ABSTRACT
IT is of some interest to follow up our study of development in the construction of angles by considering certain other figures which children learn to construct by means of measurement as their understanding of Euclidean space is elaborated. The figures we shall consider are loci, that is to say, they are defined in such a way that all points of the figure have a property in common which is not possessed by any point outside the figure. The study of loci is interesting because the subject cannot construct such figures without making a generalization based on an action or an operation which is indefinitely repeated. He must therefore recognize a principle of recurrence which is as fundamental in geometrical reasoning as it is in arithmetic. In studying loci we analyse a general problem of reasoning, just as we did in our study of the sum of the angles of a triangle. The present chapter touches on questions of perpendicularity, bisection and circularity, and is therefore correctly placed between the analysis of angles (ch. VIII) and that of curves (ch. X).
