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### Cartesian Coordinates

When Rene Descartes (1596–1650) invented the system of mapping coordinates that bears his name, he was lying ill in bed, watching a fly negotiate the space above him. To be able to determine the location of the fly as it buzzed above him, Descartes imagined a flattened world in which the fly moved around on a plane that roughly corresponded in dimensions to the ceiling.

To make it so he could trace the path of the fly on the plane, the mathematician drew axes that divided the ceiling area into four quadrants. He labeled the quadrants using Roman numerals, as shown in Figure 4.9. At the intersection he placed the origin of his mapping. The axes he divided into equal segments identified with positive and negative values. ...

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