伊本·优努斯Ibn Yunus

优努斯的全名是Abu'l-Hasan Ali ibn Abd al-Rahman ibn Ahmad 伊本·优努斯 al-Sadafi。正如名字所示，他的曾祖父叫优努斯，祖父叫Ahmad，父亲叫Abd al-Rahman。这是一个学者家族，他的父亲Abd al-Rahman是一位著名历史学家。

我们对优努斯的童年知之甚少，但我们确实知道，他成长于埃及军事征服的时期。法蒂玛政治和宗教王朝得名于先知穆罕默德的女儿法蒂玛。法蒂玛王朝领导了一场宗教运动，致力于接管整个伊斯兰政治和宗教世界。因此，他们拒绝承认阿拔斯哈里发。法蒂玛哈里发在10世纪上半叶统治北非和西西里，但在多次未能征服埃及之后，他们于969年开始大举进军该国，征服了尼罗河谷。他们建立了开罗城，作为他们新帝国的首都。

优努斯与法蒂玛王朝关系密切，有两位哈里发支持他的科学工作。其中第一位是al-Aziz，他是第一位在埃及开始统治的法蒂玛哈里发。al-Aziz在其父al-Mu'izz去世后于975年成为哈里发，两年后，优努斯开始进行天文观测。尽管关于优努斯使用了哪些仪器存在不确定性，但早期作者声称al-Aziz至少为优努斯提供了一些仪器。

优努斯以其天文观测而闻名，他也是一位占星家，但他最著名的是他众多的三角学和天文表。当然，哈里发支持优努斯所从事的那种天文工作是非常合理的。穆斯林宗教需要相当多的关于月亮和太阳的知识，以确定一年中的祈祷时间。穆斯林的阴历要求新的月份由实际可见的月牙而不是阴历月的持续时间来确定，因此有必要了解许多不同的细节，例如月亮离太阳有多远，以确定它何时变得可见。

也许，如果 al-Aziz 没有如此深陷于在叙利亚北部扩张法蒂玛帝国的军事和政治冒险中，他本会给予 优努斯 更好的支持。在他二十年的统治期间，大部分时间他都在为此目标努力，而 优努斯 则埋头于他的天文学工作。Al-Aziz 于 996 年去世，当时他正在组织一支军队去攻打拜占庭人，而当时十一岁的 al-Hakim 成为了哈里发。然而，我们应该注意到，在 [5] 中，作者提出 优努斯 在编制他的表格时很可能使用了专业计算人员，所以也许 al-Aziz 或 al-Hakim 给予他的支持比我们上面所暗示的要多。

al-Hakim当然支持优努斯的天文工作，尽管很难确定这种支持的程度。也许al-Hakim对占星术的兴趣意味着他偏爱优努斯，据其传记作者记载，优努斯投入了大量时间进行占星预测。优努斯和al-Hakim都是怪人，尽管al-Hakim的怪癖更具破坏性，而优努斯的怪癖听起来更像是一个完全沉浸于学术追求的人。

优努斯被他的传记作者al-Musabbihi描述如下，后者是优努斯的同时代人（见[1]）：-

他是个古怪、粗心、心不在焉的人，衣着寒酸，相貌滑稽。

另一方面，al-Hakim下令洗劫al-Fustat城，优努斯有时从他曾祖父的房子里观察这座城市。al-Hakim下令杀死所有的狗，因为它们的吠叫使他烦恼，他还禁止了某些蔬菜和贝类。然而，可能是因为他对占星术的兴趣，al-Hakim在他俯瞰开罗的房子里保留了一些天文仪器，我们知道至少有一次优努斯从al-Hakim的房子里观测了金星。

优努斯的主要著作是一部天文手册，即al-Zij al-Hakimi al-kabir。“Al-kabir”意为“大”，这很贴切，“al-Hakimi”意味着这部著作献给哈里发al-Hakim，他当然支持优努斯。这本书确实很大，包含81章。其中有优努斯所做的观测记录，也有其前辈所做的观测记录。事实上，一个相当引人注目的事实是，这部著作在那一时期所有同类著作中独树一帜。其他作者从不区分他们自己的观测与著作中其他科学家所做的观测。

他准确描述了40次planetary conjunctions和30次月食，这些被西蒙·纽康用于他的月球理论。为了给出Hakimi Zij中描述的行星合的一个例子，我们引用[2]（另见[1]），并将优努斯给出的日期改为现代历法的日期：-

