埃拉斯穆斯·赖因霍尔德Erasmus Reinhold

埃拉斯穆斯·赖因霍尔德的父亲是Johann Reinhold（1479-1558），一位税务官，也是Saalfeld本笃会修道院最后一位院长的秘书。关于赖因霍尔德的青年时期和早期教育所知甚少。他有一个兄弟，与他们的父亲一样名叫Johann，于1549年成为Greifswald的数学教授。赖因霍尔德和他的兄弟都于1553年去世。赖因霍尔德在Saalfeld的Stadtschule学习，然后于1530年入读维滕贝格大学，该大学当时是一所年轻的机构，成立于1502年。他在Jakob Milich（1501-1559）指导下学习数学，并于1535年以Magister毕业。

1536年Johannes Volmar教授去世后，在Philipp Melanchthon的鼓动下，赖因霍尔德获得了维滕贝格大学“Mathematum Superiorum”讲席，其中包括天文学，而他的同事格奥尔格·约阿希姆·雷蒂库斯则成为“Mathematum Inferiorum”。Volmar曾在克拉科夫和维滕贝格学习，之后前往莱比锡大学。他回到维滕贝格，于1519年被任命为数学教授。他最著名的学生是格奥尔格·约阿希姆·雷蒂库斯。Philipp Melanchthon（1497-1560），马丁·路德的“得力助手”，是一位神学家、希腊语教授和教育家，他重组了德国的整个教育体系，创建并改革了多所大学。Melanchthon在促成赖因霍尔德和格奥尔格·约阿希姆·雷蒂库斯于1536年被任命到维滕贝格大学讲授数学和天文学方面发挥了重要作用。然而，格奥尔格·约阿希姆·雷蒂库斯在1538-1541这三年间离开了维滕贝格，其中两年是与尼古拉·哥白尼一起度过的。

赖因霍尔德在文学院被选为院长，在1540-41年冬季担任该职位，然后在1549年夏季担任哲学院院长。他在1549-50年冬季成为校长。对维滕贝格的人来说，这是一个困难时期，因为这里是新教改革的焦点，改革始于1517年马丁·路德将他的95条论纲钉在维滕贝格城堡的大门上。赖因霍尔德和维滕贝格的大多数人一样，是路德教徒。这座城市是萨克森的首府，由萨克森选帝侯统治。1546-47年的施马尔卡尔登战争见证了路德教徒与罗马天主教皇帝查理一世的战斗。当查理一世于1547年占领维滕贝格时，战争结束，维滕贝格投降书签署，迫使萨克森选帝侯退位。在这些戏剧性事件期间，赖因霍尔德留在大学试图继续他的工作。

赖因霍尔德与格奥尔格·约阿希姆·雷蒂库斯一起，是最早将哥白尼的日心说理论引起德国注意的学者之一。在他1542年的Theorciae novae PlanetarumⓉ（新行星理论）中，他称尼古拉·哥白尼为“第二个克劳狄乌斯·托勒密，他修复了衰败的教育大厦”。然而，赖因霍尔德在他的讲座中继续背诵托勒密学说。这可能部分是由于维滕贝格的神学权威，他们认为尼古拉·哥白尼的模型是异端，但赖因霍尔德在自己拥有的尼古拉·哥白尼的De RevolutionibusⓉ（论天球的旋转）副本上的评论似乎表明，他只对模型的数学方面感兴趣，而对宇宙学理论不感兴趣。

赖因霍尔德在其De RevolutionibusⓉ（《论天球的旋转》）副本上所写注释的鉴定，是由Owen Gingerich于1970年做出的，当时他检查了保存在苏格兰爱丁堡皇家天文台的De RevolutionibusⓉ（《论天球的旋转》）副本。以下是Gingerich对这一重要发现的描述[3]：-

我徒劳地寻找所有者的名字。开头和结尾的手写题词没有提供任何线索。然后我更仔细地观察厚重的猪皮装订。……边缘周围是带有圣经人物图案的长条。在空白的中央面板下方是日期1543，面板上方我注意到首字母ER。我震惊地反应。这些首字母可能代表赖因霍尔德，即尼古拉·哥白尼之后一代的领先数学天文学家……？我抓起铅笔和纸，想拓下模糊的印记，令我沮丧的是，发现不是两个，而是三个首字母：ERS。看来我的假设刚刚破灭了。回到剑桥……我很快发现，这三个首字母ERS，正是赖因霍尔德 Reinholdus Salveldiensis所需要的，因为在十六世纪，一个人的出生地——在这个例子中是Saalfeld——是其正式称号的一部分。……[赖因霍尔德笔迹的]样本最终证实了我最初的推断。

