米夏埃尔·梅斯特林Michael Maestlin

米夏埃尔·梅斯特林出生在格平根，这是图宾根以东约50公里的一个村庄。他的父亲Jakob Mästlin和母亲多罗西娅·西蒙都是虔诚的路德教徒，梅斯特林在这种信仰中长大，并终生坚定地信奉它。他是家中的第二个孩子，有一个姐姐和一个弟弟。他在柯尼希斯布龙的修道院学校上学，然后在那里学习后，于1568年进入图宾根大学。[3]：-

正如许多年轻学者的情况一样，包括他最著名的学生约翰内斯·开普勒，[梅斯特林]在一所预备学校完成了本科学习，然后来到大学参加期末考试并获得学士学位。

在图宾根大学，他跟随菲利普·阿皮安（彼得鲁斯·阿皮亚努斯的儿子）学习数学和天文学，攻读硕士学位。1570年，他还是学生时，从维多林·斯特里格尔的遗孀那里购买了一本尼古拉·哥白尼的De revolutionibus ，维多林·斯特里格尔曾是莱比锡的神学教授，也是一本天文学教材的作者。梅斯特林于1571年以优异成绩获得硕士学位。在攻读这个学位期间，他编辑了Prutenis Tables的新版本，该版本于1571年出版。Prutenis Tables最初由埃拉斯穆斯·赖因霍尔德编纂，他基于尼古拉·哥白尼的太阳系版本。毕业后，梅斯特林在接下来的几年里在图宾根教书，同时修读了[3]：-

……神学课程，因为图宾根大学的主要使命是为路德教牧养培养年轻人。

然后，在1576年，他被派往巴克南的路德教会担任执事，巴克南是格平根西北约30公里的一个城镇。他于1577年4月与玛格丽特·格鲁宁格（1551-1588）结婚，不久后他在巴克南就职；他们有三个儿子和三个女儿，但玛格丽特因生第六个孩子时并发症去世。梅斯特林随后与图宾根一位教授的女儿玛格丽特·伯克哈特结婚；他们有八个孩子。

梅斯特林以其对1577年彗星的出色、非常精确的观测而闻名，这些观测是他在巴克南进行的，并于1578年在图宾根以Observatio et demonstratio cometae aetherae qui anno 1577 et 1578 constitutus in sphaera Veneris apparuit cum admirandius eius passionibus varietate scilicet motus loco orbe distantia a terro centro etc. adhibitis demonstrationibus geometricis et calculo arithmetico cuius modi de alio quoquam cometa nunquam visa est Ⓣ（对1577年和1578年以太彗星的观测与论证）为题出版。我们将在下文更详细地讨论这一成就。他在巴克南待了四年，随后于1580年被任命为海德堡大学数学教授。在那里，他出版了他著名的天文学教科书Epitome astronomiae（1582年）的第一版——他生前又出版了这部广受欢迎著作的六个后续版本。尽管他坚持尼古拉·哥白尼的观点（我们将在下文用他自己的话陈述），这部教学教科书纯粹是作为基于克劳狄乌斯·托勒密地心模型的天文学描述而写的。

在海德堡待了四年后，他回到图宾根的位置，在那里度过了余下的职业生涯 [2]：-

在图宾根，梅斯特林 多次被选为文学院院长。他深受同事和学生的喜爱。梅斯特林 对家人和他人都非常慷慨。他是一个虔诚的人；他遵循路德宗路线，反对格里高利历改革，部分原因是它由教皇发起。梅斯特林 有几个学生后来成为著名数学家，最著名的是 约翰内斯·开普勒。梅斯特林 还对圣经年代学和地理学保持兴趣。

也许他最大的成就（除了是 约翰内斯·开普勒 的老师）是他第一个计算了彗星的轨道，尽管他的方法不严谨。然而，他发现了1577年彗星的日心轨道，他声称这支持了 尼古拉·哥白尼 的日心体系。他确实表明彗星比月球更远，这与 亚里士多德 的公认教义相矛盾。尽管他显然相信 尼古拉·哥白尼 提出的体系，但他使用基于 克劳狄乌斯·托勒密 体系的自己的教科书教授天文学。然而对于更高级的讲座，他采用了日心方法——约翰内斯·开普勒 将 梅斯特林 介绍哥白尼思想归功于他在图宾根学生时期（1589-94）。在 [6] 中，Methuen 审视了 梅斯特林 教学中的这两种不同世界体系。A G Molland 评论了 Methuen 的论文：-

梅斯特林 在天文学革命叙述中通常被赋予一个坚定但次要的地位，作为 约翰内斯·开普勒 的老师以及哥白尼体系物理现实性的早期信仰者。不太清楚的是这与他在图宾根大学的常规教学有何关系，有些人认为他只是谨慎和私下教授哥白尼主义。Methuen 根据 梅斯特林 已出版的著作审视了这个问题，包括他主持辩论的五组论文（两组在海德堡，一组在图宾根）。她表明他毫不犹豫地坚定主张1572年新星和1577-1578年及1580年彗星的月上天位置。总的来说，他的著作，特别是他1582年的教科书《天文学概要》，没有显示出坚定的哥白尼承诺，尽管有倾向那个方向的迹象，并且他关注强调假设的可互换性。他的基础教学当然基于传统天文学，但 Methuen 得出结论，他向更高级的学生教授了更新的材料。她声称他明确区分了“球”和“天球”，前者具有物理现实性，后者仅仅是有用的数学构造……

梅斯特林 既是球面三角学的伟大专家，也是一位出色的观测者，产生了准确的数据——他视力的质量可以从他看到并绘制了昴星团中11颗恒星的位置这一事实看出。当然那时周围没有任何明亮的城市灯光，但我们挑战任何读者，无论他们找到多么黑暗的地点，都能匹敌这一成就。他似乎是最早声称月球暗部通过地球反射的阳光发光的人，但 列奥纳多·达·芬奇 也被认为有这个想法。梅斯特林 的另一个首次是准确计算黄金比例，在他1597年写给 约翰内斯·开普勒 的信中表述为“大约0.6180340”。

他是一位创新思想家，完全准备好挑战传统观点。例如，他试图测量一颗超新星视差，在未能找到任何视差后，推断它远至“恒星”那么远。这当然与自亚里士多德以来持有的观点相矛盾，即天上所有变化都发生在比恒星领域更靠近地球的地方，而恒星领域是不变的。

梅斯特林活到了伽利略发明用于天文观测的望远镜之时。他有两台相当差的望远镜，用它们能够观测太阳黑子和木星的卫星。他在78岁时仍在进行精确观测，当时他观测了1628年的月食。

正如我们上面提到的，梅斯特林 在1570年获得了 尼古拉·哥白尼 的 De revolutionibus 的副本，并在书的前面写了大量笔记。这些笔记提供了很多关于他对 尼古拉·哥白尼 观点的见解，我们引用 Gingerich 的翻译来引用这些笔记。梅斯特林 写道 [3]：-

……本书所呈现的安排是这样一种结构，其中所有恒星运动与现象都得到了非常精确的解释。因此，这一假说本身就值得理性接受。

梅斯特林续：-

天体运动濒临崩溃，因此尼古拉·哥白尼断定需要适当的假说来解释这些运动。当他注意到通常的假说不够充分时，他最终接受了地球可动的观念，因为这一观念不仅很好地符合现象，而且不会导致任何荒谬之处。

事实上，如果有人能把通常的假说整理得与现象相符且不留下任何矛盾，那么我会感激地信任他；显然他会使很多人接受他的观点。但我看到有些人，甚至是非常杰出的数学家，为此付出了努力，最终却毫无结果。因此，我认为除非通常的假说得到改革（由于我能力不足，我无法承担这项任务），我将接受尼古拉·哥白尼的假说和观点——在克劳狄乌斯·托勒密，所有天文学家之王之后。

还有梅斯特林[3]写的进一步注释，非常有趣。在De revolutionibus标题页的背面是那条臭名昭著的告示，其中写道：“……这些假说不必是真的，甚至不必是可能的；只要计算与观测相符就足够了。”梅斯特林在他的副本上加了一条注释，写道：-

这篇前言是某个人加上的，无论其作者是谁，（因为确实，其文风的软弱和用词的选择表明它并非出自尼古拉·哥白尼之手）。

他后来补充了一条注释：-

我在菲利普·阿皮安的书（我从他的遗孀那里购得）中某处发现了以下文字；尽管未署名，但我能辨认出彼得鲁斯·阿皮亚努斯的笔迹：

由于这封信，莱比锡教授、尼古拉·哥白尼的弟子格奥尔格·约阿希姆·雷蒂库斯与印刷商发生了非常激烈的争吵，印刷商声称这封信是连同其余作品一起交给他的。然而，格奥尔格·约阿希姆·雷蒂库斯怀疑是奥西安德尔[尼古拉·哥白尼著作的校对者]将其作为序言加在了作品前面。他宣称，如果他确知此事，他将对付那个家伙，使其今后管好自己的事，不再诽谤天文学家。尽管如此，[彼得]彼得鲁斯·阿皮亚努斯告诉我，奥西安德尔曾向他公开承认，这是他自己一人添加的。

