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Projective
The Projective Postulates are:
- Any two points (.) can be connected with a unique line segment (s).
- Unlike Spherical Geometry, there are no antipodal points
- Any straight line segment can be extended indefinitely in a straight line (l).
- These lines are not indefinitely long. Their length is constrained by the maximum circumference of the sphere.
- Given any straight line segment, a circle can be drawn having the segment as the radius and one point as the center (c).
- All Right Angles are congruent.
- Given any straight line and a point not on it, there exists no straight line that passes through that point and is parallel (q) to the first line.
Projective geometry also breaks the "Plane Separation Postulate," an unstated postulate of Euclid's. (He was probably unaware that he was assuming this.)