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Mathematical Treasure: Newton's Principia

Frank J. Swetz (Pennsylvania State University)

Isaac Newton’s Principia Mathematica or the Mathematical Principles of Natural Philosophy, first published in 1687, is considered one of the greatest works of scientific literature. This edition was published in Amsterdam in 1714.

Proposition LIII, Problem xxxv reads:

Granting the quadratures of curvilinear figures, it is required to find the forces under which bodies moving in curved lines may always perform their oscillations in equal times.

Proposition XXII:

Let the density of any fluid be proportional to the compression, and its parts to be attracted downwards by gravitation reciprocally proportional to the square of the distances from the centre: I say, that if the distances be taken in harmonic progression, the densities of the fluid at those distances will be in a geometric progression.


Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Newton's Principia," Loci (September 2013)