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MENSURATION FOR BEGINNERS.

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I. TODHUNTER, M.A., F.R.S.

London and Cambridge:
MACMILLAN AND CO.

1869.

(AU Rights reserved.]

183. q. 31.

Cambridge: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.

PREFACE.

The applications of Mensuration are numerous and important, extending from practical questions of every day life to the highest investigations of science. Mensuration has therefore justly obtained a prominent position in teaching and in examinations. The value of Mensuration is increased by its close and necessary connection with Arithmetic and Geometry. The operations of Arithmetic are here illustrated by a new class of examples; and some of these operations, such as the extraction of the square root and of the cube root, thus gain their true significance and interest. Many of the principal facts of Geometry are introduced and applied, so as to furnish a good introduction to the study of Euclid's Elements, or some substitute for it, to those who have not the opportunity for that study.

The subjects included in the present work are those which have usually found a place in Elementary Treatises on Mensuration. The mode of treatment has been determined by the fact that the work is intended for the use of beginners. Accordingly it is divided into short independent chapters, which are followed by appropriate examples. A knowledge of the elements of Arithmetic is all that is assumed; and in connection with most of the Rules of Mensuration it has been found practicable to give such explanations and illustrations as will supply the place of formal mathematical demonstrations, which would have been unsuitable to the character of the work.

The Examples amount on the whole to nearly twelve hundred in number; some of them are taken from printed

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