拉斯穆·巴多林Rasmus Bartholin

拉斯穆·巴多林的父亲是Caspar Berthelsen 巴多林，母亲是Anna Fincke，即数学家汤玛斯·芬克的女儿。Caspar Bartholin是一位丹麦医生和神学家，撰写了文艺复兴时期最广为阅读的解剖学手册之一。巴多林出生时，他是哥本哈根大学的教授，但在巴多林不到四岁时去世。家中有六个儿子，巴多林有一个比他大九岁的兄弟Thomas Bartholin。这两兄弟后来变得同样著名。

巴多林最初接受私人教师的教育，随后进入一所拉丁学校。他于1642年进入哥本哈根大学，1644年获得学士学位，1647年获得硕士学位。从1645年起，他在莱顿大学学习数学，1651年前往法国，但随后前往意大利，在包括帕多瓦在内的多个地方学习，并于1654年在那里获得医学学位。从1656年起，他担任哥本哈根大学几何学教授，但次年转任医学特聘教授。1671年，他被任命为哥本哈根大学医学常任讲席，担任该职位直至去世。1667年，他被任命为皇家数学家[1]：-

他曾任哥本哈根大学医学院院长、图书馆馆长和校长，并被任命为御医和枢密顾问。

尽管长期担任医学教授，但他在该领域著述相对较少。从出版物数量来看，数学是他工作中占比最大的部分，但他在这一领域的工作并不十分重要。事实上，他最著名的工作是在另一个领域，因为他是光的双折射的发现者。

巴多林编辑了弗兰斯·范斯霍滕的Introduction to the geometry of Descartes，还将拉里萨的Optics翻译成拉丁文。在1664年至1674年间，他每年都出版一本Dissertatio de problematibus geometricisⓉ（《论几何问题》）。该书由他提出供学生答辩的论文组成。在1672年出版的第六本此类书中，他给出了对所谓Debeaune第二问题的证明，该问题是在1638年写给马兰·梅森的一封信中提出的。这个问题是反切线问题的第一个例子，用现代记号表示，它要求解微分方程

$\Large\frac{dy}{dx}\normalsize = \Large\frac{x-y}{a}\normalsize , y(0) = 0.$

其解为$y = x + a(e^{-x/a} - 1)$。勒内·笛卡儿在1639年解决了Debeaune的问题。巴多林以几何形式考虑了这个问题。在[6]中，Pedersen提出巴多林的证明实际上可能就是Debeaune的原始证明，我们知道后者将其寄给了勒内·笛卡儿。巴多林很可能在Debeaune于1652年去世前不久寄给他保管的论文中看到了这个证明。

要了解巴多林写作主题的范围，可以考虑他于1674年出版的著作De naturae mirabilibus quaestiones academicae Ⓣ（关于自然奇观的学术问题）。该书由多年间撰写的论文和讲座组成，例如：The study of the Danish language（1657年）；The shape of snow（1660年）；The pores of bodies（1663年）；On Cartesian physics（1664年）；On nature（1666年）；On judgement and memory（1667年）；On experiment（1668年）；On physical hypotheses（1669年）；On the shape of bodies（1671年）；以及Secrets of the sciences（1673年）。

巴多林写了大量数学著作，但他最为人所铭记的是发现了光通过冰洲石晶体的双折射，这种晶体是在1668年一次冰岛探险中采集到的。他于1669年撰写了关于晶体几何学的著作Experimenta crystalli Islandici disdiaclastici quibus mira & insolita refractio detegitur Ⓣ（冰洲石中奇妙而不寻常的折射实验）。他将这两条光线称为solita和insolita，并证明两者都是由折射产生的。在实验中，巴多林还观察到，当冰洲石晶体绕其轴旋转时，两个图像中的一个会围绕另一个作圆周运动。这是晶体以某种方式将光分裂成两束不同光束的有力证据。巴多林的解释基于勒内·笛卡儿的光学理论，以及他认为晶体中存在两组“孔隙”的想法。然而，真正的解释是晶体将光分裂成两束平面偏振光束。

他观察了1664年和1665年的彗星，并进行了其他天文观测，在De cometis anni 1664 et 1665 opusculum Ⓣ（关于1664年和1665年彗星的著作）（1665年）中发表了对这些事件的描述。巴多林还准备出版了第谷·布拉赫的观测结果。在这两项天文学工作中，他都得到了Ole Rømer的协助。

