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 of gravity of a group of bodies, oscillating about a horizontal axis, rises to its original height, but no higher, is expressed for the first time one of the most beautiful principles of dynamics, afterwards called the principle of the conservation of vis viva.[32] The thirteen theorems at the close of the work relate to the theory of centrifugal force in circular motion. This theory aided Newton in discovering the law of gravitation.

Huygens wrote the first formal treatise on probability. He proposed the wave-theory of light and with great skill applied geometry to its development. This theory was long neglected, but was revived and successfully worked out by Young and Fresnel a century later. Huygens and his brother improved the telescope by devising a better way of grinding and polishing lenses. With more efficient instruments he determined the nature of Saturn's appendage and solved other astronomical questions. Huygens' Opuscula posthuma appeared in 1703.

Passing now from Holland to England, we meet there one of the most original mathematicians of his day—John Wallis (1616–1703). He was educated for the Church at Cambridge and entered Holy Orders. But his genius was employed chiefly in the study of mathematics. In 1649 he was appointed Savilian professor of geometry at Oxford. He was one of the original members of the Royal Society, which was founded in 1663. Wallis thoroughly grasped the mathematical methods both of Cavalieri and Descartes. His Conic Sections is the earliest work in which these curves are no longer considered as sections of a cone, but as curves of the second degree, and are treated analytically by the Cartesian method of co-ordinates. In this work Wallis speaks of Descartes in the highest terms, but in his Algebra he, without good reason, accuses Descartes of plagiarising from Harriot. We have