格奥尔格·约阿希姆·雷蒂库斯Georg Joachim Rheticus

格奥尔格·约阿希姆·雷蒂库斯的父亲雷蒂库斯 Iserin是费尔德基希的镇医生，也是一名政府官员。因此，雷蒂库斯出生时名为雷蒂库斯 雷蒂库斯 Iserin。他的母亲Thomasina de Porris是意大利人。在他生命的最初14年里，由父亲教导他，但在1528年，他的父亲因巫术指控受审，被定罪并斩首。这种处决的一项法律要求是不能再使用他的名字，因此雷蒂库斯的母亲恢复使用娘家姓，而雷蒂库斯的名字变成了雷蒂库斯 雷蒂库斯 de Porris。“De porris”在意大利语中意为“韭葱的”，由于雷蒂库斯不认为自己是意大利人，他将其翻译成德语“von Lauchen”，并自称雷蒂库斯 雷蒂库斯 von Lauchen。他后来又以他出生的罗马行省雷蒂亚为名，取了附加名字雷蒂库斯。

在雷蒂库斯的父亲被处决后，Achilles Gasser接管了费尔德基希的医疗业务。他帮助雷蒂库斯继续学业，并给予他大力支持。父亲被处决后，雷蒂库斯在费尔德基希的拉丁学校学习，然后前往苏黎世，从1528年到1531年在Frauenmuensterschule学习。1533年，他进入维滕贝格大学，三年后于1536年4月27日获得该校的文学硕士学位。

菲利普·梅兰希通是马丁·路德的“得力助手”，是一位神学家和教育家，他重组了德国的整个教育体系，创建并改革了多所大学。梅兰希通在1536年为雷蒂库斯争取到维滕贝格大学的数学和天文学教职中发挥了重要作用。这一职位涉及教授算术和几何，给雷蒂库斯带来了100古尔登的薪水。

两年后，梅兰希通再次利用他的影响力为雷蒂库斯安排休假，以便与当时一些领先的天文学家一起学习，但他的主要原因是拜访尼古拉·哥白尼。他于1538年10月离开维滕贝格，前往纽伦堡，在那里拜访了约翰·舍纳，后者正在出版书籍，包括约翰·缪勒在60年前打算出版的那些书。在纽伦堡，雷蒂库斯还拜访了印刷商Petreius。然后他在因戈尔施塔特拜访了彼得鲁斯·阿皮亚努斯，接着在蒂宾根拜访了雷蒂库斯 Camerarius，之后他抽空拜访了他的家乡费尔德基希，去看望Achilles Gasser，并赠送给他一本约翰尼斯·德·萨克罗博斯科。

1539年5月，雷蒂库斯 抵达埃尔姆兰的弗龙堡，在那里与 尼古拉·哥白尼 共度了大约两年。雷蒂库斯 写道（[8]，[14]）：-

我听闻尼古拉·哥白尼大师在北方诸地的盛名，尽管维滕贝格大学已聘我为那些学科的公聘教授，然而，我认为除非通过那位先生的教导学到更多东西，否则我不会满足。我还要说，我既不后悔经济上的花费，也不后悔长途旅行和其余的艰辛。然而，在我看来，这些麻烦带来了巨大的回报，即，我这个相当大胆的年轻人迫使这位可敬的人更早地与全世界分享他在这一学科中的想法。

1539年9月，雷蒂库斯前往但泽，拜访了但泽市长，市长给予雷蒂库斯一些经济援助，帮助出版Narratio Prima，或者给出其全称First report to Johann Schöner on the Books of the Revolutions of the learned gentleman and distinguished mathematician, the Reverend Doctor Nicolaus Copernicus of Toruń, Canon of Warmia, by a certain youth devoted to mathematics。Swerdlow在[13]中写道：-

尼古拉·哥白尼不可能为他的新天文学向文坛作出更博学、优雅和热情的介绍；确实，时至今日，尼古拉·哥白尼著作的最佳介绍仍然是《第一报告》。当然，雷蒂库斯将一本寄给了Schöner，也寄给了Petreius，后者觉得它非常出色。

