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In geometry, the Poncelet–Steiner theorem on compass and straightedge construction states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, if given a single circle and its centre. This result is the best possible; if the centre of the circle is not given, it cannot be constructed by a straightedge alone. Also, the entire circle is not required; usually just a small arc will suffice.

The result was conjectured by Jean Victor Poncelet in 1822, and proven by Jakob Steiner in 1833.
See also

Mohr–Mascheroni theorem

External links

Jacob Steiner's theorem at cut-the-knot (It is impossible to find the center of a given circle with the straightedge alone)

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

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Mathematics Encyclopedia

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