格奥尔格·冯·波伊尔巴赫Georg von Peuerbach

格奥尔格·冯·波伊尔巴赫的父亲是Ulrich Aunpekh；冯·波伊尔巴赫这个名字只是他们居住的城镇，位于林茨以西约40公里处，他实际上应该被称为冯·波伊尔巴赫的冯·波伊尔巴赫。关于他的早年生活一无所知，最早的记录是他在1446年进入维也纳大学注册。值得记录的是，他以Georgius Aunpekh de Pewrbach的名字注册。冯·波伊尔巴赫在维也纳学习，于1446年1月2日获得学士学位。在大学里，他学习了标准的文科课程，主要包括人文学科。他很可能学过一些数学，但他在天文学方面获得的专业知识一定是自学的。最后一位在维也纳大学教授天文学家的是Gmunden的弗瑞兹·约翰，他在冯·波伊尔巴赫注册入学前四年去世，但大学仍然保存着他的图书馆和仪器，冯·波伊尔巴赫可能被允许使用这些。

他在1448年至1453年间游历欧洲，尽管没有记录留下确切的日期。尽管当时没有出版物，他已经获得了作为天文学家的国际声誉。他在德国、法国和意大利讲授天文学，在博洛尼亚和帕多瓦讲学后，这些大学向他提供了职位，但他拒绝了。他在费拉拉遇到了当时领先的意大利天文学家Giovanni Bianchini，他还试图说服冯·波伊尔巴赫接受意大利一所大学的职位。到1453年，冯·波伊尔巴赫回到了维也纳，并于2月28日在那里获得了硕士学位。

在继续之前，值得花点时间回顾一下冯·波伊尔巴赫时代天文学与占星术之间的联系。人们普遍相信天体影响着地球上人们的生活和事件。占星家想知道一个人出生时太阳、月亮和行星的精确位置，以绘制一张据信能预示一个人未来的图表。日食和月食具有重要意义，彗星的出现被视为重大预兆。今天在我们看来，天文学和占星术是分开的，但在15世纪它们密切相关。然而，基于占星考虑的预测需求确实推动了天文学科学制作更精确的表格。许多科学工作因错误的理由而获得资助，但有些人可能会说这今天仍然发生。

1454年，他被匈牙利和波希米亚国王拉迪斯拉斯五世任命为宫廷占星家。拉迪斯拉斯任命冯·波伊尔巴赫时只有14岁，但自几个月大起，他就在其表兄的监护下成为国王，其表兄后来成为神圣罗马皇帝弗雷德里克三世。拉迪斯拉斯大部分时间在布拉格和维也纳度过，冯·波伊尔巴赫也能够在维也纳大学任教。然而，他的教学似乎主要在人文学科，而不是天文学。政治阴谋导致两位主要人物被暗杀，促使拉迪斯拉斯于1457年逃往布拉格，并于当年晚些时候在那里去世（实际上是死于白血病）。冯·波伊尔巴赫没有成为波希米亚的乔治·波德布拉迪或匈牙利的马蒂亚斯一世·科尔维努斯（拉迪斯拉斯的继任者）的宫廷占星家，而是被任命为神圣罗马皇帝弗雷德里克三世的宫廷占星家。弗雷德里克对占星术、魔法和炼金术感兴趣，所以冯·波伊尔巴赫有一个会善待他的赞助人。

约翰·缪勒是维也纳大学的学生，师从冯·波伊尔巴赫。他十五岁毕业，次年即1453年开始与冯·波伊尔巴赫合作。在冯·波伊尔巴赫去世前的八年里，这两位天文学家一起做出了出色的工作。在Theoricae Novae PlanetarumⓉ（行星新理论）中，冯·波伊尔巴赫于1454年8月30日前完成该书，以浅显而透彻的方式介绍了克劳狄乌斯·托勒密的本轮行星理论。冯·波伊尔巴赫相信行星位于坚固的水晶球层中，尽管他认为它们的运动由太阳控制。该书基于冯·波伊尔巴赫1454年初在维也纳大学所授课程的讲义。J V Field写道：-

冯·波伊尔巴赫所教授的天文学是行星球层的天文学，每颗行星的运动由圆圈（代表球层）相互嵌套滚动来表示。该理论源自克劳狄乌斯·托勒密，但也源自伊斯兰天文学家。因此，这部著作往往显得“中世纪”，这一特点或许部分解释了它长期被译者忽视的原因。

事实上，这篇有趣的论文[4]提出了强有力的论据，表明冯·波伊尔巴赫使用了伊斯兰天文学家发展的技术来修改克劳狄乌斯·托勒密的模型。该书：-

……在1472年至1653年间至少印行了五十六版（将译本和评注以及拉丁文原版的各种版本计算在内）。它似乎是十六世纪使用最广泛的天文学教科书。

冯·波伊尔巴赫于1457年9月3日在维也纳附近的一个地点观测了一次月食。他测量了月食的持续时间，然后求出了中点时刻。它比阿方索星表预测的时间早了八分钟。这些星表是在西班牙托莱多为国王阿方索十世编制的，于1252年完成。基于克劳狄乌斯·托勒密的理论，它们代表了冯·波伊尔巴赫时代可获得的最佳数据。冯·波伊尔巴赫在Tabulae Ecclipsium中编制了一套新的月食计算星表，于1459年左右完成。当他在1460年7月3日和12月27-28日观测月食时，他能够将时间与他自己星表中的预测进行比较。