金星和水星在双子座的合，在西方天空观测到：这两颗行星在[1000年5月19日星期日]夜晚日落后相合。时间大约是星期天正午后八个赤道小时……水星在金星以北，它们的纬度差为三分之一度。

我们可以利用关于行星位置的现代知识确认，优努斯的描述完全正确，他给出的三分之一度的距离也完全正确。他还描述了一次月食[2]：-

这次月食发生在[981年4月22日]。我们聚集在al-Qarafa的优努斯 Nasr al Maghribi清真寺观测这次月食。当月亮高度约为21°时，我们察觉到了初亏。大约四分之一月面直径被食，复圆发生在日出前约一刻钟。

Hakimi Zij的第一章给出了穆斯林、科普特、叙利亚和波斯历法的日历表。优努斯给出了在这些历法之间转换日期的表格。还给出了计算复活节日期的表格。三角函数以弧而非角的形式给出。球面三角学在这部著作中达到了高度精密的水平。

许多其他表格被归功于优努斯。例如在[9]中，作者写道：-

在本文中，我描述了一组用于求月球经度的表格，归功于十世纪埃及天文学家优努斯。其背后的月球理论是克劳狄乌斯·托勒密的理论，但这些表格的设计使用户免于与克劳狄乌斯·托勒密的月球表格相关的计算。优努斯的表格，如果确实如此的话，包含超过34000个条目……这些表格之所以引人注目，是因为它们是中世纪学者根据精密的托勒密理论解决确定月球位置这一计算问题的最早尝试。

在[5]中描述了优努斯的Very useful tables for finding the time since sunrise, the hour angle and the solar 方位角 from the solar altitude。作者指出，优努斯使用了他为Hakimi Zij收集的数据来制作这些表格。这些表格所显示的高度精确性使D A King认为优努斯使用了非线性插值系统。

也许值得一提的是，与人们常说的相反，没有证据表明优努斯曾使用摆来进行时间测量。D A King在[8]中指出，这一说法是1684年由英国历史学家Edward Bernard开始流传的。

优努斯在身体健康时预言自己将在七天后去世。他整理了自己的事务，把自己关在屋里，诵读《古兰经》，直到在他预言的那一天去世。

Ibn Yunus's full name is Abu'l-Hasan Ali ibn Abd al-Rahman ibn Ahmad ibn Yunus al-Sadafi. As the name indicates, his great-grandfather was called Yunus, his grandfather was Ahmad, and his father Abd al-Rahman. It was a family of scholars, his father Abd al-Rahman being a noted historian.

We know little of ibn Yunus's childhood but we do know that he grew up in a period of military conquest in Egypt. The Fatimid political and religious dynasty took its name from Fatimah, the daughter of the Prophet Muhammad. The Fatimids headed a religious movement dedicated to taking over the whole of the political and religious world of Islam. As a consequence they refused to recognise the 'Abbasid caliphs. The Fatimid caliphs ruled North Africa and Sicily during the first half of the 10th century, but after a number of unsuccessful attempts to defeat Egypt, they began a major advance into that country in 969 conquering the Nile Valley. They founded the city of Cairo as the capital of their new empire.

Ibn Yunus was closely connected with the Fatimids and two Caliphs supported his scientific work. The first of these Caliphs was al-Aziz, who was the first of the Fatimid caliphs to begin his reign in Egypt. Al-Aziz became Caliph in 975 on the death of his father al-Mu'izz and, two years later, ibn Yunus began to make astronomical observations. Although there is uncertainty about the instruments that ibn Yunus used, it is claimed by early writers that al-Aziz provided ibn Yunus with at least some instruments.

Famed for his astronomical observations, ibn Yunus was also an astrologer but he is most famous for his many trigonometrical and astronomical tables. Of course it was very reasonable for a Caliph to support the type of astronomical work that ibn Yunus was undertaking. The Muslim religion required considerable knowledge of the moon and the sun to determine the times of prayer during the year. The Muslin lunar calendar required that the new months be determined by actual visibility of the lunar crescent rather than duration of the lunar month, so it was necessary to know a number of different details such as how far the moon was from the sun to determine when it became visible.

Perhaps al-Aziz would have given better support to ibn Yunus if he had not been so involved in military and political ventures in northern Syria trying to expand the Fatimid empire. For most of his 20 year reign he worked towards this aim while ibn Yunus toiled on his astronomical work. Al-Aziz died in 996 while organising an army to march against the Byzantines and al-Hakim, who was eleven years old at the time, became Caliph. We should note, however, that in [5] the author suggests that Yunus probably had the use of professional calculators in preparing his tables so perhaps al-Aziz or al-Hakim gave him more support than we have suggested above.

