Rene Descartes

“I Think Therefore I Am” “Cogito Ergo Sum” Descartes said that his thinking proved his existence.He also argued the existence of God and said, “God according to his philosophy, created two classes of substance that make up reality.” One class was thinking substance (minds), and the other was extended substances (bodies).

Rene Descartes was a famous French mathematician, scientist and philosopher, who was born in La Haye in By 1606 he was studying at the college Jesuit College of La Fleche. In 1616 he went to Germany in the army where he dreamed of finding a Universal science. Throughout his lifetime, Descartes confronted many scientists and mathematicians that everything isn’t based on probability, he claimed that certainty is the only basis of knowledge.

Compendium Musicae ( attempted to work out a theory of harmony) Discours de la Methode ( discourse the method) Regulae ad directionem Ingenii ( Rules for the direction of the mind) Dioptrique ( The Optics) Meteors ( meteorology) Le Monde( The World) Traite de L’homme (treaties on man)

f(x) = x n + a n-1 x n-1 + … + a 1 x + a 0 1.) The number of positive real zeros of f is either equal to the number of variations in sign of f(x) or less than that number by an even integer. 2.) The number of negative real zeros of f is either equal to the number of variations in sign of f(-x) or less than that number by an even integer.

Descartes made this chart to show exact time.

The Cartesian plane, named after the Rene Descartes, is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.

Throuhgout his life, Descartes attempted to apply the rational inductive methods of science and mathematics, to philosophy. Before his time, philosophy had been based on comparing and contrasting the views of recognized authorities. Descartes stated, "In our search for the direct road to truth, we should busy ourselves with no object about which we cannot attain a certitude equal to that of the demonstration of arithmetic and geometry." In mathematics, the most notable contribution that Descartes made was the systematization of analytic geometry. He was the first mathematician to attempt to classify curves according to the types of equations that produce them. He also made contributions to the theory of equations. Descartes was the first to use the last letters of the alphabet to designate unknown quantities and the first letters to designate known ones. He also invented the method of indices to express the powers of numbers. Also, he formulated the rule, which is known as Descartes's rule of signs, for finding the number of positive and negative roots for any algebraic equation. In conclusion, Descartes contributed a lot to modern sciences and mathematics.