ABSTRACT
The packet in Newton’s possession contained the outline of a new proof to the solution to the duration of play problem. When all the details are considered, it is a long and difficult proof that requires the development of a new mathematical theory of recurring series to get things started. It ends with some trigonometric arguments such that the numerical solution to the duration of play problem can be found easily using tables of sines or cosines. The trigonometric part of the solution harks back to his 1707 paper, with the explanation of it delayed until 1722, in which trigonometric methods are used to find the roots of a certain polynomial equation.1
