"The subject of Euclid's fifth book is PROPORTION—universal proportion; that is, not numerical proportion merely, but proportion in reference to all magnitudes and quantities whatever, whether numbers, lines, surfaces, solids, or concrete quantities of any kind. With proportion in numbers you are already familiar:—this will be a help. I hope, too, by this time you are also somewhat acquainted with proportion in Algebra: this will be a greater help; for proportion in Geometry really accomplishes no more for things in general than the same doctrine in arithmetic and algebra accomplishes for what the notation of those sciences specially represents; and if this kind of proportion would do for geometry, the fifth book of Euclid would become a very easy matter indeed."