I do not think any apology is needed for asking the Society to consider the treatment of Proportion in Elementary Geometry. Although the fifth book of Euclid's Elements appears in all editions of Euclid, I know of no school or college where it is read; I know of no examination for which it is prescribed, and I have never seen an examination paper which contained a question based upon it, except in regard to its definitions. Indeed I believe it is not unfair to say that even among teachers themselves a thorough knowledge of Euclid's fifth book is very rare.