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What is Roche geometry?

The axiom system of Luo Barczewski's geometry is different from Euclid's geometry only in that the geometric parallel axiom of "a pair of scattered straight lines are infinitely far on both sides of their only common vertical line" is replaced by "at least two straight lines can be parallel to this straight line from a point outside the straight line", and other axioms are basically the same. Due to the difference of parallel axioms, a series of new geometric propositions different from Euclidean geometry are derived through deductive reasoning.