Philosophiae Naturalis Principia Mathematica

by Sir Isaac Newton
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Last Updated on May 6, 2015, by eNotes Editorial. Word Count: 407

In the summer of 1684, the astronomer Edmond Halley asked Isaac Newton for his thoughts on planetary motion. Newton’s response, based on his early mathematical calculations, was that the planets would travel around the Sun in elliptical paths. Some months later, Newton provided Halley with a written mathematical proof of his prediction. At Halley’s request, Newton then set about to further explain the forces of nature that governed the motion of objects, including the movement of celestial bodies. By July 5, 1687, the results of this work appeared as the first edition of Newton’s Principia.

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Newton was totally absorbed in the writing of the Principia for eighteen months. He would frequently forget to eat and slept only when overcome with exhaustion. Although it is not without errors, it has often been said that the Principia is the greatest work of science ever published. However, without considerable mathematical skills, it is difficult to follow and virtually impossible to comprehend. In addition to its complex mathematical language, the Principia was written in Latin (and not translated into English until two years after Newton’s death). By writing for an elite audience, Newton hoped he would be spared the annoyance of debating his work with those of lesser education. Nevertheless, its influence on the scientific revolution of the seventeenth century was crucial in overturning the prevailing philosophers’ view of the universe forever.

Newton divided the Principia into three books. In books 1 and 2, Newton describes the motions of bodies and outlines his mathematical treatments of both terrestrial and celestial mechanics. Book 1 contains almost one hundred propositions in which Newton develops a general theory of motion, including the motion of celestial bodies such as the planets. He describes how objects behave when subjected to forces. Book 2 examines resisted motions and the influence of fluids on a body’s motion (for example, the effect of air resistance on a moving object). Newton’s conclusion—that planetary motion is not impeded by any fluid object in space—was a departure from the long-held philosophical belief that a fluid substance, called ether, permeated space and affected the motion of heavenly bodies. In book 3, Newton uses his mathematical concepts from the first two books to describe his system of the world. He discusses the law of gravitation, tidal motion, and comet theory and calculates the speed of sound. Throughout the work, Newton relies on experiments and observations, both his and others’ to derive his mathematical laws.

Motion and Forces

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Last Updated on May 6, 2015, by eNotes Editorial. Word Count: 600

The Principia opens with a series of definitions and laws, which are followed by numerous explanatory notes and comments (scholia and corollaries). Included in these laws are Newton’s three laws of motion: First, every body will continue in its state of rest or uniform motion in a straight line unless it is compelled to change its state by an external force impressed on it (law of inertia); second, a change of motion is always proportional to the force being applied to the body and the new motion will be in the straight line in which the force is impressed; and third, for every action there is always an equal and opposite reaction. From these laws, Newton developed his law of universal gravitation.

Mechanics is the branch of applied mathematics that deals with the motion of objects, and it had advanced considerably by the seventeenth century. However, the field of dynamics, which explains how forces influence motion, was not well understood until Newton introduced his laws of motion in the Principia . Of particular interest to Newton were forces that resulted in an object...

(The entire section contains 2066 words.)

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