ABSTRACT
It will be noticed that in all the systems of geometry which we have discussed so far, there is one expression that recurs in all. While primitive relations vary, the fundamental terms, namely, points, remain always the same. Might the point not be the indispensable element of geometry? Now, nature does not exactly present any simple objects having the properties assigned to points by the geometer. In order to obtain them it seems necessary to posit other terms not given in immediate apprehension and different in nature from the first. We ordinarily qualify the application of geometry in this way, because geometry, we say, is complete and rigorous when it posits points that are “simple and indivisible.”
