巴塔尼Al-Battani

巴塔尼有时以其名字的拉丁化版本而闻名，变体有Albategnius、Albategni或Albatenius。他的全名是巴塔尼 巴塔尼 Mohammad ibn Jabir ibn Sinan al-Raqqi al-Harrani al-Sabi 巴塔尼。

巴塔尼出生在哈兰，早期被罗马人称为卡雷，位于巴利赫河畔，乌尔法东南38公里处。他的家族曾是萨比教派的成员，这是一个来自哈兰的拜星宗教教派。作为星辰的崇拜者，意味着萨比教徒对天文学研究有强烈的动力，他们产生了许多杰出的天文学家和数学家，如塔比·伊本·库拉。事实上，塔比·伊本·库拉也出生在哈兰，在巴塔尼出生时可能仍然住在那里。与塔比·伊本·库拉不同，巴塔尼并不信仰萨比教，然而，因为“巴塔尼 巴塔尼 Mohammad”表明他肯定是穆斯林。

尽管这一认定并非绝对确定，但很可能巴塔尼的父亲是Jabir ibn Sinan al-Harrani，他在哈兰作为仪器制造者享有很高的声誉。这个名字无疑使这一认定相当确定，而巴塔尼本人擅长制造天文仪器这一事实也很好地表明他从父亲那里学到了这些技能。

巴塔尼在叙利亚的安条克和拉卡进行了极为精确的天文观测。拉卡镇是巴塔尼进行大部分观测的地方，当哈伦·拉希德于786年9月14日成为阿拔斯王朝第五任哈里发时，他在那里建造了几座宫殿，该镇因此繁荣起来。当时该镇被更名为拉希德，但到巴塔尼开始在那里观测时，它已恢复为拉卡这个名字。该镇位于幼发拉底河上，就在它与巴利赫河（哈兰位于该河上）汇合处的西边。

Fihrist（索引）是书商Ibn an-Nadim于988年编纂的一部著作。它全面记述了10世纪可获得的阿拉伯文献，并简要描述了其中一些作者。Fihrist对巴塔尼的描述如下（例如见[1]）：-

……著名的观测者之一，几何学、理论天文学与实践天文学以及占星学的领袖。他撰写了一部附有表格的天文学著作，其中包含他自己对太阳和月亮的观测，以及对它们运动的比克劳狄乌斯·托勒密的“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”）中所给出的更为精确的描述。此外，他在其中给出了五颗行星的运动，连同他成功作出的改进观测，以及其他必要的天文计算。他表格之书中提到的一些观测是在880年以及后来在900年作出的。在伊斯兰世界，没有人以在观测恒星和细察其运动方面达到类似完美而闻名。除此之外，他对占星学极感兴趣，这促使他也就此主题写作：关于他在这一领域的作品，我提及他对克劳狄乌斯·托勒密的Tetrabiblos的评注。

Fihrist中关于巴塔尼的其他信息是，他在877年至918年之间进行观测，并且他的星表以880年为基准。它还描述了他生命的终结，这似乎发生在他前往巴格达的旅途中，他代表来自ar-Raqqah的一群人前去抗议，因为他们被不公平地征税。巴塔尼到达巴格达并提出了他的论据，但在返回ar-Raqqah的旅途中去世。

Fihrist还引用了巴塔尼的若干著作。其中有他的Kitab al-Zij，这是他在天文学方面的主要著作，附有表格，上文已提及。我们稍后将更详细地考察这部著作。此外还有上文提到的对克劳狄乌斯·托勒密的Tetrabiblos的注释，以及另外两个书名：On ascensions of the signs of the 黄道带和On the quantities of the astrological applications。Kitab al-Zij中有一章的标题是“论黄道十二宫的上升”，因此Fihrist认为这是一部独立著作可能是错误的。这一点似乎仍不清楚。

巴塔尼的Kitab al-Zij是他迄今为止最重要的著作，我们应当简要考察它所涵盖的主题。该著作包含57章。它首先描述将天球划分为黄道十二宫和度数。然后引入了必要的背景数学工具，如六十进制分数的算术运算和三角函数。第4章包含来自巴塔尼自己观测的数据。第5至26章讨论了大量不同的天文学问题，在某种程度上遵循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'）的材料。太阳、月亮和五颗行星的运动在第27至31章中讨论，其中给出的理论是克劳狄乌斯·托勒密的理论，但对巴塔尼来说，这一理论似乎不如实际方面重要。

在给出允许将一个历元的数据转换为另一个历元的结果之后，巴塔尼接着用16章解释如何阅读他的表格。第49至55章涵盖占星学问题，第56章讨论日晷的构造，最后一章讨论若干天文仪器的构造。

