# James Gregory

Date of Birth: 1638

Age: 37

Place of birth: Dramouk

Citizenship: United Kingdom

**The founder of mathematical analysis**

James Gregory was the youngest of the sons of John Gregory, servant of the Scottish Episcopal Church. Born James Dramoake, Aberdeenshire; at first education he received at home, under the guidance of his mother Janet Anderson. It was his mother instilled a love of geometry James. Uncle Gregory, Alexander Anderson, was a pupil of the legendary poet and editor Francois Vieta.

In 1651-m, died John Gregory; head of the family was the eldest of the sons of David - and it was he who took over responsibility for the further training of James. In 1657-m Man sent to Aberdeen grammar school, and then - in Marishelya College. Gregory graduated from college in 1657-m.

In 1663-m James went to London. There he met John Collins and his friend and colleague Scott Robert Moray - the first president of the Royal Society. In 1664-m Gregory moved to the University of Padova, Venice; on the way he passed through Flanders, Paris and Rome. In Padua, James lived in the house of his countryman, James Kaddenheda, professor of philosophy; science he learned under the guidance of Stefano Angeli.

Back in the 1668 meters in London, Gregory became a member of the Royal Society. In the end, he went to St. Andrews, where he became the first manager of the Department of Mathematics - the post has been specially created for him by Charles the Second (rumors say that at the request of Robert Moray). Later Gregory first became a professor at the University of St Andrews, and then at the University of Edinburgh. It is in Edinburgh and died Gregory; This happened in October of 1675 th - mathematics at that time was only 36 years old.

Among the extensive legacy of James, notably the two works - `Optica Promota` and` Vera Circuli et Hyperbolae Quadratura`. The first work was dedicated to reflecting the (Gregorian) telescope; In addition, Gregory describes how to use the Venus can measure the distance from Earth to the Sun; Later this method was used by Edmund Halley, and formed the basis of the first truly accurate measurement of the value of the astronomical unit.

`Vera Circuli et Hyperbolae Quadratura` came out in 1667-m; James it demonstrated how a circle and square hyperbola can be represented as a converging infinite series. It is in this work were invited to a statement stating that the terms of an arbitrary ratio of the sector to those described or inscribed polygons can be generally represented by the expression of finite length; obrazomGregori thus proved that the famous problem of squaring the circle has no solution. Later, Jean-Etienne Montuklya precisely on the basis of this evidence could show that certain sectors may still be `kvadratizirovany` - and in the particular case of this sector can show a full circle. Anyway it is the first time Gregory spoke about what is now called transcendental numbers. In addition, James is credited with the discovery of Taylor series and the first proof of the theorem Newton-Leibniz. Also, `Vera Circuli et Hyperbolae Quadratura` considered converting classical functions sin (x), cos (x), arcsin (x) and arccos (x). In 1668-m was republished; it added a new chapter, `Geometriae Pars`, where James was talking about the calculation of the volume of the different bodies of rotation.