他于1456年6月观测到爱德蒙·哈雷的彗星，并撰写了一份观测报告。他进一步观测了彗星，并发表了更多星表，这些星表由他自己的月食观测加以校验，他还设计了天文仪器。作为他设计的一种仪器的例子，我们注意到冯·波伊尔巴赫发现了罗盘的偏差。随后，他大约在1451年设计了最早的带有罗盘并标出偏差的平板日晷：-

平板日晷由两个小型日晷（一个水平日晷和一个垂直正南日晷）组成，它们用一个共同的晷针铰接在一起；该仪器可在铰链处折叠，然后放入口袋。

他还建造了天球，即描绘恒星的大型球体。他撰写了关于在Tractatus super propositiones Ptolemaei de sinubus et chordis中计算正弦和弦的著作，其中使用了基于伊斯兰天文学家的解释以及基于克劳狄乌斯·托勒密的解释。他的书Algorismus是一本关于整数和分数实际计算的初级教科书，很受欢迎并多次重印。

约翰内斯·贝萨里翁于1437年被任命为尼西亚大主教，两年后被教皇尤金四世任命为枢机主教。他是当时最博学的学者之一，并通过个人藏书传播希腊语言和学识，其中包括大量希腊手稿。1460年5月5日，他抵达维也纳，调解腓特烈三世与其兄弟之间的争端。他此次访问还有另一个目的，因为君士坦丁堡已于1453年落入土耳其人之手，贝萨里翁正在寻求支持以发动十字军夺回该城。贝萨里翁会见了冯·波伊尔巴赫和约翰·缪勒，他告诉他们，除了政治目标外，他还有科学目标。他想向冯·波伊尔巴赫推销的想法是从希腊文翻译出更好的AlmagestⓉ（主要论题：源自阿拉伯语“al-majisti”——希腊语“Mathematike Syntaxis”的阿拉伯语译本，后来译为拉丁语“Magna Syntaxis”）。贝萨里翁建议，一个缩短的版本将适合作为教学文本，冯·波伊尔巴赫同意从事该项目。冯·波伊尔巴赫去世时已完成六卷，但约翰·缪勒同意完成这项工作。最终形式共有十三卷，其余各卷由约翰·缪勒撰写。它于1462年以Epitome in Ptolemaei Almagestum出版，献给贝萨里翁（他可能贡献了导言的部分内容）。这部著作标志着：-

……从对克劳狄乌斯·托勒密和古代的崇敬转向尊重与自信的创新相结合。

[1]的作者写道：-

冯·波伊尔巴赫的早逝对天文学的进步是一个严重损失，即便仅仅因为与比他更能干、更勤奋的学生约翰·缪勒的合作，本可望取得比两人各自所能完成的更多有价值的工作。在他们的同代人中，只有比他们年长许多的Bianchini具备与之相当的造诣和独创性。

Georg Peurbach's father was Ulrich Aunpekh; the name Peurbach is just the town in which they lived, about 40 km west of Linz, and he should really be known as Georg of Peurbach. Nothing is known of his early life, the first record being his matriculation at the University of Vienna in 1446. It is worth recording that he matriculated under the name Georgius Aunpekh de Pewrbach. Georg studied at Vienna, graduating with a bachelor's degree on 2 January 1446. At university he studied the standard arts course consisting mainly of the humanities. It is likely that he would have studied some mathematics but the expertise which he gained in astronomy must have been self taught. The last astronomer to teach at the University of Vienna was John of Gmunden who died four years before Peurbach matriculated there, but the university still held his library and instruments to which Peurbach probably was given access.

He travelled through Europe between 1448 and 1453 although no record remains of the precise dates. He had already acquired an international reputation as an astronomer despite having no publications at that time. He lectured in Germany, France and Italy on astronomy and after giving lectures in Bologna and Padua he was offered appointments in these universities but turned them down. He met the leading Italian astronomer of the day, Giovanni Bianchini, in Ferrara and he also tried to persuade Peurbach to accept a post in an Italian university. By 1453 Peurbach was back in Vienna and there he was awarded a Master's Degree on 28 February.

Before continuing it is worth spending a moment reviewing the connection between astronomy and astrology in Peurbach's time. There was a widely held belief that the heavenly bodies influenced the lives and events of those on earth. The astrologer wanted to know the precise position of the sun, moon and planets at the time of a person's birth to draw up a chart which was believed foretold a person's future. Eclipses were of great significance and the appearance of a comet was treated as a major portent. Astronomy and astrology are separate to our minds today but were intimately connected in the 15th century. The desire for predictions based on astrological considerations did, however, drive the science of astronomy to make more accurate tables. Much scientific work was funded for the wrong reasons, but some might say this still happens today.

