Projective Geometry as the Fundamental Geometry

Abstract

By the 1870s, geometry was beginning to be a well-understood subject, with clear research programmes. The study of algebraic curves could be undertaken in several ways, projective geometry was acquiring its status as a fundamental branch of geometry, devoted to the most basic properties of figures (those deeper than the metrical ones), non-Euclidean geometry was acceptable to, and accepted by, most mathematicians (but probably not philosophers). This is indeed the perception of most mathematicians at the time, and most historians of mathematics since, but, as we shall see later, there is another aspect to the story too. But first let us document that projective geometry had become central to many mathematicians perception of geometry.