Proof
By the same argument as III.5: a shared centre and a common point on
the circumference of both circles force equal radii, hence coincident
circles.
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Full neighborhood
Depends on (3)
- III.5Proposition III.5If two circles cut one another, they will not have the same centre.
- I.15Definition I.15A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among…
- III.3Definition III.3Circles are said to touch one another which, meeting one another, do not cut one another.
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