# Analytic geometry.

The French mathematician Rene Descartes (1596-1650) published, in 1637, his Discours de la methode (Discussions on the Method)--of finding scientific truth by good reasoning, that is.

In a hundred-page appendix to this book, Descartes combined algebra and geometry. He pointed out that if one drew two perpendicular straight lines, marked the intersection 0, and laid off units on each line, positive numbers to the right and up, negative numbers to the left and down, then every point in the plane could be represented by two numbers, one for its position along the horizontal axis and the second for its position along the vertical axis.

(One could add a third axis, in and out, and locate every point in the Universe by three numbers.) Straight lines and curves could then be expressed by algebraic equations, which would locate every point on the line or curve with reference to the two axes. This combination of disciplines, producing analytic geometry, strengthened both. Geometric problems could be solved algebraically, and algebraic equations could be illustrated geometrically.

It also laid the foundation for the development of the calculus, which is essentially the application of algebra to smoothly changing phenomena that can be represented geometrically by curves of various sorts.