Using Dedekind axiom of continuity to proof the circular continuity principle

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Important note: Somehow similar question have been asked before and unfortunately the reference link for the answer of that post is dead. So please don't flag this question as repeated :)

I tried to explore

T.Heath 1956 book series on ED geometry

to find out the answer, but my effort was helpless. Can somebody help me? thanks.

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Here is the link to the pdf you're looking for: https://drive.google.com/file/d/0B9uh0VymSVrpYWtHYXZ2d3Z2Rjg/view