**Anders Lexell** made major contributions to spherical geometry and trigonometry.

- In 1768 Lexell was invited to St Petersburg.
- By this time Euler was getting quite old, being 62 years of age when the young mathematician Lexell arrived in 1769.
- However, working in the same Academy as Euler and other high quality scientists was something which Lexell found exciting and enjoyable.
- Euler discussed research plans with Lexell and the other mathematicians at the Academy.
- They shared ideas while Lexell sometimes developed further ideas suggested by Euler, sometimes calculating tables, and compiling examples.
- For example Lexell is given full credit on the title page for his help with Euler's 1772 publication Theoria motuum lunae, nova methodo pertractata Ⓣ(The theory of the motions of the moon: a new method of examination).
- In 1771 Lexell was appointed professor of astronomy at the St Petersburg Academy of Sciences and a few years later he was approached by the Swedish government trying to persuade him to return to Sweden.
- By this time Lexell had achieved quite a fine reputation as both a mathematician and astronomer and he was highly involved in the exciting work at the Academy.
- Despite the attractive proposition, Lexell was having none of it and turned it down in favour of staying permanently in St Petersburg.
- Despite wanting to remain in St Petersburg after 1780, Lexell did in fact spend two years travelling through to the mathematical centres of excellence throughout Europe, in particular visiting Germany, France and England.
- He returned to St Petersburg in 1782 and, following Euler's death in 1783, Lexell was appointed to succeed him to the chair of mathematics at the St Petersburg Academy of Sciences.
- Lexell's work in mathematics is mainly in the area of analysis and geometry.
- Lexell made a detailed investigation of exact equations differential equations.
- Lexell made major contributions to spherical geometry and trigonometry.
- Trigonometry was the main tool used by Lexell in his work on polygonometry.
- Specific problems which Lexell studied in astronomy were his calculation of the solar parallax and his calculation of the orbits of several comets.
- Lexell found that it had a period of five and a half years which made it the first comet to be discovered with a short period.
- He observed it pass close to Jupiter and its moons and since the moons were unaffected Lexell deduced that, despite the large size of comets, their mass was extremely low.
- When William Herschel discovered a new body in the solar system on 13 March 1781, Lexell computed its orbit which showed that it was a planet (later named Uranus) twice as far from the sun as Saturn, rather than a comet as had been thought at first.
- Although he did not predict the position of Neptune, as did Adams and Le Verrier, Lexell's initial calculations of the orbit of Uranus showed that it was being perturbed and he deduced that the perturbations were due to another more distant planet.

Born 24 December 1740, Äbo, Sweden (now Turku, Finland). Died 11 December 1784, St Petersburg, Russia.

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Astronomy, Origin Finland, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive