LATE JUNIOR PROFESSOR OF MATHEMATICS IN THE STAFF COLLEGE. With Numerous Examples. CAMBRIDGE: DEIGHTON, BELL, AND CO. LONDON: BELL AND DALDY. 1863. 100. c. 169. 183. c. 49. PREFACE. THE following Treatise differs essentially from many existing works on Mensuration, inasmuch as all the rules and formulæ employed in it are strictly demonstrated; and, in no case, is any one of them introduced to the notice of the Student in the repulsive form of an empirical rule. At the same time, the methods employed are such that the Student who takes up this Treatise will not require any higher knowledge than a fair acquaintance with Euclid, Algebra, and Plane Trigonometry, together with a knowledge of the forms of the Conic Sections, and of their more simple properties. The want of a Treatise of this nature has long been felt and admitted, and it is in the hope of supplying this want that I have undertaken the present work. The arrangement of the subject, and its scope, will be seen from the Table of Contents. The first five Chapters treat, chiefly, of the areas of plane rectilinear figures, and of the volumes of solids bounded by them. In Chapter II. I have given the Method of Coordinates as applied to the determination of the areas of plane rectilinear figures. This method, on account of its simplicity, generality, and facility |