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The school had very good education and discipline. On account of his delicate health, he was permitted to lie in bed until late in the mornings. In 1647, he visited Pascal, he told himself that the only way to do good work in math, and to keep his health was to never allow anyone to make him get up in the morning before he felt he had to. In 1612, Descartes went to Paris to be introduced to the world of fashion. There he met up with his old friend from school-Mersenne, and together they devoted the two years of 1615 and 1616 to the study of math. Then in 1617 he joined the army of Prince Maurice of Orange, and then at Breda, which is a school. One time when Rene was walking through the streets and he saw a sign in Dutch, which “excited his curiosity”. He stopped the first passer and asked him to translate it into either French or Latin. The man he had stopped happened to be Isaac Beckman, the head of the Dutch college at Dort. Isaac said he would translate it if Rene would answer it. The sign was in fact a challenge to the entire world to solve a geometrical problem. Rene got the answer within a few hours, then him and Isaac’s friendship was the result. In 1621, he quit the army and spent the next five years in travel, most of the time he studied math. Rene saw that a point in a plane could be completely determined if its distances, say “x” and “y”, from two fixed lines drawn at right angles in the plane. With positive and negative values and that though an equation “f(x,y)=0” was unexplained and could be figured out by an infinite number of values of “x” and “y”. The values of “x” and “y” determined the co-coordinates of a number of points which forms a curve, of which the equation “f(x,y)=0” has a geometrical property. Rene said that a point in a space could be determined by three co-coordinates. Rene pointed out the very important facts that two or more curves can be referred to one and the same system of co-coordinates, and that the points in which two curves intersect can be determined by finding the roots common to their equations. Rene wrote three Geometric books. The first two are about analytical geometry, and the third is an analysis of algebra that was current then. Rene also paid particular attention to the theory of tangents to curves. Back then the current definition of a tangent at a point was a straight line through the point such that between it and the curve no other straight line could be drawn, that is the straight line of closet contact. Rene described his theory by giving the general rule for drawing tangents and normals to a roulette. The method that Rene used to find the tangent or normal at any point of a given curve was he determined the center and radius of a circle, which should cut the curve in two consecutive points. The tangent to the circle at that point will be the In modern text books it is usual to express the condition that two of the points which a straight line cuts the curve should be the same as the given point, that allows us to determine manse, and the then the equation of the tangent there is found. Rene did not choose to do this, but selecting a circle as the simplest curve and one “in which he knew how to draw a tangent”, he fixed his circle to make it touch the given curve at the point in question, and this lessoned the problem to drawing a tangent to a circle. He only used this method to curves, which are the same on each side about an axis. One of Rene’s last piece of work was he started a discussion on motion and then he laid down ten laws of nature. The first two are almost the same with the first two laws of motion which as given by Newton. The rest of the eight laws are inaccurate. He assumes that the matter of the universe must result in a number of varieties, which is a whirling mass of water. He says that the sun is in the center on a large whirlpool, in which the planets float and are swept round like straws in a whirlpool of water. Each planet is supposed to be in the center of a secondary whirlpool by which it’s satellites are carried. Rene still mad of its crudeness and its inherent defects the theory of vortices marks a fresh “era” in astronomy. It was an attempt to explain the phenomena of the whole universe by the same mechanical laws, which experiments shows to be true on the earth. Bibliography: Word Count: 899
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