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It was the French mathematician Rene Descartes who created the slope-intercept form of geometry.
Algebraic Geometry - book - was created in 1977.
Euclid came up with the most common form of geometry.
Geometry has been studied in every civilization that we have written records of. In that sense, no mathematician can have created geometry. Euclid is generally recognized as having pioneered the use of the axiomatic method in mathematics. Of that work, his most famous is his work in geometry.
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.