ABSTRACT
There seems to be much confusion about the history of non-Euclidean geometries . Let us try now to look through the lenses of strands in the history of geometry (Chapter 3) to see how non-Euclidean geometries developed. We have talked already a little bit about how mathematicians started to think about the hyperbolic plane and a new type of geometry in the nineteenth century. Often this is considered to be the beginning of non-Euclidean geometries. But is it really true that non-Euclidean geometry was fi rst discovered only in the nineteenth century? Euclid himself studied geometry on different surfaces!
