Geometry (Part I)
In two dimensions, it is called plane geometry
In three dimensions, it is called solid geometry
Pascal's Theorem for non-convex hexagons
Brianchon's Theorem for circumscribed hexagon.
Simpson's Theorem for co-linear points.
Riemannian Geometry (brief description in lay terms). Riemannian geometry is an integral part of Einstein's theory of general relativity.
Hyperbolic Geometry is an integral part of Einstein's thoery of special relatvity.
Journal of Algebraic Geometry (Online from AMS)
The application of coordinates to geometry, and the creation of analytic geometry is due to Rene' Descartes
[Additional material can be found in Chapter 11 of Boas&Geller].