He was appointed court astrologer by King Ladislas V of Hungary and of Bohemia in 1454. Ladislas was only 14 years of age when he appointed Peurbach but he had been King since he was a few months old under the guardianship of his cousin, who was later to become Holy Roman emperor Frederick III. Ladislas spent most of his time in Prague and Vienna and Peurbach was able to also teach at the University of Vienna. His teaching seems to be mostly in the humanities, however, and not in astronomy. Political intrigues, leading to assassinations of two leading figures, caused Ladislas to flee to Prague in 1457 and he died there later that year (actually of leukaemia). Peurbach did not become court astrologer to George of Podebrady of Bohemia or Matthias I Corvinus of Hungary, Ladislas's successors, but rather was appointed as court astrologer to the Holy Roman emperor Frederick III. Frederick was interested in astrology, magic, and alchemy so Peurbach had a patron who would treat him well.

Regiomontanus was a student at the University of Vienna where he was taught by Peurbach. He graduated at the age of fifteen and in the following year of 1453 he began collaborating with Peurbach. For eight years, until Peurbach's death, the two astronomers did excellent work together. In Theoricae Novae Planetarum Ⓣ, which he completed by 30 August 1454, Peurbach presented Ptolemy's epicycle theory of the planets in an elementary but thorough way. Peurbach believed that the planets were in solid crystalline spheres although he believed that their motions were controlled by the Sun. The book was based on lecture notes of a course given by Peurbach at the University of Vienna earlier in 1454. J V Field writes:-

The astronomy Peurbach teaches is that of planetary spheres, the motion of each planet being shown by circles (standing for spheres) rolling one inside the other. The theory is derived from Ptolemy but also from Islamic astronomers. The work consequently tends to look "medieval", a characteristic that may perhaps partly account for its long neglect by translators.

In fact the interesting paper [4] puts forward a strong case that Peurbach used techniques developed by the Islamic astronomers to modify Ptolemy's model. The book:-

... went into at least fifty-six printed editions between 1472 and 1653 (counting translations and commentaries as well as editions of the original Latin text). It seems to have been the most widely used astronomical textbook of the sixteenth century.

Peurbach observed a lunar eclipse on 3 September 1457 from a site near Vienna. He measured the duration of the eclipse and then found the time of the midpoint. It was eight minutes earlier than the time predicted by the Alphonsine Tables. These tables, prepared in Toledo, Spain, for King Alfonso X, were completed in 1252. Based on Ptolemy's theory, they represented the best data available in Peurbach's time. Peurbach produced a new collection of tables of eclipse calculations in Tabulae Ecclipsium which he completed around 1459. When he observed eclipses on 3 July and 27-28 December 1460 he was able to compare the times with the predictions contained in his own tables.

He observed Halley's comet in June 1456 and wrote a report on his observations. He made further observations of comets and, published further tables, checked by his own eclipse observations, and devised astronomical instruments. As an example of an instrument he devised we note that Peurbach discovered the deviation of the compass. He then devised the earliest tablet dial with a compass and with indicated deviation in around 1451:-

A tablet dial consists of two small sundials (horizontal and a vertical direct-south dial) hinged together with a common gnomon; the instrument can be folded at the hinge and then fits in the pocket.

He also constructed celestial spheres, large globes which depicted the stars. He wrote on the computation of sines and chords in Tractatus super propositiones Ptolemaei de sinubus et chordis using and explanation based on that of Islamic astronomers as well as one based on Ptolemy. His book Algorismus, an elementary textbook on practical calculations with integers and fractions, was popular and reprinted several times.

Johannes Bessarion was made archbishop of Nicaea in 1437 and was made a cardinal by Pope Eugenius IV two years later. He was one of the most learned scholars of his time, and spread knowledge of Greek language and learning with a personal library that included a large collection of Greek manuscripts. On 5 May 1460 he arrived in Vienna to mediate in a dispute between Frederick III and his brother. He had another purpose for his visit for Constantinople had fallen to the Turks in 1453 and Bessarion was seeking support for a crusade to recapture the city. Bessarion met both Peurbach and Regiomontanus and he told them that, in addition to his political objectives, he also had scientific objectives. The idea which he wanted to sell to Peurbach was to produce a better translation of the Almagest Ⓣ from the Greek. Bessarion suggested that a shortened version would make a suitable teaching text and Peurbach agreed to work on the project. Peurbach had completed six books at the time of his death but Regiomontanus had agreed to complete the work. In finished form there were thirteen books, the remaining ones having been written by Regiomontanus. It was published as Epitome in Ptolemaei Almagestum in 1462 and dedicated to Bessarion (who may have contributed parts of the introduction). The work marks:-

... a shift from reverence for Ptolemy and antiquity to respect coupled with confident innovation.

The authors of [1] write:-

Peurbach's early death was a serious loss to the progress of astronomy, if for no other reason than that the collaboration with his even more capable and industrious pupil Regiomontanus promised a greater quantity of valuable work than either could accomplish separately. Of their contemporaries, only Bianchini, who was considerably their senior, possessed a comparable proficiency and originality.