The difficulty that is often felt by beginners as to the generality of the proof by projection of the addition theorem in trigonometry and of the formulae for change of axes in coordinate geometry seems to me to be due chiefly to the incomplete treatment of the fundamental theorems on projection. I do not mean that the proofs in the text-books are inaccurate, but only that sufficient pains are not always taken to show how the projection of a directed segment is to be measured so that the generality of subsequent proofs shall be beyond all question.