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A surface with no holes, like a beach ball, naturally admits spherical or elliptic geometry.

The constant γ, which appears in the formulae both of hyperbolic and elliptic geometry, does not by its variation produce different types of geometry.

The theory of parallels as it exists in hyperbolic space has no application in elliptic geometry.

But another property of Euclidean parallel lines holds in elliptic geometry, and by the use of it parallel lines are defined.

Many of those properties of Euclidean parallels, which do not hold for Lobatchewsky’s parallels in hyperbolic geometry, do hold for Clifford’s parallels in elliptic geometry.