A geometric construction done with a movable compass alone. All constructions possible with a compass and straightedge are possible with a movable compass alone, as was proved by Mascheroni. Mascheroni's results are now known to have been anticipated largely by Mohr. An example of a Mascheroni construction of the midpoint M of a line segment specified by two points A and B illustrated above. Without loss of generality, take A B = 1. 1. Construct circles centered at A and B passing through B and A. These are unit circles centered at (0, 0) and (1, 0).
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