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Descartes discovered that he could identify the exact location of every point in a plane using the coordinate system In fact, the coordinate system could be extended to the normal 3-dimensional space as well as more exotic, multi-dimensional spaces.

Furthermore, he could use algebraic expressions to describe shapes such as lines, circles and other conic sections, as well as more complicated shapes. This meant that the analytical tools and power of algebra could then be used to solve problems in geometry. Conversely, the properties of geometrical shapes could be used to solve algebraic problems.

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