In the Shadow of Euclid

Euclidean geometry, in a postulational setting, had come far as the golden era ended and the times of the commentators began. But, over the years, other theorems in the mold of Euclid would make an appearance through the contributions of Gauss, Euler, Klein, Hilbert, Morley, and many more. The guiding rules as set forth in the Elements of 300 BC might well be described as the first steps of a journey through a million theorems. These foundational rules and theorems essentially were to appear with a new look. Hence, the geometry of René Descartes (1596-1650) and others close in time must be noted. The names of emerging mathematicians compose an impressive list. Perhaps it is here, at the advent of modern mathematics, that we find the history of the discipline split in half. It is the times of the calculus and allied fields. In such a setting, geometry was to prosper.