Newton's theory of fluxions

Newton regarded curves as paths of a moving point. This motion is dependent on time. Newton called a quantity that varies when moving (for example x) a fluent. He called the velocity at which the fluent was moving the fluxion. This is marked with a dot, as ẋ. In the infinitely brief time o, the point thus moves ẋo. We can get an idea of how Newton conceived of his calculations in his Method of Fluxions, which was first published nine years after his death. Pay particular attention to paragraphs 13–18 in the copy below.