I've been studying analytic geometry and I'm wondering "Why the Cartesian equations, are called 'Cartesian,'" I know that the name is from the René Descartes philosopher. But in that one case why is it called like that? is there something about the method used on the equation?
Before Decartes, functions and geometry were largely separate areas of mathematics. People studies lines, circles, even conic sections independent of functions we now use to study these objects. Functions were not connected to any sort of "graph," or "plot," which is an indispensable part of studying functions today. To Descrates is attributed the notion of describing the plane in terms of coordinates, and considering the input of a function as one coordinate, and the output as another. Alternatively, the two coordinates could be thought of as inputs of a function, and setting that function equal to zero would have a collection of coordinate pairs as its solution, which collection forms a geometric object in the plane. These types of functions are what is today termed a "Cartesian equation." This was a fantastic leap in understanding functions and geometry. Mathematicans began to understand that the two are very closely related. Because of the importance of this idea, it is termed after Descartes. The coordinates are Cartesian, and equations described with respect to these coordinates are also called Cartesian.
So the story goes, René Descartes was lying in his bed staring at a fly on the ceiling, when it occurred to him that the position of the fly could be described by its distance from each wall.
But, more importantly Descartes derived the system of algebra that could translate the world of Euclidean Geometry to this coordinate system.
Until Descartes, Geometry and Algebra were largely independent branches of mathematics.
It is because of the arguments are expressed in Cartesian coordinates, which turns out was developed by Rene Descartes.