Explain in detail the Historical Significance of the following:

During the 19th century, Carl Friedrich Gauss started to work on non-Euclidean Geometry, but Nikolai Lobachevsky and Jnos Bolyai formally discovered non-Euclidean geometry.

Non-Euclidean Geometry Theorems.

Gauss's definition of what Non -Euclidean Geometry is and Hyperbolic Geometry.

Hyperbolic Geometry versus Non-Euclidean Geometry.