Geometry was documented by the Sumerian civilization around 5,000 years ago; it was used by them in setting out temples (look up Gilgamesh). The Egyptians also studied and applied a sophisticated knowledge of geometry. In building Stonehenge, around 2,500 BC Neolithic surveyors also used survey methods based on geometric principals.
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In my World History book it says, EUCLID.
Shulba Sutras
Geometry was not really invented. There is a long history of the early discoveries in geometry. I will provide you with a reference. http://en.wikipedia.org/wiki/History_of_geometry
Euclid developed Euclidean geometry around 300 BC. I cannot get much briefer than that.
If you don't know then we certainly do not!