巴塔尼的⟦E1⟧的主要成就是什么？他编目了489颗恒星。他改进了年长度的现有数值，给出365天5小时46分24秒，以及季节的长度。他计算出岁差为每年54.5″，并得到inclination of the ecliptic的值为23°35'。

巴塔尼没有像克劳狄乌斯·托勒密那样使用几何方法，而是使用了三角学方法，这是一项重要进展。例如，他给出了直角三角形的重要三角公式，如

$b \sin(A) = a \sin(90° - A)$。

巴塔尼表明太阳到地球的最远距离会变化，因此，太阳的annular eclipses以及全食都是可能的。然而，正如Swerdlow在[8]中指出的，克劳狄乌斯·托勒密的影响对所有中世纪作者都异常强大，甚至像巴塔尼这样杰出的科学家可能也不敢声称地球到太阳的距离与克劳狄乌斯·托勒密所给出的值不同。尽管巴塔尼能够从自己的观测中推演出一个与克劳狄乌斯·托勒密大不相同的距离值。

在1中，Hartner对巴塔尼受克劳狄乌斯·托勒密影响的方式给出了略有不同的看法。他写道：-

虽然巴塔尼总体上对托勒密运动学没有采取批判态度，但他表现出……对克劳狄乌斯·托勒密的实际结果持有非常合理的怀疑态度。因此，依靠自己的观测，他——无论是默然还是公开地——纠正了克劳狄乌斯·托勒密的错误。这既涉及行星运动的主要参数，也涉及从不足或有缺陷的观测中得出的错误结论，例如黄赤交角或太阳远地点的不变性。

巴塔尼在科学发展中之所以重要有诸多原因，但其中之一必定是他的工作对第谷·布拉赫、约翰内斯·开普勒、伽利略和尼古拉·哥白尼等科学家产生了巨大影响。在5中讨论了巴塔尼如何能够比尼古拉·哥白尼产生更精确的太阳运动测量结果。作者提出，巴塔尼获得更精确的结果仅仅是因为他的观测是在更靠南的纬度进行的。对于巴塔尼而言，折射对他冬季至点的子午线观测几乎没有影响，因为在他更靠南的ar-Raqqah观测点，太阳在天空中的位置更高。

巴塔尼的Kitab al-Zij由蒂沃利的柏拉图译为拉丁文De motu stellarumⓉ（论星辰的运动）。该译本于1116年问世，而蒂沃利的柏拉图译本的印刷版于1537年出版，1645年再次出版。13世纪有人将其译为西班牙文，该译本和蒂沃利的拉丁文译本柏拉图都留存了下来。

Al-Battani is sometimes known by a latinised version of his name, variants being Albategnius, Albategni or Albatenius. His full name was Abu Abdallah Mohammad ibn Jabir ibn Sinan al-Raqqi al-Harrani al-Sabi al-Battani.

Al-Battani was born in Harran, called Carrhae in earlier times by the Romans, which lies on the Balikh River, 38 km southeast of Urfa. His family had been members of the Sabian sect, a religious sect of star worshippers from Harran. Being worshipers of the stars meant that the Sabians had a strong motivation for the study of astronomy and they produced many outstanding astronomers and mathematicians such as Thabit ibn Qurra. In fact Thabit was also born in Harran and would have still have been living there at the time that al-Battani was born. Al-Battani, unlike Thabit, was not a believer in the Sabian religion, however, for "Abu Abdallah Mohammad" indicates that he was certainly a Muslim.

Although the identification is not absolutely certain, it is probable that al-Battani's father was Jabir ibn Sinan al-Harrani who had a high reputation as an instrument maker in Harran. The name certainly makes the identification fairly certain and the fact that al-Battani himself was skilled in making astronomical instruments is a good indication that he learnt these skills from his father.

Al-Battani made his remarkably accurate astronomical observations at Antioch and ar-Raqqah in Syria. The town of ar-Raqqah, where most of al-Battani's observations were made, became prosperous when Harun al-Rashid, who became the fifth Caliph of the Abbasid dynasty on 14 September 786, built several palaces there. The town had been renamed al-Rashid at that time but, by the time al-Battani began observing there, it had reverted to the name of ar-Raqqah. The town was on the Euphrates River just west of where it joins the Balikh River (on which Harran stands).

