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The doctrine of proportion laid down by Euclid, and the application of it given by him in his Elements, form the basis of almost all the geometrical reasoning made use of by mathematicians both ancient and modern. But the reasonings of geometers with regard to proportional magnitudes have seldom been carried beyond the triplicateratio , which is the proportion that similar solids have to one another when referred to their homologous linear dimensions. This boundary, however, comprehends but a very limited portion of universal comparison, and almost vanishes into nothing when referred to that endless variety of relations, which must necessarily take place between geometrical magnitudes, in the infinite possible degree of increase and decrease.

philosophical transactions of the royal society of london

XXIII. The general mathematical laws which regulate and extend proportion universally; or, a method of comparing magnitudes of any kind together, in all the possible degrees of increase and decrease