[4]的作者们讨论了赖因霍尔德在这本De RevolutionibusⓉ（《论天球的旋转》）副本中所作的注释：-

赖因霍尔德的注释既广泛又彻底：很难在文本中找到一处他尚未标出的错误。通篇看来，赖因霍尔德对哥白尼的资料来源（如Giorgio Valla、约翰尼斯·维尔纳或约翰·缪勒的《概要》）表现出惊人的了解，即便尼古拉·哥白尼并未明确提及它们。赖因霍尔德用题页上的一句题词概括了他对尼古拉·哥白尼著作的处理方式，那是对第I,4章标题的改写：“天文学的 axiom：天体运动是均匀且圆周的，或由均匀且圆周的运动组成”。这里没有任何关于革命性新宇宙论的内容，没有任何关于地球像行星一样绕静止太阳运行的内容。相反，赖因霍尔德着迷于用纯圆来取代托勒密的本轮，以另一种机制替代。全书页边的批注证实了对赖因霍尔德兴趣的这一解读。宇宙论那一章几乎未加注释，只更正了金星和水星的周期。第三卷涉及岁差以及地球与太阳的相对运动，与宇宙论部分不同，注释十分丰富。若干长注讨论年代学。其他注释涉及岁差和倾角的观测基础，其中赖因霍尔德经常提到约翰尼斯·维尔纳，一个尼古拉·哥白尼刻意回避提及的对手。

维滕贝格大学没有天文台，所以赖因霍尔德只得将就使用一个木制象限仪。他确实出版过一些星历表，但他的大部分工作并非观测性的。如上所述，他于1542年出版了一部带注释的格奥尔格·冯·波伊尔巴赫（1423-1461）Theorciae novae PlanetarumⓉ（《新行星理论》）版本，该书当时仍在许多大学使用。在注释中，他表明水星和月球的轨道描述出一个卵形图形，并首次公开发表了对暗箱的描述。1549年，他出版了克劳狄乌斯·托勒密的Almagest第一卷，附希腊文原文和拉丁文译本，题为Ptolomaei Mathematicae constructionis liber primusⓉ（《托勒密数学构造第一卷》）。在这部作品的献词中，赖因霍尔德写道：-

为了公立学校的利益与幸福，我开始编辑克劳狄乌斯·托勒密的杰出著作，其中关于天体运动的普遍理论在其最初基础上得以建立。当前出版的第一卷旨在让学生熟悉天文学的基础知识，这些知识是正确理解《天文学大成》其余各卷的前提。毫无疑问，向年轻人呈现这门学科的这些源头是非常有用的。然而，由于初学者尚未通晓希腊语，我添加了一个拉丁文译本，对于其中的不准确之处，我恳请专家们原谅。我也希望最终有人能为公众利益完成一部完整而清晰的克劳狄乌斯·托勒密译本。此外，为了帮助学生，我对一些难解的段落作了注释和解释。我希望所有这些努力都能蒙上帝喜悦，并得到所有专家的认可。事实上，我的意图是，年轻人不应仅仅追求学说的空洞影子，而应熟悉数学以及这门对人类生活与和平有用的技艺。

他打算完成这项工作，但英年早逝使他未能如愿。1554年，他的Primus liber Tabularum DirectionarumⓉ（《方向表第一卷》）遗作出版，这是对约翰·缪勒三角函数表的改进，包含了象限每一分的正弦值。他还教学生如何使用这些表来解决球面问题。

赖因霍尔德对尼古拉·哥白尼的De revolutionibusⓉ（《论天球的运行》）中所包含的表不满意，因此决定以更有用的形式重制它们。为此项目，他找到了普鲁士公爵阿尔弗雷德作为赞助人。1551年，经过七年漫长的工作，他出版了他的Prutenicae Tabulae Coelestium MotuumⓉ（《普鲁士天体运动表》）。这是一系列天文表，表明日心模型在实践中是适用的。直到约翰内斯·开普勒的Tabulae Rudolphinae Ⓣ（《鲁道夫星表》）（1627年）之前，它们一直是天文计算最重要的资源。其重要性的一个证明是，它们在三十五年内四次印刷：1551年、1562年和1571年在图宾根，1585年在维滕贝格。他在表中写道（见[9]）：-

