How Did Isaac Newton Discover Gravity?

We have all heard the story that an apple fell off a tree and struck Newton on the head and that's how he discovered gravity. While there may be some truth in the story especially about the apple, Newton utilized the findings of Galileo and other great scientists, of the time, to research and experiment to determine how the universe works. It was through this investigation and research Newton wanted to know if gravity was just limited to the earth and using mathematics he calculated the force to keep the moon in orbit around the earth. He then compared that calculation to the force needed to cause the apple to fall downward. Allowing for the difference in distance and mass Newton was able to deduct that the forces were the same and the moon is held in its orbit by the gravitational pull of the earth.