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An essay on the foundations of geometry

Note 164 — Introductory material

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It might be objected, to the above argument, that it involves a petitio principii. For it has been assumed that the two points and their relation form a figure, to which other figures can be congruent. Now if two points have no intrinsic relation, it would seem that they cannot form such a figure. The argument, therefore, apparently assumes what it had to prove. Why, it may be asked, should not three points be required, before we obtain any relation, which Free Mobility allows us to construct afresh in other parts of space?

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