尼古拉·哥白尼，除阿特拉斯和克劳狄乌斯·托勒密之外我们所能提及的最博学之人，尽管他以最博学的方式教授了基于观测的运动论证和原因，却回避了构建表的工作，以至于如果有人根据他的表进行计算，计算结果甚至与作为工作基础的他的观测都不一致。因此，我首先将尼古拉·哥白尼的观测与克劳狄乌斯·托勒密及其他人的观测进行比较，以确定哪些最为准确，但除了纯粹的观测之外，我从尼古拉·哥白尼那里只取了论证的痕迹。至于平均运动表、加减表以及所有其余部分，我重新构建了这些，绝对没有遵循任何其他推理，只遵循我认为具有最大和谐性的推理。

赖因霍尔德结过两次婚：第一次是在1537年1月22日与来自萨尔费尔德的市民的女儿玛格丽塔·鲍尔（卒于1548年10月7日）结婚；后来在1550年与玛莎（卒于1552年）结婚。他的两个妻子都死于分娩。他的第一次婚姻给他生了一个儿子，也叫赖因霍尔德（1538-92）。他还有两个女儿，玛格丽塔和卡塔琳娜。小赖因霍尔德 [12]：-

……在维滕贝格在梅兰希顿的照顾下学习数学和医学，然后在耶拿学习，并在安贝格和萨尔费尔德成为医学博士和市政医生。后来他成为萨克森选帝侯的“矿山管家”，并撰写了关于土地测量以及历书的著作，这些历书在爱尔福特定期出版多年。

1552年，赖因霍尔德为了躲避腺鼠疫，搬到萨克森与父母同住，但最终他还是死于鼠疫。他的遗言是“Vixi et quem dederas cursum mihi, Christe, peregi” Ⓣ（我活过，你赐予我的生命，哦上帝，我坚持到了最后）。他的学生卡斯帕·佩乌策（1525-1602）于1554年接替他成为维滕贝格的数学教授。

1575年，第谷·布拉赫在维滕贝格拜访了赖因霍尔德的儿子，并研究了他 annotated 的De Revolutionibus Ⓣ（《论天球的旋转》）副本。赖因霍尔德的笔记启发了第谷·布拉赫考虑行星轨道的替代排列，从而形成了自己的地日心体系。事实上，卡塞尔的宫廷数学家克里斯托夫·罗斯曼在1588年第谷·布拉赫出版De mundi aetherei recentioribus phaenomenis Ⓣ（《论以太世界中最新的现象》）时写道：-

我不认为这个地日心理论是一种新方法，而正是尼古拉·哥白尼的，除了我可以以相反的方式处理此事，将尼古拉·哥白尼的假设带回到太阳运动。此外，我认为格奥尔格·约阿希姆·雷蒂库斯和赖因霍尔德也考虑了同样的方法。

Erasmus Reinhold's father was Johann Reinhold (1479-1558), a tax collector and also the secretary of the last abbot of the Benedictine monastery at Saalfeld. Little is known about Erasmus's youth and early education. He had a brother, named Johann like their father, who became Professor of Mathematics at Greifswald in 1549. Both Erasmus and his brother died in 1553. Erasmus studied at the Stadtschule in Saalfeld then, in 1530, he enrolled in the University of Wittenberg which was at that time a young institution having been founded in 1502. He studied mathematics under Jakob Milich (1501-1559), and graduated as Magister in 1535.

After Professor Johannes Volmar's death in 1536, at the instigation of Philipp Melanchthon, Reinhold obtained the professorship of "Mathematum Superiorum" in the University of Wittenberg, which included astronomy, while his colleague Georg Joachim Rheticus became "Mathematum Inferiorum". Volmar had studied at Kraków and Wittenberg before moving to the University of Leipzig. He returned to Wittenberg where he was appointed as professor of mathematics in 1519. His most famous student was Joachim Rheticus. Philipp Melanchthon (1497-1560), Martin Luther's "right hand man", was a theologian, Greek professor and educator who reorganised the whole educational system of Germany, founding and reforming several of its universities. Melanchthon played a major role in getting both Reinhold and Rheticus appointed to teach mathematics and astronomy at the University of Wittenberg in 1536. Rheticus, however, spent the three years 1538-1541 away from Wittenberg, two of these years being spent with Copernicus.

