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# 12.8: Axiom h-V

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Finally, we need to check that the Axiom h-V holds; that is, we need to prove the following claim.

Theorem $$\PageIndex{1}$$

Claim For any h-line $$\ell$$ and any h-point $$P\notin\ell$$ there are at least two h-lines that pass thru $$P$$ and have no points of intersection with $$\ell$$. Applying the main observation we can assume that $$P$$ is the center of the absolute.

The remaining part of the proof can be guessed from the picture

Exercise $$\PageIndex{1}$$

Show that in the h-plane there are 3 mutually parallel h-lines such that any pair of these three lines lies on one side of the remaining h-line.

Hint

Look at the diagram and think. 