatise, to be used as a Text Book after the Sixth Book of Euclid had been learned and some knowledge of Algebra acquired, which should contain satisfactory demonstrations of the propositions to be used in teaching Junior Students the Solution of Triangles, and should at the same time lay a solid foundation for the study of Analytical Trigonometry.

This want I have attempted to supply by applying, in the first Chapter, Newton's Method of Limits to the mensuration of circular arcs and areas; choosing that method

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