PREFACE. THIS section has been written to fulfil the promise, formerly made, of completing the Text Book of Geometry. The writer regrets that the pressure of his duties has prevented such careful revision of it as was desirable. He is indebted for much valuable assistance in revising proof-sheets to the Rev. T. Perkins, M.A., Mathematical Master in the Reading Grammar School. The treatment of the subject is somewhat new, and it is hoped the work may be found useful. SECTION D. PROPORTION. INTRODUCTION, DEF. A measure of a magnitude is a magnitude which measures it, that is, is contained in it a certain number of times exactly. A multiple of a magnitude is a magnitude that contains it a certain number of times exactly. . A common measure of two magnitudes is a magnitude which measures both of them. The greatest common measure of two magnitudes is the greatest magnitude which measures both of them. The following truths should be noticed, though the proof may be left to the student, 1. The sum or difference of equimultiples of two magnitudes is equal to the like multiple of the sum or difference of the magnitudes themselves. 2. When the difference of two magnitudes is taken from a third magnitude, the remainder is equal to the third magnitude A. G. 10 |