As noted in the introduction, we end our main story with 1855. We do this because the geometry practiced by mathematicians underwent a great change once the viewpoint expressed by Riemann in 1854 was absorbed by those mathematicians. Further, an exposition of geometry after 1855 would take us to a level well above that intended for this book; to move beyond 1855 generally takes us to graduate level mathematics, as found in university departments of mathematics and physics.