Works by the same authors. BY MR. BLAIKIE. THE ELEMENTS OF DYNAMICS (Mechanics), with numerous Examples and Examination Questions, 24th Thousand, revised and enlarged. Edinburgh: James Thin. Price 3s. 60. *A good introductory Text-Book for young Students.'-Nature. By Professor THOMSON. ALGEBRA, for the Use of Schools and Colleges. London: Sampson Low, Martin, Searle, and Rivington. Price 5s. • The great feature of the work is thoroughness and fulness of explanation. -Atheneum. AN INTRODUCTION TO DETERMINANTS, with numerous EXAMPLES, for the Use of Schools and Colleges. Edinburgh : James Thin. Price 5s. It fulfils everything that can fairly be demanded in a scientific elementary treatise.'-Scotsman. Wulan W. THOMSON, M.A., B.Sc. PROFESSOR OF MATHEMATICS, VICTORIA COLLEGE, UNIVERSITY OF THE CAPE OF GOOD HOPE FORMERLY EXAMINERS IN MATHEMATICS IN THE UNIVERSITY OF EDINBURGH ci LONDON 1891 PREFACE The object of this treatise is to afford a systematic course of training in the art of solving Geometrical Deductions or Riders. With this view it is divided into sections, each section consisting of three parts. There is first a deduction worked out in full, which is intended to serve as a model for the student. This is followed by a number of similar deductions, which are to be written out by the student, the figure being given in each case, and such hints regarding the mode of solution as experience shows are required by beginners. Lastly, each section contains some deductions to be accomplished without this aid, no figures or assistance being given except an occasional reference to the proposition on which the proof depends, or to a previous example. As a rule it is desirable that the proofs should depend upon propositions of Euclid, and not upon previous examples, the only exception being in the case of certain standard theorems which are indicated in the text. For convenience of reference, especially in the case of those who have used text-books other than Euclid's, the |