安德斯·约翰·莱克塞尔Anders Johan Lexell

安德斯·约翰·莱克塞尔有时以他名字的俄语版本Andrei Ivanovich Lexell为人所知。他的父亲Jonas Lexell是一名珠宝商，但也作为地方议员参与政治。莱克塞尔的母亲是Magdalena Catharina Björckegren。他在奥布接受教育，就读于那里的大学，并于1760年毕业。三年后，他被任命为乌普萨拉航海学校的助理教授，1766年成为那里的数学教授。

1768年，莱克塞尔受邀前往圣彼得堡。St Petersburg Academy of Sciences由彼得大帝的妻子叶卡捷琳娜一世于1725年创立，莱昂哈德·欧拉自1727年起在那里工作。此时莱昂哈德·欧拉已相当年迈，当年轻的数学家莱克塞尔于1769年到来时，他已62岁。然而，与莱昂哈德·欧拉和其他高素质科学家在同一科学院工作，是莱克塞尔觉得兴奋和愉快的事情。莱昂哈德·欧拉与莱克塞尔和科学院的其他数学家讨论研究计划。他们分享想法，而莱克塞尔有时进一步发展莱昂哈德·欧拉提出的想法，有时计算表格，并编纂例子。例如，莱克塞尔在莱昂哈德·欧拉1772年出版物Theoria motuum lunae, nova methodo pertractata Ⓣ（月球运动理论：一种新的检验方法）的扉页上因他的帮助而获得充分赞誉。

1771年，莱克塞尔被任命为圣彼得堡科学院的天文学教授，几年后瑞典政府试图说服他返回瑞典。此时，莱克塞尔作为数学家和天文学家已享有相当好的声誉，并且高度参与科学院令人兴奋的工作。了解到这一点，瑞典政府试图用一个巧妙制定的提议吸引他回来。他将立即被任命为奥布大学的讲席（这是在1775年），但由于他如此投入圣彼得堡科学院正在进行的工作，他将被允许在那里再留五年以完成工作，然后返回奥布。尽管这个提议很有吸引力，莱克塞尔完全不接受，并拒绝了它，选择永久留在圣彼得堡。

尽管希望在1780年后留在圣彼得堡，莱克塞尔实际上花了两年时间游历欧洲各地的数学卓越中心，特别是访问了德国、法国和英国。他于1782年返回圣彼得堡，在莱昂哈德·欧拉于1783年去世后，莱克塞尔被任命接替他担任圣彼得堡科学院的数学讲席。他没有担任这个讲席很长时间，因为他在次年去世。

莱克塞尔在数学方面的工作主要是在分析和几何领域。莱克塞尔对恰当方程微分方程进行了详细研究。他在这里的工作扩展了早先由尼古拉·德·孔多塞和莱昂哈德·欧拉发现的一个必要条件。他还给出了一个不基于使用变分法的证明。此外，莱克塞尔与莱昂哈德·欧拉同时发展了微分方程的积分因子理论，但是，尽管人们常常认为他从莱昂哈德·欧拉那里学到了这项技术，[2]的作者认为他独立发现了解决莱昂哈德·欧拉所研究问题的原创方法。

莱克塞尔在分析方面的工作涉及微分方程以外的主题，例如他提出了elliptic integrals的分类，并研究了约瑟夫·拉格朗日级数。他也是第一个发展出一般多边形测量系统的人。这是对多边形的研究，类似于早期对三角形的工作。它涉及给定某些边和它们之间的角来解多边形，它们的测量，用对角线分割，围绕圆外接多边形和在圆内接多边形。他在这个主题上的工作由Lhuilier继续。

莱克塞尔在球面几何学和三角学方面做出了重大贡献。事实上，三角学是莱克塞尔在其多边形测量工作中使用的主要工具。球面几何学是他天文研究中的主要工具。

莱克塞尔在天文学中研究的具体问题包括他对太阳视差的计算以及他对几颗彗星轨道的计算。他计算轨道的一颗彗星是由Messier发现的。莱克塞尔发现它的周期为五年半，这使它成为第一颗被发现具有短周期的彗星。他观察到它靠近木星及其卫星，由于卫星未受影响，莱克塞尔推断出，尽管彗星体积巨大，它们的质量却极低。

当威廉·赫歇尔于1781年3月13日发现太阳系中的一个新天体时，莱克塞尔计算了它的轨道，结果表明它是一颗行星（后来命名为天王星），距离太阳是土星的两倍，而不是最初认为的彗星。尽管他没有像约翰·柯西·亚当斯和于尔班·勒维耶那样预测海王星的位置，但莱克塞尔对天王星轨道的初步计算表明它受到了摄动，他推断这些摄动是由另一颗更遥远的行星引起的。

Anders Lexell is sometimes known by the Russian version of his name which is Andrei Ivanovich Lexell. His father, Jonas Lexell, was a jeweller by trade but was also involved in politics as a local councillor. Anders' mother was Magdalena Catharina Björckegren. He was educated in Abo, attending the university there and graduating in 1760. Three years later he was appointed assistant professor at Uppsala Nautical School and in 1766 he became professor of mathematics there.

In 1768 Lexell was invited to St Petersburg. The St Petersburg Academy of Sciences had been founded by Catherine I, the wife of Peter the Great, in 1725 and Euler had worked there since 1727. 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 Ⓣ.

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. Knowing this, the Swedish government tried too attract him with back with a cleverly worked out offer. He would be appointed to a chair at the University of Abo immediately (this was in 1775) but since he was so involved at work being undertaken at the St Petersburg Academy he would be allowed to remain there for five years to complete the work before returning to Abo. 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. He did not hold this chair for very long since he died in the following year.

Lexell's work in mathematics is mainly in the area of analysis and geometry. Lexell made a detailed investigation of exact equations differential equations. His work here extended a necessary condition which had been discovered earlier by Condorcet and Euler. He also gave a proof which was not based on using the calculus of variations. In addition Lexell developed a theory of integrating factors for differential equations at the same time as Euler but, although it has often been thought that he learnt of the technique from Euler, the author of [2] argues that he independently discovered original methods to solve problems investigated by Euler.

Lexell did work in analysis on topics other than differential equations, for example he suggested a classification of elliptic integrals and he worked on the Lagrange series. He was also the first to develop a general system of polygonometry. This is a study of polygons similar to earlier work on triangles. It involves the solution of polygons given certain sides and angles between them, their mensuration, division by diagonals, circumscribing polygons around circles and inscribing polygons in circles. His work on this topic was continued by Lhuilier.

Lexell made major contributions to spherical geometry and trigonometry. In fact trigonometry was the main tool used by Lexell in his work on polygonometry. Spherical geometry was a major tool in his astronomical studies.

Specific problems which Lexell studied in astronomy were his calculation of the solar parallax and his calculation of the orbits of several comets. One comet for which he calculated an orbit had been discovered by Messier. 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.