Reinhold was elected dean in the college of arts, holding the position during the winter of 1540-41, and then dean in the college of philosophy during the summer of 1549. He became rector in the winter of 1549-50. This was a difficult time for those in Wittenberg which was a focal point of the Protestant Reformation which had begun in 1517 when Martin Luther nailed his 95 theses to the door of the castle in Wittenberg. Reinhold, like the majority of those in Wittenberg, was a Lutheran. The city was the capital of Saxony, ruled by the Elector of Saxony. The Schmalkaldic War of 1546-47 saw the Lutherans fighting against the Roman Catholic Emperor Charles I. When Charles I captured Wittenberg in 1547 the war was over and the Capitulation of Wittenberg was signed which compelled the Elector of Saxony to resign. Reinhold remained at the University attempting to continue his work during these dramatic events.

Reinhold, along with Rheticus, was one of the first scholars to draw attention towards the Copernican theories of heliocentrism in Germany. In his 1542 Theorciae novae Planetarum Ⓣ, he called Copernicus a "second Ptolemy, who restores the decaying building of education". However, Reinhold continued to recite Ptolemaic doctrine in his lectures. This might have been in part due to the theological establishment in Wittenberg, which considered Copernicus's model to be heretical, but Reinhold's comments on his own copy of Copernicus's De Revolutionibus Ⓣ seem to indicate that he was only interested in the mathematical aspects of the model and not in the cosmological theory.

The identification of Reinhold's annotations on his copy of De Revolutionibus Ⓣ was made by Owen Gingerich in 1970 when he examined the copy of De Revolutionibus Ⓣ held in the Royal Observatory in Edinburgh, Scotland. Here is Gingerich's description of this important discovery [3]:-

I searched in vain for an owner's name. The manuscript inscriptions at the beginning and end provided nary a clue. Then I looked more closely at the heavy pigskin binding. ... Around the edges were long patterned strips with biblical figures. Below an empty central panel was the date 1543, and above the panel I noticed the initials ER. I reacted with shock. Could the initials stand for Erasmus Reinhold, the leading mathematical astronomer in the generation after Copernicus ... ? I seized a pencil and paper to make a rubbing of the dim impression and, to my dismay, found not two, but three, initials: ERS. It seemed my hypothesis had just evaporated. Back in Cambridge ... I soon discovered that those three initials, ERS, were exactly what was required for Erasmus Reinholdus Salveldiensis, for in the sixteenth century a man's birthplace - in this case Saalfeld - was a part of his formal designation. ... specimens [of Reinhold's handwriting] eventually confirmed my original deduction.

The authors of [4] discuss the annotations made by Reinhold in this copy of De Revolutionibus Ⓣ:-

Reinhold's annotations are extensive and thorough: it is difficult to find an error in the text not already marked by him. Throughout, Reinhold proves remarkably aware of Copernicus's sources (such as Giorgio Valla, Johannes Werner, or Regiomontanus's 'Epitome'), even when Copernicus does not credit them explicitly. Reinhold sums up his approach to Copernicus's opus by a motto inscribed on the title page, a paraphrase of the chapter title I,4 'The Axiom of astronomy: Celestial motion is uniform and circular, or composed of uniform and circular motions'. There is nothing here about a revolutionary new cosmology, nothing about the earth orbiting like a planet about a stationary sun. Instead, Reinhold is fascinated by the use of pure circles to replace the Ptolemaic equant by an alternative mechanism. The marginalia throughout the volume verify this interpretation of Reinhold's interests. The cosmological chapter is virtually unglossed except for the correction of the periods of Venus and Mercury. Book III, concerning the precession and the relative motion of the earth and the sun, in contrast to the cosmological sections is generously annotated. Several long glosses discuss chronology. Others concern the observational basis for precession and the obliquity, where Reinhold regularly includes Johannes Werner, an antagonist whom Copernicus assiduously avoids mentioning.

