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Mathematical Treasure: Newton's Principia Mathematica

Frank J. Swetz (The Pennsylvania State University)

Isaac Newton’s opus magnum was Philosophiae Naturalis Principia Mathematica published in 1687. It revolutionized scientific thinking by formulating the laws of motion and universal gravitation. The Principia laid the foundation of classical mechanics. Shown above is the title page of the 1714 European release of the second edition first published in England in 1713. It was republished for a wider European audience by Sumptibus Societatis in Amsterdam.

This is the preface to the second edition included by the editor Roger Cotes. In his important preface, Cotes attacked the Cartesian philosophy then still in vogue in the universities, and refuted an assertion that Newton's theory of attraction was a causa occulta. This volume contains a second preface by Newton and considerable additions, the chapters on the lunar theory and the theory of comets being much enlarged. Also included is a laudatory poem on Newton’s work by his colleague Edmond Halley.

Pages 48 and 49 begin Section III of Book I of the Principia, “Of the motion of bodies on eccentric conic sections.”

Problem VI reads: “If a body revolves in an ellipse; it is required to find the law of the centripetal force tending to the focus of the ellipse.”

Problem VII reads: “Suppose a body to move in an hyperbola; it is required to find the law of centripetal force tending to the focus of the figure.”

The images above are supplied through the courtesy of the Rare Books and Manuscripts Collection of the Pennsylvania State University Library and the assistance of Dr. Sandra Stelts, Curator of the Collection.

For images from Newton's work as of 1779-1787, see Isaac Newton's Collected Works.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Newton's Principia Mathematica," Convergence (June 2015)