1541年8月，雷蒂库斯向普鲁士公爵亚伯拉罕·阿德里安·艾伯特呈献了他关于普鲁士地图的著作副本，次日又送给他一个他制作的用于测定日长的仪器。雷蒂库斯知道公爵艾伯特曾试图弄清如何计算日出时间但未成功。在获得公爵的好感后，他提出了自己想要的恩惠：公爵是否允许出版尼古拉·哥白尼的De Revolutionibus。公爵艾伯特迅速回复，准许出版，同时要求雷蒂库斯保留其讲席。1541年10月，雷蒂库斯回到维滕贝格大学，并在那里被选为文学院院长。

1541年初，雷蒂库斯出版了尼古拉·哥白尼的De Revolutionibus中的三角学部分，并添加了他自己的正弦和余弦表（尽管他并未用这些名称称呼它们）。这是第一份出版的正弦表，参见[1]，雷蒂库斯的：-

……在数学史上的地位正是由于他计算了创新且具有里程碑意义的三角函数表。

雷蒂库斯 Camerarius是图宾根大学的校长，他与Melanchthon合作，安排雷蒂库斯到莱比锡大学任职。1542年，雷蒂库斯被任命为莱比锡的高等数学教授。起初，他获得的薪水与他在维滕贝格大学时相同，但他很快谈成了40%的加薪。他于1542年5月离开维滕贝格，前往纽伦堡，在那里监督De Revolutionibus的印刷，但在工作完成之前，他不得不前往莱比锡，于1542年10月开始授课。

雷蒂库斯留在莱比锡直到1545年，当时他再次安排休假以便出国留学。最初回到家乡费尔德基希后，他在意大利度过了一段时间，在那里他参观了米兰的吉罗拉莫·卡尔达诺。雷蒂库斯继续旅行，直到在林道——巴伐利亚州康斯坦茨湖中一个岛上的城市——他的健康崩溃，并在1547年上半年出现严重的精神问题。他的健康恢复到足以在1547年底在康斯坦茨教授数学三个月，然后在苏黎世学习医学，之后于1548年2月返回莱比锡。在梅兰希通的影响下，雷蒂库斯成为莱比锡神学院的成员。

作为一个多才多艺的人，雷蒂库斯出版了1550年的历书和星历表，以及1551年的星历表和历书。然而，一场丑闻迫使他在1551年4月离开莱比锡；他被指控与一名学生有同性恋关系。他不得不迅速逃离，在开姆尼茨待了一段时间，又在布拉格待了一段时间。他在缺席的情况下受审，他的朋友如梅兰希通停止支持他：如果他们想保住自己的职位，可能别无选择。尽管他不在场为自己辩护，雷蒂库斯被判处101年流放。

在1551-52年，他在布拉格大学学习医学，但他对医学的兴趣似乎只用于治疗病人，从未进行学术研究，因此他似乎从未像在数学方面那样在医学上产生创新。1553年，他被邀请担任维也纳的数学教授。他去了维也纳，但从未接受任命。他于1554年搬到克拉科夫，在那里作为执业医生待了20年。

他在克拉科夫期间当然没有放弃数学兴趣，因为他致力于他著名的三角函数表，以及制作仪器、进行天文观测和炼金术实验。事实上，在这个阶段他做得相当不错，雇佣了六名研究助理，并且他的三角函数表工作得到了皇帝马克西米利安二世的资助，这为他的助理提供了相当不错的薪水。雷蒂库斯关于三角学的重要著作Opus Palatinum de triangulis使用了所有六个三角函数。他在这部主要著作中给出了所有这六个函数的表格，该著作在雷蒂库斯去世多年后由瓦伦丁·奥托于1596年完成并出版。

Otho曾在维滕贝格学习，然后出发去拜访雷蒂库斯，方式类似于雷蒂库斯本人拜访尼古拉·哥白尼的方式。Otho写道（见[14]：-

我们刚就这那聊了几句，当他得知我来访的原因时，便脱口而出：“你来找我时的年龄，正是我当年拜访哥白尼时的年龄。如果我没有拜访他，他的作品一部也不会问世。”

雷蒂库斯的其他作品包括关于地图制作的（他出版了一幅普鲁士地图），以及关于航海仪器的作品，Chorographia tewsch。他设计了许多仪器，如海罗盘和显示全年日长的仪器，正如我们上面提到的，他将后者赠予了艾伯特公爵。

