Commentary on Proposition III.5¶
Back to Proposition III.5.
The propositions III. 5, 6 could be combined in one. It makes no difference whether the circles cut, or meet without cutting, so long as they do not coincide altogether; in either case they cannot have the same centre. The two cases are covered by the enunciation: If the circumferences of two circles meet at a point they cannot have the same centre. On the other hand, If two circles have the same centre and one point in their circumferences common, they must coincide altogether.