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The three problems were:
* To construct a square with area equal to a given circle ("squaring the circle"). * Given a cube, to construct the edge length of another cube which would have double the volume of the given cube ("duplicating the cube") * Given an arbitrary angle, to construct an angle one third that of the given angle ("angle trisection"). These problems were to be solved using compass and unmarked straight-edge only.
It is apparently not known who first proposed these problems. Two of them (squaring the circle and angle trisection) date to at least 100 years before Euclid. The problem of duplicating the cube also predates Euclid, though maybe not by 100 years.
In the 19th century, all three problems were shown to be impossible with the restriction to compass and straight-edge. (Despite this, people persist in trying, but they have to be classified as cranks.)
Even in ancient times, methods of solution were given, but they used more than just a compass and straight-edge.
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