A pupil has a passing interest in geometric design. He should learn to use the instruments of geometry, and he learns this most easily by drawing a few such patterns. But to keep him week after week on questions relating to such designs of however great variety, and especially to keep him upon designs relating to only one or two types, is neither sound educational policy nor even common sense. That this enthusiastic teacher or that one succeeds by such a plan is of no significance; it is the enthusiasm that succeeds, not the plan. The experience of the world is that pupils of geometry like to use the subject practically, but that they are more interested in the pure theory than in any fictitious applications, and this is why pure geometry has endured, while the great mass of applied geometry that was brought forward some three hundred years ago has long since been forgotten. The question of the real applications of the subject is considered in subsequent chapters. In Chapter VI we considered the question of the number of regular propositions to be expected in the text, and we have just considered the nature of the exercises which should follow those propositions. It is well to turn our attention next to the nature of the proofs of the basal theorems. Shall they appear in full? Shall they be merely suggested demonstrations? Shall they be only a series of questions that lead to the proof? Shall the proofs be omitted entirely? Or shall there be some combination of these plans? The natural temptation in the nervous atmosphere of America is to listen to the voice of the mob and to proceed at once to lynch Euclid and every one who stands for that for which the "Elements" has stood these two thousand years. This is what some who wish to be considered as educators tend to do; in the language of the mob, to "smash things"; to call reactionary that which does not conform to their ephemeral views. It is so easy to be an iconoclast, to think that _cui bono_ is a conclusive argument, to say so glibly that Raphael was not a great painter,--to do anything but construct. A few years ago every one must take up with the heuristic method developed in Germany half a century back and containing much that was commendable. A little later one who did not believe that the Culture Epoch Theory was vital in education was looked upon with pity by a considerable number of serious educators. A little later the man who did not think that the principle of Concentration in education was a _regula aurea_ was thought to be hopeless. A little later it may have been that Correlation was the saving factor, to be looked upon in geometry teaching as a guiding beacon, even as the fusion of all mathematics is the temporary view of a few enthusiasts to-day.[35]