鉴于雷蒂库斯所过的戏剧性且多事的一生，思考他的个性是很有趣的。Westman在[14]中写道：-

如果……要根据雷蒂库斯著作的语调、同时代人的证词以及他自己的生活活动，指出他个性中最突出的单一特质，那就必须抓住他那巨大的精力和强度——无论是在他工作的活力中，在他广泛的旅行中，还是在他明显追求平息内心某种东西的努力中。

Georg Joachim von Lauchen Rheticus's father, Georg Iserin, was the town doctor in Feldkirch and also a government official. Rheticus was, therefore, born Georg Joachim Iserin. His mother, Thomasina de Porris, was Italian. He was taught by his father for the first 14 years of his life but, in 1528, his father was tried on a charge of sorcery, convicted and beheaded. One of the legal requirements of such an execution was that his name could no longer be used, so Rheticus's mother reverted to her maiden name and Rheticus's became Georg Joachim de Porris. 'De porris' means 'of the leeks' in Italian and, since Rheticus did not consider himself Italian he translated it into German 'von Lauchen' and called himself Georg Joachim von Lauchen. He later took the additional name of Rheticus after the Roman province of Rhaetia in which he had been born.

Achilles Gasser took over the medical practice in Feldkirch after Rheticus's father was executed. He helped Rheticus continue his studies and was a strong support to him. After his father's execution, Rheticus studied at the Latin school in Feldkirch, then went to Zürich where he studied at the Frauenmuensterschule from 1528 to 1531. In 1533 he entered the University of Wittenberg receiving his M.A. from that university three years later on 27 April 1536.

Philipp Melanchthon, Martin Luther's "right hand man", was a theologian, and educator who reorganised the whole educational system of Germany, founding and reforming several of its universities. Melanchthon played a major role in getting Rheticus an appointment to teach mathematics and astronomy at the University of Wittenberg in 1536. This appointment, which involved teaching arithmetic and geometry, gave Rheticus a salary of 100 gulden.

Two years later Melanchthon again used his influence to arrange leave for Rheticus to study with some of the leading astronomers of the day, but his main reason was to visit Copernicus. Leaving Wittenberg in October 1538 he travelled to Nuremberg and there visited Johann Schöner who was publishing books, including those that Regiomontanus had intended to publish 60 years earlier. In Nuremberg Rheticus also visited the printer Petreius. He then visited Peter Apianus in Ingolstadt, next Joachim Camerarius in Tübingen and then he fitted in a visit to his home town of Feldkirch to visit Achilles Gasser whom he presented with a copy of Sacrobosco.

In May 1539 Rheticus arrived at Frauenburg in Ermland where he spent about two years with Copernicus. Rheticus wrote ([8], [14]):-

I heard of the fame of Master Nicolaus Copernicus in the northern lands, and although the University of Wittenberg had made me a Public Professor in those arts, nonetheless, I did not think that I should be content until I had learned something more through the instruction of that man. And I also say that I regret neither the financial expenses nor the long journey nor the remaining hardships. Yet, it seems to me that there came a great reward for these troubles, namely. that I, a rather daring young man compelled this venerable man to share his ideas sooner in this discipline with the whole world.

In September 1539 Rheticus went to Danzig, visiting the mayor of Danzig, who gave Rheticus some financial assistance to help publish the Narratio Prima or, to give it its full title First report to Johann Schöner on the Books of the Revolutions of the learned gentleman and distinguished mathematician, the Reverend Doctor Nicolaus Copernicus of Toruń, Canon of Warmia, by a certain youth devoted to mathematics. Swerdlow writes in [13]:-

Copernicus could not have asked for a more erudite, elegant, and enthusiastic introduction of his new astronomy to the world of good letters; indeed to this day the Narratio Prima remains the best introduction to Copernicus's work. Of course Rheticus sent a copy to Schöner and also to Petreius, who found it splendid.

