It is not certain when geometry was founded because it's one of the oldest sciences in the world. However, one of the oldest form of geometry called Euclidean geometry was practiced in the 3rd century B.C.
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Coordinate Geometry is also Analytic Geometry, founded by Rene Descartes.
Geometry was not founded by any one person. Ancient Egyptians have been used an early stage of geometry as well as the Greeks.
The formal study of geometry has been attributed to Euclid, who lived in Alexandria about 300 BC.
Rene Descartes who was a French mathematician.
Analytical geometry was founded by the French mathematician, Renee Descartes. As for subsequent contributors to that subject, I will leave that for other contributors to add.