d 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 required tangent to the curve. 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 m...
