This is a passage from Leon Lederman and Dick Teresi's The God Particle: If the Universe Is the Answer, What Is the Question?.
Most Newtonian scholars agree that he believed in a particle-like structure of matter. Gravity was the one force Newton treated mathematically. He reasoned that the force between bodies, whether they be earth and moon or earth and apple, must be a consequence of the force between constituent particles. I would hazard a guess that Newton’s invention of the calculus is not unrelated to his belief in atoms. To understand the earth-moon force, for example, one has to apply our formula II. But what do we use for R, the earth-moon distance? If earth and moon were very small, there would be no problem in assigning R. It would be the distance between the centers of the objects. However, to know how the force of a very small particle of earth influences the moon and to add up all the forces of all the particles requires the invention of integral calculus, which is a way of adding an infinite number of infinitesimals. In fact, Newton invented calculus in and around that famous year, 1666, when the physicist claimed his mind was “remarkably fit for invention.”
I'm particularly interested in the last sentence. Call it idle curiosity, but I was interesting in finding where this quote was pulled from. Unfortunately, the text doesn't specify a source. The author continues into talking about Opticks, but the Gutenberg EBook doesn't seem to contain the phrase. A Google and a Google Books search just take me back to The God Particle. The book provides a bibliography of sorts, but it's very scattered. To quote:
I profited from several biographies of Newton, especially the version by John Maynard Keynes and Never at Rest by Richard Westfall (Cambridge: Cambridge University Press, 1981). Abraham Pais’s Inward Bound: Of Matter and Forces in the Physical World (New York: Oxford University Press, 1986) was an invaluable source, as was the classic A History of Science by Sir William Dampier (Cambridge: Cambridge University Press, 1948). The recent biographies Schrödinger: Life and Thought by Walter Moore (Cambridge: Cambridge University Press, 1989) and Uncertainty: The Life and Science of Werner Heisenberg by David Cassidy (New York: W. H. Freeman, 1991) were also of great help, as were The Life and Times of Tycho Brake by John Allyne Gade (Princeton: Princeton University Press, 1947), Galileo at Work: His Scientific Biography by Stillman Drake (Chicago: University of Chicago Press, 1978), Galileo Heretic by Pietro Redondi (Princeton: Princeton University Press, 1987), and Enrico Fermi, Physicist by Emilio Segré (Chicago: University of Chicago Press, 1970). We are indebted to Heinz Pagels for two books: The Cosmic Code (New York: Simon & Schuster; 1982) and Perfect Symmetry (New York: Simon & Schuster; 1985), and to Paul Davies for Superforce (New York: Simon & Schuster; 1984).
Some books by nonscientists provided anecdotes, quotes, and other valuable information—most notably Scientific Temperaments by Philip J. Hilts (New York: Simon & Schuster, 1982) and The Second Creation: Makers of the Revolution in Twentieth-Century Physics by Robert P. Crease and Charles C. Mann (New York: Macmillan, 1986).
I've dug through what I can using just a computer, but I haven't had much success myself. At this point, I'm more confused that I can't find any trace of this quote, and yet the author uses it as if it was as ubiquitous as the story of Newton observing a falling apple. Is there anything to suggest that Isaac Newton said it?