Before the 16th century Some of the roots of algebraic geometry date back to the work of the Hellenistic Greeks from the 5th century BC. The Delian problem, for instance, was to construct a length x so that the cube of side x contained the same volume as the rectangular box a2b for given sides a and b. Menaechmus () considered the problem geometrically by intersecting the pair of plane conics ay = x2 and xy = ab. In the 3rd century BC, Archimedes and Apollonius systematically studied additional problems on conic sections using coordinates. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding coordinates using geometric methods like using parabolas and curves. Medieval mathematicians, including Omar Khayyam, Leonardo of Pisa, Gersonides and Nicole Oresme in the Medieval Period, solved certain cubic and quadratic equations by purely algebraic means and then interpreted the results geometrically. The Persian mathematician Omar Khayyám (born 1048 AD) believed that there was a relationship between arithmetic, algebra and geometry. This was criticized by Jeffrey Oaks, who claims that the study of curves by means of equations originated with Descartes in the seventeenth century.
Before the 16th century Some of the roots of algebraic geometry date back to the work of the Hellenistic Greeks from the 5th century BC. The Delian problem, for instance, was to construct a length x so that the cube of side x contained the same volume as the rectangular box a2b for given sides a and b. Menaechmus () considered the. problem geometrically by intersecting the pair of plane conics ay = x2 and xy = ab. In the 3rd century BC, Archimedes and Apollonius systematically studied additional problems on conic sections. using coordinates. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates He further developed relations between the abscissas and the corresponding coordinates using geometric methods like using parabolas and curves. Medieval mathematicians, including Omar Khayyam, Leonardo of Pisa, Gersonides and Nicole Oresme ,in the Medieval Period, solved certain cubic and quadratic equations by purely algebraic means and then interpreted the results geometrically. The Persian mathematician Omar Khayyám (born 1048 AD) believed that there was a relationship between arithmetic, algebra and geometry. This was criticized by Jeffrey Oaks, who claims that the study of curves by means of equations originated with Descartes in the seventeenth century.