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In geometry the following theorems are attributed to him —and their character shows how the Greeks had to begin at the very beginning of the theory— that a circle is bisected by any diameter , that the angles at the base of an isosceles triangle are equal , that, if two straight lines cut one another, the vertically opposite angles are equal , that, if two triangles have two angles and one side respectively equal, the triangles are equal in all respects . He is said to have been the first to inscribe a right-angled triangle in a circle: which must mean that he was the first to discover that the angle in a semicircle is a right angle. He also solved two problems in practical geometry: he showed how to measure the distance from the land of a ship at sea above), and he measured the heights of pyramids by means of the shadow thrown on the ground . (en) |
