In 1684 came the famous visit to Newton by the astronomer Edmund Hailey. He had a problem concerning the gravitational attraction between the sun and the planets. Hailey and Hooker had concluded from Johannes Kepler's accounting of planetary motions that the force of attraction mustvary inversely with the square of the distance between a planet and the sun. But they had been unable to prove their idea. "What," Hailey asked Newton, "would be the curve described by the planets on the supposition that gravity diminished as the square of the distance?" Newton answered without hesitation: "An ellipses." How did he know that? "Why," replied Newton, "I havecalculated it. " These four words informed Hailey that Newton had worked out one of the most fundamental laws of the universe — the law of gravity. Hailey wanted to see the calculations at once, but Newton could not find his notes. He promised to write out the theorems and proofs. Under Hailey's insistent urging he completed a manuscript for the Royal Society. Thus was born the Philosophiae Naturalis Principia Mathematica, known ever since simply as the Principia.
1684年，天文学家埃德蒙·哈雷拜访了牛顿，这次访问后来广为人 知。哈雷在太阳与行星间的引力方面有个问题尚未解决。他和胡克从约翰尼斯·开普勒对行星运行的描述中得出结论，引力必然和行星与太阳间距离的平方成反比，但他们一直未能证明这一想法。哈雷问牛顿："假设引力随距离平方变化而减小，小行星运行的曲线是怎样的？"牛顿毫不犹豫地回答说："椭圆。" 他怎么会知道的呢？ "呃，"牛顿答道，"我计算过。"这四个字告诉哈雷，牛顿已经解决了宇宙中最基本的法则之一---引力定律。哈雷想要马上看看他的演算，但牛顿找不到笔记，于是答应把定理与演算全都写出来。在哈雷一再催促下，他为皇家学会完成了一篇稿子，《自然哲学的数学原理》就这样诞生了， 此稿自问世以来一直被简称为《原理》。