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Euclidean
Euclidian
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It is important to note, however, that the extra dimension, though curled up, was still Euclidean in nature.
A hyperbolic display contains much more space than a simple Euclidean plane because the circumference and area of the circle it's mapped upon grows exponentially with the length of its radius.
In 1869, after Beltrami's letter… he realized he had made a mistake: the empirical concept of a rigid body and mathematics alone were not enough to characterize Euclidean geometry.
From this point of view, Euclidean geometry is a very favorable place to begin a student's serious mathematical training.
The first two volumes cover the foundations of Euclidean geometry and the introduction of a coordinate system, volume 3 studies solid geometry considering quadrics, cubic curves in space, and cubic surfaces.
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