It seems that they author of those words in red is saying that, or something very close to that. Whether that is his meaning or not is one question. The question of whether Newton experimented with and understood the ideas underlying the Taylor series, is certainly answered as "yes". Newton was one of those very rare genius' on the level of Gauss, Hilbert, Einstein and Bohr. People with those gifts see way beyond what they formally prove and publish. Newton intuitively knew many many things that were later proved formally by mathematician's decades, and even centuries later. For example, Newton developed the basic principles of Calculus of Variations long before is was formalized by Euler and Lagrange, about 50-70 years later." Does the part in red mean that Newton had experimented with a form of Taylor series in his work even before the series was formally introduced by Brook Taylor?