# Gregory, James

### series functions calculus newton

(1638–75) Scottish mathematician: contributed to discovery of calculus.

A graduate of Aberdeen, Gregory went on to study at Padua, and became the first professor of mathematics at St Andrews when he was 30. After 6 years he moved to Edinburgh, but died a year later. While in Italy he published a book in which he discussed convergent and divergent series (terms he used for the first time), the distinction between algebraic and transcendental functions and circular, elliptic and hyperbolic functions. He found series expressions for the trigonometric functions and gave a proof of the fundamental theorem of calculus (in 1667), although he did not note its significance. In letters of 1670 he used the binomial series and interpolation formula (both independently of Newton) and the series named after B Taylor (1685–1731).

He also contributed to astronomy; when he was 25 he suggested that transits of Venus (or Mercury) could be used to find the distance of the Sun from the Earth, and the method was later used. He proposed in the same book that telescopes could be made using mirrors in place of lenses, avoiding the colour aberration inevitably introduced by a lens. About 5 years later Newton made such a reflecting telescope, and large telescopes have usually been reflectors ever since.

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