Letter, from Brook Taylor to [John] Machin, dated at Bifrons House, Kent Addressed to Childs Coffeehouse in St Pauls Church Yard. Inspired by a discussion with Machin at Childs Coffeehouse, Taylor provides a solution for [Johannes] Kepler's theorem [second law of planetary motion]. His solution is a generalization of [Edmund] Halley's extraction of roots of polynomial equations. Includes figures and equations. [Clarification: This is the first mention of what will later be called Taylor's theorem or Taylor series and published in his Methodus incrementorum directa et inversa, 1715] 26 July 1712