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RE: Searching for Proof: Three points determine a circle
Posted:
May 7, 2004 2:58 AM


> Original Message > From: ownergeometrycollege@mathforum.org [mailto://ownergeometry > college@mathforum.org] On Behalf Of Bill Kleinhans > Sent: Friday, May 07, 2004 12:46 AM > To: geometrycollege@mathforum.org > Subject: Re: Searching for Proof: Three points determine a circle > > On 5 May 04 18:20:59 0400 (EDT), Paul wrote: > >I am searching for a formal proof (if there is one). > > > >Prove that three noncolinear points determine one and only one > >circle. None of three points can be the center of the circle. > > > >I have searched the web and discovered that Euclid never proved this. >
Not so. Euclid has this at Book 4, Proposition 5 of his Elements. See for example
http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV5.html
Note that on the same book Euclid also has (the much harder) problems of inscribing certain regular polygons into circles.
Have fun.
Michael Lambrou
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