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What is the history of the Cartesian plane?

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Although certain concepts key to the Cartesian plane are found in works as early as ancient Greece, scholars credit Rene Descartes with the critical concept of applying algebra to geometry. Descartes introduced the notion of arithmetizing analytical geometry by assigning coordinates to two points in a plane. After Descartes published his theories, other mathematicians immediately began expanding upon his ideas and developing the Cartesian plane.

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Apollonius of Greece found rudimentary ways to solve geometrical problems, and the French cleric Nicole Oresme of the 14th century used systems similar to Cartesian coordinates. However, it was not until Rene Descartes in 1637, that Euclidean geometry and algebra were at last united.

Scholars named the coordinate system after Descartes; however, many of the features of the modern Cartesian plane were additions by subsequent mathematicians. Descartes only worked with the x-axis and in the first quadrant; up until that time, the concepts of zero and negative numbers were not common.

It was Isaac Newton who first went beyond the use of positive distances. In his publication "Enumerations of Curves of Third Degree," Newton pioneered the use of perpendicular axes that included both positive and negative numbers. He even set the precedent of using x to label the horizontal axis, y for the vertical axis and 0 for the intersection.

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