Certainly al-Hakim supported ibn Yunus in his astronomical work, although it is hard to determine the strength of that support. Perhaps al-Hakim's interest in astrology meant that he favoured ibn Yunus who is reported by his biographers to have devoted considerable amounts of time to making astrological predictions. Ibn Yunus and al-Hakim were both eccentrics, although al-Hakim's eccentricities were more damaging, while ibn Yunus's sound rather typical of someone totally absorbed in academic pursuits.

Ibn Yunus was described by his biographer al-Musabbihi, who was a contemporary of ibn Yunus, as follows (see [1]):-

He was an eccentric, careless and absent-minded man who dressed shabbily and had a comic appearance.

On the other hand al-Hakim ordered the sacking of the city al-Fustat, the city in which ibn Yunus sometimes observed from his great-grandfather's house. Al-Hakim ordered the killing of all dogs, since their barking annoyed him, and he banned certain vegetables and shellfish. However, probably because of his interest in astrology, al-Hakim kept some astronomical instruments in his house overlooking Cairo and we know that on at least one occasion ibn Yunus observed Venus from al-Hakim's house.

Ibn Yunus's major work, an astronomical handbook, was al-Zij al-Hakimi al-kabir. 'Al-kabir' means 'large' which is apt and 'al-Hakimi' means that the work is dedicated to Caliph al-Hakim who certainly supported ibn Yunus. The book is certainly large, containing 81 chapters. There are lists of observations made by Yunus and also observations made by his predecessors. In fact it is a rather remarkable fact that singles the work out from all similar works of that period. Other authors never distinguished between their observations and those in their works which had been made by other scientists.

He describes 40 planetary conjunctions accurately and 30 lunar eclipses which were used by Simon Newcomb in his lunar theory. To give an example of a planetary conjunction described in the Hakimi Zij we quote from [2] (see also [1]) having changed the dates given by ibn Yunus to those of a modern calendar:-

A conjunction of Venus and Mercury in Gemini, observed in the western sky: The two planets were in conjunction after sunset on the night [of Sunday 19 May 1000]. The time was approximately eight equinoctial hours after midday on Sunday ... . Mercury was north of Venus and their latitude difference was a third of a degree.

We can confirm, using modern knowledge of the positions of the planets, that ibn Yunus was exactly right in his description and that the distance of one third of a degree that he gives is again exactly right. He also describes an eclipse of the moon [2]:-

This lunar eclipse was [on 22 April 981]. We gathered to observe this eclipse at al-Qarafa, in the Mosque of Ibn Nasr al Maghribi. We perceived first contact when the altitude of the moon was approximately 21°. About a quarter of the lunar diameter was eclipsed, and reemergence occurred about a quarter of an hour before sunrise.

The first chapter of the Hakimi Zij gives calendar tables for Muslim, Coptic, Syrian and Persian calendars. Ibn Yunus gives tables to convert dates between these calendars. Tables to compute the date of Easter are also given. Trigonometric functions are given as arcs rather than angles. Spherical trigonometry reaches a high level of sophistication in this work.

Many other tables have been attriributed to ibn Yunus. For example in [9] the author writes:-

In this paper I describe a set of tables for finding the longitude of the moon, attributed to the tenth century Egyptian astonomer ibn Yunus. The underlying lunar theory is that of Ptolemy, but these tables are so devised that the user is spared the calculations which are associated with Ptolemy's lunar tables. Ibn Yunus's tables, if such they are, contain over 34000 entries ... . The tables are of interest as the earliest attempt by a medieval scholar to solve the computational problem of the determination of the lunar position according to the sophisticated Ptolemaic theory.

In [5] ibn Yunus's Very useful tables for finding the time since sunrise, the hour angle and the solar azimuth from the solar altitude are described. The author notes that ibn Yunus used data for these tables that he had collected for the Hakimi Zij. The high degree of accuracy displayed by these tables suggests to D A King that ibn Yunus used systems of nonlinear interpolation.

Perhaps it is worth mentioning that, contrary to claims which are often made, there is no evidence to suggest that ibn Yunus used a pendulum for time measurements. D A King in [8] shows that this myth was started in 1684 by the English historian Edward Bernard.

Ibn Yunus predicted the date of his own death to be in seven days time when he was in good health. He tidied up his business affairs, locked himself in his house and recited the Qur'an until he died on the day he predicted.