What Newton and Leibniz found was a way to work out the slope (or the speed in the distance example) exactly, using simple and logical rules. They divided the curve into an infinite number of very small pieces. They then chose points on either side of the range they were interested in and worked out tangents at each. As the points moved closer together towards the point they were interested in, the slope "approached" a particular value as the tangents approached the real slope of the curve. The particular value it approached was the actual slope.