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Rene Descartes was the first to do anything really interesting with them. The Latin form of Descartes is Cartesius and the familiar X-Y coodinates are known as Cartesian coordiates after Descartes.
Descartes reasoning was based on deriving principles that were then the premise of deductive reasoning. Bacon, on the other hand, used empirical observations that were then used for inductive reasoning.
Although Descartes is generally credited with inventing analytical geometry, several aspects had been used by the Greek mathematicians Menaechmus (4th century BC) and Apollonius of Perga (3rd century BC). Much later (11th century), the Persian mathematician Omar Khayyam, used methods which modern mathematicians consider akin to analytical geometry. In 1637 Rene Descartes published his work on the topic but it was incomplete and was in French. It took another decade or so before it was translated into Latin and some of the gaps filled that Descartes' ideas took off.
Aquaducts, cement, roads, domed shaped roofing, andalso they were the first ones to have written laws ;)
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.