How did Isaac Newton’s tract De Motu develop into the Principia?

In 1684, astronomer Edmond Halley visited Isaac Newton to discuss the problem of orbital dynamics. Newton revealed he had already solved the issue, and three months later, he provided Halley with a short tract titled De Motu ("On Motion").1

Newton immediately began expanding and refining this work, which evolved into his masterpiece, the Philosophiae Naturalis Principia Mathematica, over the next two and a half years. The development process was transformative:1

• Incorporating Laws of Motion: Unlike De Motu, the Principia integrated Newton’s three laws of motion, which were essential to his system of nature.1
• Quantifying Force: Newton embraced the principle of inertia and formulated the second law of motion, providing a precise quantitative description of forces between bodies.1
• Universal Gravitation: Through these revisions, Newton applied his mechanics to planetary motion, leading to the formulation of the law of universal gravitation.1
• Mathematical Foundation: Newton introduced his calculus—a geometric theory of limits—in the Principia to provide the necessary mathematical basis for his dynamics.1

Halley played a crucial role in this transition by encouraging Newton’s expansion, editing the text, and financing its publication in 1687.12