The Fihrist (Index) was a work compiled by the bookseller Ibn an-Nadim in 988. It gives a full account of the Arabic literature which was available in the 10th century and it describes briefly some of the authors of this literature. The Fihrist describes al-Battani as (see for example [1]):-

... one of the famous observers and a leader in geometry, theoretical and practical astronomy, and astrology. He composed a work on astronomy, with tables, containing his own observations of the sun and moon and a more accurate description of their motions than that given in Ptolemy's "Almagest" Ⓣ. In it moreover, he gives the motions of the five planets, with the improved observations he succeeded in making, as well as other necessary astronomical calculations. Some of his observations mentioned in his book of tables were made in the year 880 and later on in the year 900. Nobody is known in Islam who reached similar perfection in observing the stars and scrutinising their motions. Apart from this, he took great interest in astrology, which led him to write on this subject too: of his compositions in this field I mention his commentary on Ptolemy's Tetrabiblos.

Other information about al-Battani contained in the Fihrist is that he observed between the years 877 and 918 and that his star catalogue is based on the year 880. It also describes the end of his life which seems to have occurred during a journey he made to Baghdad to protest on behalf of a group of people from ar-Raqqah because they had been unfairly taxed. Al-Battani reached Baghdad and put his arguments but died on the return journey to ar-Raqqah.

The Fihrist also quotes a number of works by al-Battani. There is his Kitab al-Zij which is his major work on astronomy with tables, referred to above. We shall examine this in more detail in a moment. There is also the commentary on Ptolemy's Tetrabiblos referred to above and two other titles: On ascensions of the signs of the zodiac and On the quantities of the astrological applications. One of the chapters of the Kitab al-Zij has the title "On ascensions of the signs of the zodiac" and so the Fihrist may be wrong in thinking this is a separate work. This point still appears unclear.

Al-Battani's Kitab al-Zij is by far his most important work and we should examine briefly the topics which it covered. The work contained 57 chapters. It begins with a description of the division of the celestial sphere into the signs of the zodiac and into degrees. The necessary background mathematical tools are then introduced such as the arithmetical operations on sexagesimal fractions and the trigonometric functions. Chapter 4 contains data from al-Battani's own observations. Chapters 5 to 26 discuss a large number of different astronomical problems following to some extent material from the Almagest Ⓣ. The motions of the sun, moon and five planets are discussed in chapters 27 to 31, where the theory given is that of Ptolemy but for al-Battani the theory appears less important than the practical aspects.

After giving results to allow data given for one era to be converted to another era, al-Battani then gives 16 chapters which explain how his tables are to be read. Chapters 49 to 55 cover problems in astrology, while chapter 56 discusses the construction of a sundial and the final chapter discusses the construction of a number of astronomical instruments.

What are the main achievements of al-Battani's Zij? He catalogued 489 stars. He refined the existing values for the length of the year, which he gave as 365 days 5 hours 46 minutes 24 seconds, and of the seasons. He calculated 54.5" per year for the precession of the equinoxes and obtained the value of 23° 35' for the inclination of the ecliptic.

Rather than using geometrical methods, as Ptolemy had done, al-Battani used trigonometrical methods which were an important advance. For example he gives important trigonometric formulae for right angled triangles such as

$b \sin(A) = a \sin(90° - A)$.

Al-Battani showed that the farthest distance of the Sun from the Earth varies and, as a result, annular eclipses of the Sun are possible as well as total eclipses. However, as Swerdlow points out in [8], the influence of Ptolemy was remarkably strong on all medieval authors, and even a brilliant scientist like al-Battani probably did not dare to claim a different value of the distance from the Earth to the Sun from that given by Ptolemy. This was despite the fact that al-Battani could deduce a value for the distance from his own observations that differed greatly from Ptolemy's.

In [1] Hartner gives a somewhat different opinion of the way that al-Battani is influenced by Ptolemy. He writes:-

While al-Battani takes no critical attitude towards the Ptolemaic kinematics in general, he evidences ... a very sound scepticism in regard to Ptolemy's practical results. Thus, relying on his own observations, he corrects - be it tacitly, be it in open words - Ptolemy's errors. This concerns the main parameters of planetary motion no less than erroneous conclusions drawn from insufficient or faulty observations, such as the invariability of the obliquity of the ecliptic or of the solar apogee.

Al-Battani is important in the development of science for a number of reasons, but one of these must be the large influence his work had on scientists such as Tycho Brahe, Kepler, Galileo and Copernicus. In [5] there is a discussion on how al-Battani managed to produce more accurate measurements of the motion of the sun than did Copernicus. The author suggests that al-Battani obtained much more accurate results simply because his observations were made from a more southerly latitude. For al-Battani refraction had little effect on his meridian observations at the winter solstice because, at his more southerly site of ar-Raqqah, the sun was higher in the sky.

Al-Battani's Kitab al-Zij was translated into Latin as De motu stellarum Ⓣ by Plato of Tivoli. This appeared in 1116 while a printed edition of Plato of Tivoi's translation appeared in 1537 and then again in 1645. A Spanish translation was made in the 13th century and both it and Plato of Tivoli's Latin translation have survived.