Michael Mästlin was born in Göppingen which was a village about 50 km east of Tübingen. His father, Jakob Mästlin, and his mother, Dorothea Simon, were both devout Lutherans and Michael was brought up in that faith and remained strongly committed to it throughout his life. He was the middle child of the family, having an older sister and a younger brother. He attended the monastic school in Königsbronn then, after his studies there, entered Tübingen University in 1568. [3]:-

As was the case with many young scholars including Kepler, his most famous student, [Mästlin] did his undergraduate studies at a preparatory school and came to the university to take his final exams and pick up his baccalaureate degree.

At Tübingen University he studied mathematics and astronomy for a Master's degree under Philipp Apian who was Peter Apian's son. In 1570, while a student, he purchased a copy of Copernicus's De revolutionibus from the widow of Victorin Strigel, who had been professor of theology at Leipzig and the author of an astronomy text. Mästlin was awarded a Master's degree with distinction in 1571. While studying for this degree he had edited a new edition of the Prutenis Tables which was published in 1571. The Prutenis Tables had been originally compiled by Erasmus Reinhold who had based them on Copernicus's version of the solar system. After graduating, Mästlin spent the following years teaching in Tübingen, and at the same time took [3]:-

... the theological programme, because Tübingen University's primary mission was to prepare young men for the Lutheran ministry.

Then, in 1576, he was sent to be a deacon at the Lutheran Church in Backnang, a town about 30 km northwest of Göppingen. He married Margarete Gruuninger (1551-1588) in April 1577 not long after he took up the position in Backnang; they had three sons and three daughters but Margarete died due to complications with the birth of their sixth child. Mästlin then married Margarete Burkhardt, daughter of a professor at Tübingen; they had eight children.

Mästlin is famous for his excellent, very accurate, observations of the comet of 1577, observed while he was in Backnang, and published in Tübingen in 1578 as Observatio et demonstratio cometae aetherae qui anno 1577 et 1578 constitutus in sphaera Veneris apparuit cum admirandius eius passionibus varietate scilicet motus loco orbe distantia a terro centro etc. adhibitis demonstrationibus geometricis et calculo arithmetico cuius modi de alio quoquam cometa nunquam visa est Ⓣ. We discuss this achievement in more detail below. He remained in Backnang for four years, then was appointed as professor of mathematics at the University of Heidelberg in 1580. There he published the first edition of his famous astronomy textbook Epitome astronomiae (1582) - he published six further editions of this popular work during his lifetime. Despite his commitment to the views of Copernicus (which we state below in his own words) this teaching textbook was written purely as a description of astronomy based on the geocentric model of Ptolemy.

After four years in Heidelberg he returned to his position in Tübingen where he spent the rest of his career [2]:-

At Tübingen, Mästlin was elected dean of the arts faculty several times. He was well liked by both his colleagues and his students. Mästlin was very generous both to his family and to others. He was a religious man; he followed the Lutheran line in opposing the Gregorian calendar reform partly because it was initiated by the Pope. Mästlin had several students who became noted mathematicians, the most famous being Kepler. Mästlin also maintained interests in Biblical chronology and geography.

Perhaps his greatest achievement (other than being Kepler's teacher) is that he was the first to compute the orbit of a comet, although his method was not sound. He found, however, a sun centred orbit for the comet of 1577 which he claimed supported Copernicus's heliocentric system. He did show that the comet was further away than the moon, which contradicted the accepted teachings of Aristotle. Although clearly believing in the system as proposed by Copernicus, he taught astronomy using his own textbook which was based on Ptolemy's system. However for the more advanced lectures he adopted the heliocentric approach - Kepler credited Mästlin with introducing him to Copernican ideas while he was a student at Tübingen (1589-94). In [6] Methuen looks at these two different world systems in Mästlin's teaching. A G Molland reviews Methuen's paper:-

