Rene Descartes was born near Tours in 1596. When eight, he was sent to the Jesuit school at La Fleche. It was there that he developed (at first because of delicate heath ) his lifelong  habit of lying in bed till late in the morning. These meditative hours of morning rest were later regarded by Descartes as his most productive periods. In 1612, Descartes left school and shortly after went to Paris, where, with Mersenne and Mydorge, he devoted some time to the study of mathematics. In 1617, he commenced several years of soldiering by joining the army of Prince Maurice of Orange. Upon quitting military life, he spent four or five years traveling through Germany, Denmark, Holland, Switzerland and Italy. After resettling for a couple of years in Paris, where he continued his mathematical studies and philosophical contemplation’s and where for a while he took up the construction of optical instruments, he decided to move to Holland, then at the height of its power. There he lived for twenty years, devoting his time to philosophy, mathematics and science. In 1649, he reluctantly went to Sweden at the invitation of Queen Christina. A few months later he contracted lung inflammation and died in Stockholm in 1650. The great philosopher cum mathematician was entombed in Sweden and efforts to have his remains transported to France failed. Then, seventeen years after Descartes’ death, his bones, except for those of his right hand, were returned to France and reentered in Paris at what is now the Pantheon. The bones of the right hand were secured, as a souvenir, by the French Treasurer-General who had arranged the transportation of the bones.

It was during his stay of twenty years in Holland that Descartes accomplished his writing. He spent the first four years writing Le monde, a physical account of the universe, but this was prudently abandoned and left incomplete when Descartes heard of Galileo’s condemnation by the church. He turned to the writing of a philosophical treatise on universal science under the title of Discours de la method pour bien conduire sa raison e chercher la verite dans les sciences (A Discourse on the Method of Rightly Conducting the Reason and Seeking Truth in the Sciences); this was accompanied by three appendices entitled La dioptrique, Les meteores, and La geo metrie. The Discours, with the appendices, was published in 1637, and it is in the last of three appendices that descartes’s contributions to analytic geometry appear.

La geometrie, the famous third appendix of the Discours,occuplies about one hundred pages of the complete work and is itself divided into three parts. The first part contains an explanation of some of the principles of algebraic geometry and shows a real advance over the Greeks. To the Greeks, the product of two variables to the area of some rectangle, and the product of three variables to the volume of some rectangular parallelepiped. Beyond this the Greeks could not go. That Descartes’s analytic can cope with the general problem is a fine tribute to the power of the new method.It is said that Descartes’s attempt to solve this problem that inspired his invention of
analytic geometry.

The second part of La geometrie deals, among other things, with a now-obsolete classification of curves and with an interesting method of constructing tangents to curves.

There are a couple of legends describing the initial flash that Descartes to the contemplation of analytic geometry. According to one story, it came to him in a dream. On St. Martin’s Eve, November 10, 1616, while encamped in the army’s winter quarters on the banks of the Danube, Descartes experienced three singularly vivid and coherent dreams that, he claimed, changed the whole course of his life. The dreams, he said, clarified his purpose in life and determined his future endeavors by revealing to him “ a marvelous science” and “ a wonderful discovery.” Descartes never explicitly disclosed just what were the marvelous science and the wonderful discovery, but some believe them to have been analytic geometry, or the application of algebra to geometry, and then the reduction of all science to geometry. It was eighteen years later that he expounded some of his ideas in his Discours.

Another story, perhaps on par with the story of Isaac Newton and the falling apple, says that the initial flash of analytic geometry came to Descartes by watching the fly crawling about on the ceiling near a corner of his room. It struck him that the path of the fly on the ceiling could be described if only one knew the relation connecting the fly’s distances from two adjacent walls . Even though this second story may be apocryphal, it has good pedagogic value.

Of the other two appendices to the Discours, one is devoted to optics and the other to an explanation of numerous meteorological, or atmospheric, phenomena, including the rainbow.