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In geometry, the Poncelet-Steiner theorem on ruler-and-compass constructions states that whatever can be constructed by straightedge with compass, can be constructed by straightedge alone, if you are given a single circle and the location of its centre. This result is the best possible: a straightedge alone, without being given a circle, is not sufficient. (A straightedege alone cannot construct square roots.)
The result was conjectured by Jean Victor Poncelet in 1822, and proven by Jakob Steiner in 1833.
See also: Mohr-Mascheroni theorem.
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