Michael Mästlin is regularly ascribed a firm if minor place in accounts of the Astronomical Revolution, as the teacher of Johannes Kepler and as an early believer in the physical reality of the Copernican system. What has been less clear is how this related to his regular teaching at the University of Tübingen, with some having argued that he only taught Copernicanism cautiously and in private. Methuen examines this question in the light of Maestlin's published writings, including five sets of theses over whose disputations (two at Heidelberg, one at Tübingen) he presided. She shows that he had no compunction about firmly asserting the supralunar position of the New Star of 1572 and of the comets of 1577 - 1578 and 1580. In general, his writings, especially his textbook 'Epitome astronomiae' of 1582, show no firm Copernican commitment, although there are signs of a leaning in that direction, and he was concerned with emphasizing the interconvertibility of hypotheses. His elementary teaching was certainly based on traditional astronomy, but Methuen concludes that he taught newer material to his more advanced students. She claims that he made a clear distinction between "spheres" and "orbs", with the former possessing physical reality and the latter being merely useful mathematical constructions ...

Mästlin was both a great expert on spherical trigonometry and also a fine observer producing accurate data - the quality of his eyesight is seen from the fact that he saw, and sketched the positions of, 11 stars in the Pleiades cluster. Of course there were not any bright city lights around then, but we challenge any reader to equal this achievement however dark a site they find. He seems to have been the first to claim that the dark part of the moon shone through sunlight reflected from the earth but Leonardo da Vinci has also been credited with this idea. Another first for Mästlin is an accurate calculation of the golden ratio as "approximately 0.6180340" stated in a letter he wrote to Kepler in 1597.

He was an innovative thinker who was quite prepared to challenge conventional views. For example he attempted to measure the parallax of a supernova and, having failed to find any, deduced that it was as far away as the "fixed stars". This of course contradicted the view, held since Aristotle, that all changes in the heavens occurred closer to earth than the realm of the stars which was unchanging.

Mästlin lived to see the invention of the telescope for astronomical observations by Galileo. He had two, rather poor, telescopes with which he was able to observe sunspots and the moons of Jupiter. He was still making accurate observations at the age of 78 when he observed the lunar eclipse of 1628.

As we mentioned above Mästlin acquired a copy of Copernicus's De revolutionibus in 1570 and he wrote extensive notes near the beginning of the book. These give much insight into his views on Copernicus and we quote the notes using Gingerich's translations. Mästlin wrote that [3]:-

... the arrangement presented in this book is the sort of structure in which all the sidereal motions and phenomena are explained very exactly. Therefore this hypothesis recommends itself to the intellect.

Mästlin continued:-

The heavenly motions were at the point of collapse, and so [Copernicus] concluded that appropriate hypotheses were needed to explain these motions. When he noticed that the common hypotheses were insufficient, he eventually accepted the idea of the Earth's mobility, since indeed, it not only satisfied the phenomena very well but it didn't lead to anything absurd.

In fact, if anyone would straighten out the common hypotheses so that they would agree with the phenomena and allow no inconsistencies, then I would gratefully trust him; clearly he would bring very many to his views. But I see that some, even very outstanding mathematicians, have laboured on this yet, in the end, without results. Therefore, I think that unless the common hypotheses are reformed (a task that I am not up to because of my inadequate abilities), I will accept the hypotheses and opinion of Copernicus - after Ptolemy, the prince of all Astronomers.

There are further annotations written by Mästlin [3] which are very interesting. On the back of the title page of De revolutionibus is the infamous notice which states that "... these hypotheses need not be true nor even probable; it is sufficient if the calculations agree with the observations." Mästlin adds a note to his copy stating:-

This preface was added by someone, whoever its author may be, (for indeed, its weakness of style and choice of words reveal that it is not by Copernicus).

He later added a further note:-

I found the following words written somewhere among the books of Philipp Apian (which I bought from his widow); although no author was given I could recognise Apian's hand:

On account of this letter Georg Joachim Rheticus, the Leipzig professor and disciple of Copernicus, became involved in a very bitter wrangle with the printer, who asserted that it had been turned over to him with the rest of the work. Rheticus, however, suspected that Osiander [the proof-reader of Copernicus's book] had prefaced it to the work. If he knew this for certain, he declared, he would handle that fellow so that in future he would mind his own business and not slander astronomers any more. Nevertheless, [Peter] Apian told me that Osiander had openly admitted to him that he had added this all by himself.