This fifth volume presents the surviving correspondence from the period of almost four years which is, from a bibliographical point of view, the most important time in Newton's life: with Roger Cotes, Newton revised his Philosophise Naturalis Principia Mathematics and saw it through the press. Considered as a single group of letters, the Newton-Cotes correspondence is the largest and most important section of Newton's scientific correspondence that we have. Nowhere else can one witness Newton in a detailed debate about scientific argument and scientific conclusions - a debate from which he did not always emerge victorious. Nowhere else does Newton write in detail about the text of the Principia. And all scholars agree that this text which was hammered out between Cotes and Newton was the most important of all versions, printed and unprinted; this was (to all intents and purposes) the Principia of subsequent history.