Menaechmus, an ancient Greek mathematician, solved and proved problems in a way very similar to the coordinate system used now, so he is sometimes regarded as the founder of analytic geometry. Apollonius's method of solving problems in On Touch is now called one-dimensional analytic geometry; He used a straight line to find the ratio between one point and other points. Apollonius further developed this method in conic curve theory, which is very similar to analytic geometry, and earlier than Descartes 1800 years. There is no essential difference between the reference line, diameter and tangent used by him and the current coordinate system, that is, the distance measured along the diameter from the tangent point is the abscissa, while the line segment parallel to the tangent line and intersecting with the number axis and curve is the ordinate. He further developed the relationship between abscissa and ordinate, that is, they are equivalent to exaggerated curves. But Apollonius's work is close to analytic geometry, but it can't be completed because it doesn't bring negative numbers into the system. The equation here is determined by the curve, and the curve is not derived from the equation. Coordinates, variables and equations are just footnotes of some given geometric problems.

1 1 century, Omar Khayyam, a mathematician of Persian Empire, discovered the close relationship between geometry and algebra, and made great progress in solving cubic equations. But the most crucial step was completed by Descartes.

Traditionally, analytic geometry was founded by rene descartes. Descartes' pioneering work was recorded in La Geometrie and published in 1637 together with his Methodology. These efforts were written in French, and the philosophical thoughts in them provided the foundation for the creation of Infinity. At first, these works were not recognized, partly because of the discontinuity of discussion and the complexity of equations. It was not until 1649 was translated into Latin and praised by Van Short that it was accepted by the public.

Fermat also contributed to the development of analytic geometry. Although his Ad Locos Planos et Solidos Isagoge was not published before his death, the manuscript appeared in Paris on 1637, just before Descartes' methodology. The text of the introduction is clear and accepted, which paves the way for analytic geometry. The difference between Fermat and Descartes lies in the starting point. Fermat starts with an algebraic formula and then describes its geometric curve. Descartes starts with the geometric curve and ends with the equation. Therefore, Descartes' method can deal with more complex equations and develop to use higher-order polynomials to solve problems.