On Proportion applied to Geometry.
1. “On Proportion applied to Geometry,” by D. Brent, M.A. The author gives an outline of the treatment of proportion in the fifth book of Euclid, and shows how arithmetic should be applied to geometry, and to magnitude in general. In concluding he states that, “although in favour of the substitution of a chapter of arithmetic applied to magnitude for the now nearly obsolete fifth book of Euclid, he does not, therefore, advocate the introduction of arithmetical or algebraical symbols of quantity into pure geometry—far from it, for in the very absence of these symbols consists its great value for mental training, inasmuch as at every step there is an appeal to the reason. The pure geometry also more clearly exhibits the processes of the demonstration and the relations of the figure than does the younger and far more powerful sister
science analytical geometry, in which, by the use of symbols, the reasoning is carried on independent to a great extent of the ideas of the magnitudes themselves.”