Philosophiae naturalis principia mathematica (Mathematical principles of natural philosophy) is Sir Isaac Newton’s masterpiece. Its appearance was a turning point in the history of science, and the treatise is considered by many as the most important scientific work ever published. Newton (1642–1727) was a professor of mathematics at Trinity College, Cambridge, when he produced the work. It presents the basis of physics and astronomy, formulated in the language of pure geometry. It is a deductive work in which, from very general propositions, mechanical properties are demonstrated in the form of theorems. It lays the foundations of hydrostatics, hydrodynamics, and acoustics, and systematizes a method for the study of nature by mathematical means. The work was written in Latin, which indicates its intended audience: experts in mathematics and mechanics, astronomers, philosophers, and university graduates. The Principia, as the work is known, consists of three books, preceded by a preliminary chapter of definitions and another that deals with axioms or the laws of movement. The “definitions,” eight in total, define the vocabulary that is used throughout the text and introduce the concept of absolute space and time. Book 1, “Axioms and the Laws of Movement” is by far the best-known part of the work. Newton’s first law states that every object continues to do what it happens to be doing in its state of rest or uniform motion unless a force is exerted upon it. The state of inertia thus becomes the first law or axiom. The second law states that the net force on an object is equal to the rate of change of its linear momentum in an inertial reference frame. The third law states that all forces between two objects exist in equal magnitude and opposite direction. It is on this third law that gravitational dynamics as a system of reciprocal attraction is based. Book 2 deals with the movement of bodies in relation to resistance and velocity. In this central part of the work, the first chapter deals with the movement of objects in a vacuum, i.e., the motion of objects that encounter no resistance. Book 3, “The System of the World,” is where the principles of astronomy elaborated previously are applied. Newton explores derivation of the laws of gravity, implications for planetary orbits, the moon and equinoxes in their relation to gravitational theory, and the study of comets. He finishes the treatise with the text of the “General Scholium,” added from the second edition onward. This infers a rational explanation for the existence of a superior being and is famous for his statement “I do not feign hypotheses” about his methodology. The Principia appeared in three editions during Newton’s lifetime: the first in 1687, with a print run of 300–400 copies; this was followed by the 1713 edition, revised, amended, and expanded by the author; which in turn was followed by the 1726 edition, revised by Newton and edited by Henry Pemberton. Andrew Motte’s English translation did not appear until 1729 (after Newton’s death). The French edition was published in 1756; it was translated by the Marquise de Châtelet, with additions by the mathematician Alexis-Claude Clairaut, and a foreword by Voltaire.

Last updated: March 30, 2016