In the Principia, Newton's laws appear under what heading?

In the Principia, Newton’s laws appear under the heading “Axioms, or Laws of Motion.” The heading comes near the beginning of Philosophiæ Naturalis Principia Mathematica, after the opening definitions and before the work’s three main books.

Newton presented the laws as foundational principles for analyzing motion. They describe inertia, the relation between force and changing motion, and the equal-and-opposite character of mutual forces. Together with his law of universal gravitation, they gave a mathematical framework for explaining both ordinary terrestrial motion and the motions of heavenly bodies.

The Principia was written in Latin and first published in 1687. Its full title means “Mathematical Principles of Natural Philosophy.” Newton’s original presentation is not identical to the simplified textbook versions commonly memorized today: it uses geometric arguments and defines “motion” through what is now understood as momentum.

Readers sometimes confuse the heading with other sections of the book. “Definitions” comes first, while “Rules of Reasoning” is a later methodological section associated with Book III. “System of the World” refers to a major part of the work’s content, not the heading under which the three laws are introduced.