In August 1541 Rheticus presented a copy of his work on a map of Prussia to Duke Albert of Prussia and the following day he sent him an instrument he had made to determine the length of the day. Rheticus knew that Duke Albert had tried unsuccessfully to find out how to compute the time of sunrise. Having put himself in good favour with the Duke he asked for the favour he wanted: would the Duke permit the publication of Copernicus's De Revolutionibus. Duke Albert replied quickly giving permission for the publication and, at the same time requesting that Rheticus retain his chair. In October 1541 Rheticus returned to the University of Wittenberg and there he was elected dean of the Faculty of Arts.

In early 1541 Rheticus published the trigonometrical sections of Copernicus's De Revolutionibus adding tables of his own giving tables of sines and cosines (although he did not call them by these names). This was the first published table of cosines and, see [1], Rheticus's:-

... place in the history of mathematics is due precisely to his computation of innovative and monumental trigonometrical tables.

Joachim Camerarius, who was head of the University of Tübingen, working with Melanchthon, arranged for Rheticus to be offered a post at the University of Leipzig. In 1542 Rheticus was appointed professor of higher mathematics at Leipzig. Initially he was offered the same salary as he had received from the University of Wittenberg but he soon negotiated a 40% rise. He left Wittenberg in May 1542, travelling to Nuremberg where he supervised the printing of De Revolutionibus but before the work was finished he had to go to Leipzig to begin teaching in October 1542.

Rheticus remained at Leipzig until 1545 when he again arranged leave to allow him to study abroad. After initially returning to his home town of Feldkirch he spent some time in Italy, where he visited Cardan in Milan. Rheticus continued on his travels until, at Lindau, a city in Bavaria on an island in Lake Constance his health broke down and he had severe mental problems during the first half of 1547. His health recovered sufficiently to allow him to teach mathematics at Constance for three months in late 1547 then he studied medicine in Zürich before he returned to Leipzig in February 1548. With Melanchthon's influence Rheticus was made a member of the theological faculty at Leipzig.

A man of many talents, Rheticus published a calendar and ephemeris of 1550 and also an ephemeris and calendar of 1551. However a scandal forced him to leave Leipzig in April 1551; he was accused of having a homosexual affair with one of his students. He had to flee and this he did rapidly, spending some time at Chemnitz and a further period in Prague. He was tried in his absence and his friends, such as Melanchthon, stopped supporting him: they probably had little option if they were to retain their own positions. Although he was not present to defend himself, Rheticus was sentenced to 101 years in exile.

In 1551-52 he studied medicine at the University of Prague but his interest in medicine only ever seemed to be used to treat patients and never to undertake scholarly research so he never seems to have produced innovations in medicine in the way he did in mathematics. In 1553 he was offered an appointment as professor of mathematics at Vienna. He went to Vienna but never took up the appointment. He moved to Kraków in 1554 where he remained for 20 years as a practising doctor.

He certainly did not give up his mathematical interest while in Kraków, for he worked on his famous trigonometric tables as well as making instruments, carrying out astronomical observations and alchemy experiments. In fact he did rather well for himself at this stage employing six research assistants and he was funded by Emperor Maximilian II for his work on trigonometric tables which went a long way to providing rather good salaries for his assistants. Rheticus's important work on trigonometry Opus Palatinum de triangulis uses all six trigonometric functions. He gave tables of all these six functions in this major work which was completed and published in 1596 by Valentine Otho many years after Rheticus's death.

Otho had studied at Wittenberg and then set out to visit Rheticus in a similar way to that in which Rheticus himself had visited Copernicus. Otho writes (see [14]:-

We had hardly exchanged a few words on this and that when, on learning the cause of my visit, he burst forth with these words: "You come to see me at the same age as I was myself when I visited Copernicus. If I had not visited him, none of his works would have seen the light."

Other works by Rheticus include ones on map making (he published a map of Prussia), and works on navigational instruments, Chorographia tewsch. He designed many instruments such as sea compasses and the instrument to show the length of the day throughout the year which he gave to Duke Albert as we mentioned above.

Given the dramatic and eventful life that Rheticus led it is interesting to think about his personality. Westman writes in [14]:-

If ... one were to point to the single most prominent trait in Rheticus's personality, based upon the tone of his writings, the testimonies of his contemporaries, and his own life activities, one would have to seize upon his great energy and intensity - whether in the vitality of his work, in his widespread travels, or in his evident pursuit to lay to rest something inside himself.