The University of Wittenberg lacked an observatory so Reinhold had to make do with a wooden quadrant. He did publish some ephemerides, but most of his work was not observational. As stated above, he published a commented edition of Georg van Peurbach's (1423-1461) Theorciae novae Planetarum Ⓣ, which was still at use in many universities, in 1542. In his comments, he showed that the orbits of Mercury and the Moon describe an oval figure and he makes the first published description of a camera obscura. In 1549, he published the first book of Ptolemy's Almagest in Greek with a Latin translation, under the title Ptolomaei Mathematicae constructionis liber primus Ⓣ. In his dedication of this work Reinhold wrote:-

For the advantage and happiness of the public schools, I began an edition of Ptolemy's excellent work, in which the universal theory of heavenly motions is raised on its first foundations. The present edition of the first book is aimed at making students familiar with the basics of astronomy, which are preliminary to a correct understanding of the other books of the 'Almagest'. Without any doubt, it is very useful to present to young people these sources of the discipline. Still, since beginners are not yet conversant with the Greek language, I have added a Latin translation, for whose inaccuracy I beg the pardon of the experts. I also hope that somebody will eventually accomplish a complete and clear translation of Ptolemy for public interest. Moreover, to help students, I have commented and explained some difficult passages. I hope that all these efforts will be pleasing to God and that all experts will approve them. My intention is, in fact, that the young will not strive merely for the empty shadow of the doctrine, but that they are made familiar with mathematics and with this art that is useful for human life and peace.

He intended to finish this work, but his early death did not allow him. Posthumously, in 1554, his Primus liber Tabularum Directionarum Ⓣ was published, an improvement of Regiomontanus's trigonometric tables that includes the sines for every minute of the quadrant. He also teaches students how to use the tables to solve spherical problems.

Reinhold was dissatisfied with the tables included in Copernicus's De revolutionibus Ⓣ, so he decided to remake them in a more useful form. For this project, he found a patron in Duke Alfred of Prussia. In 1551, after seven long years of work, he published his Prutenicae Tabulae Coelestium Motuum Ⓣ. They were a series of astronomical tables that showed that the heliocentric model was applicable in practice. They remained the most important resource for astronomical calculation until Kepler's Tabulae Rudolphinae Ⓣ (1627). A testament of their importance is the fact that they received four printings in thirty-five years: in 1551, 1562, and 1571 in Tubingen, and in 1585 in Wittenberg. He wrote in the tables (see [9]):-

Copernicus, the most learned man whom we are able to name other than Atlas and Ptolemy, even though he taught in a most learned manner the demonstrations and causes of motion based on observation, nevertheless fled from the job of constructing tables, so that if anyone computes from his tables, the computation is not even in agreement with his observations on which the foundation of the work rests. Therefore first I have compared the observations of Copernicus with those of Ptolemy and others as to which are the most accurate, but besides the bare observations, I have taken from Copernicus nothing other than traces of demonstrations. As for the tables of mean motion, and of prosthaphaereses and all the rest, I have constructed these anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.

Reinhold married twice: first with Margaretha Bauer (died 7 October 1548), the daughter of a burgher from Saalfeld, on 22 January 1537; and later with Martha (died 1552) in 1550. Both of his wives died in childbirth. His first marriage gave him a son, also named Erasmus (1538-92). He also had two daughters, Margareta and Katharina. Erasmus Jr [12]:-

... studied mathematics and medicine in Wittenberg under the care of Melanchthon, and then in Jena, and became doctor of medicine and municipal doctor in Amberg and Saalfeld. Later he became 'mountain steward' to the Elector of Saxony, and wrote works on land surveying as well as calendars, which appeared regularly for many years in Erfurt.

In 1552, Reinhold moved to stay with his parents in Saxony, fleeing from the bubonic plague, but he eventually succumbed to it. His last words were "Vixi et quem dederas cursum mihi, Christe, peregi" Ⓣ. His student, Kaspar Peucer (1525-1602), succeeded him as professor of mathematics in Wittenberg in 1554.

In 1575, Tycho Brahe visited Reinhold's son in Wittenberg and studied his annotated copy of the De Revolutionibus Ⓣ. Reinhold's notes inspired Brahe to consider alternative arrangements of planetary circles that led to his own geo-heliocentric system. In fact Christoph Rothmann, court mathematician of Kassel, wrote in 1588 when Brahe published De mundi aetherei recentioribus phaenomenis Ⓣ:-

I did not consider this geo-heliocentric theory to be a new approach but precisely Copernicus's, apart from the fact that I could treat the matter in the reverse manner by bringing Copernicus's hypotheses back to the solar motion. Moreover, I assumed that Rheticus and Reinhold also took that same approach into consideration.