Philosophiae Naturalis Principia Mathematica Summary

Sir Isaac Newton


(Critical Survey of Literature for Students)

One of the most influential books in history is Sir Isaac Newton’s Principia. Published in 1687, the book immediately led to intellectual controversy among the scientists and philosophers of the day, including Gottfried Wilhelm Leibniz, Robert Hooke, and John Flamsteed, who felt it necessary to argue with many of the propositions and conclusions Newton advances. These arguments give at least as much testimony to the importance of Principia as they undermine its theories. Newton’s book remained the principal document in the field of physics for two hundred years.

Newton’s work in physics has never been supplanted or debunked; relativity and other discoveries of the twentieth century are modifications and additions to his scientific discoveries rather than replacements. The philosophical implications of relativity and other discoveries of the twentieth century, however, are radically different from the philosophical implications of Newton’s discoveries. During the eighteenth century and after, Newton’s masterpiece also was a highly revered work of philosophy. Newton became one of the most honored figures in Western culture, one of the first formulators of scientific method, and the person whose work formed the basis for scientific study and application of principles. Physics, as a field of theory and knowledge, did not exist before Newton’s work.

Newton’s preface to the Principia announces that he is interested in the laws of mathematics as a means of discovering nature, or getting at philosophical truth. He thinks that mathematics is not a pure, abstract system, but rather a human and rational means for discovering the principles of the universe, for making a kind of universal order out of the disparate experience of the senses. In fact, he believes in this function of mathematics so strongly that, in the body of the Principia, every experiment or demonstration is concluded with a scholium. Each scholium is a short essay giving the philosophical implications or the speculative use of the mathematical or physical principle just demonstrated. Thus, Newton’s book is a philosophical as well as a scientific work.

After the preface, Newton supplies a series of definitions for such terms as “motion,” “force,” and “quantity,” terms necessary for even an elementary understanding of his work. These definitions are still standard among students of physics. Newton thereupon states his famous three axioms or laws of motion. These axioms are still relevant in any account of physical forces in the everyday world; relativity comes into play to a significant extent at the level of the atom and at speeds at or near the speed of light. Newton states these laws as axioms on which his whole account of the universe rests.

The first axiom states that a body remains in its existing state of motion or rest unless acted upon by an outside force. This is also known as the law of inertia. The second axiom states that the change in motion of a body is proportional, in precise mathematical terms, to the force applied to it. This is known as the law of acceleration. The third axiom states that for every action there is an equal and opposite reaction. Newton could not prove these axioms universally; rather, these principles are what best explain the various facts and data that people find in physical phenomena around them. The axioms, like the definitions, are necessary beginnings, points that must be accepted in order that all physical data can make rational sense. The axioms have six corollaries, propositions that can be established from the axioms and that can be used in turn to establish other propositions.

In the first book of the Principia, Newton deals with the motion of bodies. To simplify and explain his theories, in the first book he confines his observations and proofs to bodies moving in a vacuum. He begins with the more purely mathematical: establishing ratios (demonstrating the logic of the number system), determining the...

(The entire section is 1650 words.)