Elementary Geometry, Then and Now

What is elementary geometry, and when did it originate? The first of these questions—the content of elementary geometry—is not at all simple, and a clear-cut answer is not possible. The most natural answer for present purposes would be the following: “Elementary geometry is the collection of those geometric concepts and theorems taken up in secondary school, together with immediate consequences of these theorems.” However, in spite of the seeming simplicity of this answer, it raises at once a host of objections. The appeal to the word “geometric” in the definition is in itself hard to interpret, since the question “what is geometry?” also admits no clear-cut answer (on that, more below); but in any case, the rapid rate of change in school curricula in all countries of the world, currently seeming to reach its maximum, would oblige us if we adopted that definition to accept the existence of indefinitely many elementary geometries. The concept would have to change not merely from country to country, but for each given country also from year to year if not even from school to school. In addition, such a definition clearly refers only to the content of the school subject “elementary geometry,” while we are here asking about the content of the corresponding science—or, since the word “science” here may seem pompous, about the corresponding direction of scientific thought.