巴多林还因其医学工作而闻名，特别是他在抗击疟疾中引入了奎宁。他的一些医学贡献是与他的兄弟Thomas Bartholin共同做出的，后者从1646年到1661年担任哥本哈根大学的解剖学教授。Thomas Bartholin创办了期刊Acta medica et philosophica Hafniensia，巴多林为其投稿。

Erasmus Bartholin's father was Caspar Berthelsen Bartholin and his mother was Anna Fincke, daughter of the mathematician Thomas Fincke. Caspar Bartholin was a Danish physician and theologian who wrote one of the most widely read Renaissance manuals of anatomy. He was a professor at the University of Copenhagen when Erasmus was born but died when Erasmus was less than four years old. There were six sons in the family, and Erasmus had a brother, Thomas Bartholin, who was nine years older than himself. These two brothers went on to become equally famous.

Erasmus received his first education from private tutors, then he attended a Latin school. He entered the University of Copenhagen in 1642, receiving his B.A. in 1644 and an M.A. in 1647. From 1645 he studied mathematics at the University of Leiden, travelling to France in 1651 but then going to Italy where he studied at a number of places including Padua from where he received a medical degree in 1654. From 1656 he was professor of geometry at the University of Copenhagen but transferred to become an extraordinary professor of medicine in the following year. In 1671 he was appointed to an ordinary chair of medicine at Copenhagen, a post to held until his death. In 1667 he was appointed Royal Mathematician [1]:-

He served the University of Copenhagen as dean of the faculty of medicine, librarian, and rector, and was appointed royal physician and privy councillor.

Despite being professor of medicine for a long period, he wrote relatively little on that topic. In terms of the number of publications, mathematics was the largest part of his work, but his work in this area is not of great importance. In fact he is best known for work in yet another area, for he was the discoverer of the double refraction of light.

Bartholin edited Introduction to the geometry of Descartes by van Schooten and also translated Optics of Larissa into Latin. Every year between 1664 and 1674 he produced a book Dissertatio de problematibus geometricis Ⓣ. This consisted of theses which he had proposed for his students to defend. In the sixth such book, published in 1672, he gave a proof of what is known as the second problem of Debeaune, formulated in a letter to Mersenne written in 1638. The problem is the first example of an inverse tangent problem which in modern notation results in requiring the solution to the differential equation

$\Large\frac{dy}{dx}\normalsize = \Large\frac{x-y}{a}\normalsize , y(0) = 0.$

This has solution $y = x + a(e^{-x/a} - 1)$. Descartes solved Debeaune's problem in 1639. Bartholin considered the problem in geometric form. In [6] Pedersen suggests that Bartholin's proof may actually be Debeaune's original proof which we know he sent to Descartes. Bartholin could well have come across the proof in papers which Debeaune sent him for safe keeping shortly before his death in 1652.

To see the range of topics on which Bartholin wrote, consider his book De naturae mirabilibus quaestiones academicae Ⓣ which he published in 1674. This consists of essays and lectures written over a number of years such as: The study of the Danish language (1657); The shape of snow (1660); The pores of bodies (1663); On Cartesian physics (1664); On nature (1666); On judgement and memory (1667); On experiment (1668); On physical hypotheses (1669); On the shape of bodies (1671); and Secrets of the sciences (1673).

Bartholin wrote a large number of mathematical works but he is best remembered for his discovery of the double refraction of light through a crystal of Iceland spar which had been gathered in an expedition to Iceland in 1668. He wrote his text Experimenta crystalli Islandici disdiaclastici quibus mira & insolita refractio detegitur Ⓣ on the geometry of crystals in 1669. The two rays he called solita and insolita and he showed that both were produced by refraction. During his experiments, Bartholin also observed that when the crystals of Iceland spar are rotated about their axis, one of the two images moves in a circle around the other. This is strong evidence that the crystals are somehow splitting the light into two different beams. Bartholin's explanation was based on Descartes' theory of light along with his idea that there were two sets of "pores" in the crystal. However, the true explanation is that the crystal splits the light into two plane-polarized beams.

He observed the comets of 1664 and 1665, and made other astronomical observations, publishing his descriptions of these events in De cometis anni 1664 et 1665 opusculum Ⓣ (1665). Bartholin also prepared for publication the observations of Tycho Brahe. In both these pieces of work in astronomy he was assisted by Ole Rømer.

Bartholin is also famed for his medical work, in particular his introduction of quinine in the fight against malaria. Some of his medical contributions were made in conjunction with his brother Thomas Bartholin who was a professor of anatomy at the University of Copenhagen from 1646 to 1661. Thomas Bartholin founded the journal Acta medica et philosophica Hafniensia to which Erasmus Bartholin contributed papers.