Steiner's Porism

摘要

The first half of the 19th century saw a revival of interest in classical Euclidean geometry, in which figures are constructed with straight-edge and compass and theorems are proved from a given set of axioms. This "synthetic," or "pure," geometry had by and large been thrown by the wayside with the invention of analytic geometry by Pierre de Fermat and Rene Descartes in the first half of the 17th century. Analytic geometry is based on the idea that every geometric problem could, at least in principle, be translated into the language of algebra as a set of equations, whose solution (or solutions) could then be translated back into geometry. This unification of algebra and geometry reached its high point with the invention of the differential and integral calculus by Newton and Leibniz between 1666 and 1676; it has remained one of the chief tools of mathematicians ever since. The renewed interest in synthetic geometry came, therefore, as a fresh breath of air to a subject that had by that time been considered out of fashion.