Coordinates before Descartes
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Some consider Apollonius of Perga to be the inventor of coordinates. Indeed, in his study of conics, he reduces the problem to the axes of the curve and gives relations between lengths at particular points on each axis. These relations can obviously be translated into coordinates, but Apollonius does not fix an origin and does not carry the approach through to completion: we cannot say that he works with coordinates.
Hipparchus, in defining a latitude and a longitude in his geographical work, also comes close to this idea but does not use it as a computational tool.
The medieval scholar Nicole Oresme, for his part, uses a method of locating a point by means of two coordinates, which he calls longitudino and latitudino. He uses them for graphical representations such as temperature as a function of time.