贾比尔·伊本·阿弗拉赫Ǧābir Ibn-Aflāḥ

Jabir ibn Aflah通常以其名字的拉丁化形式为人所知，即贾比尔·伊本·阿弗拉赫。尽管他并非一流的阿拉伯数学家，但他在数学发展中很重要，因为他的著作被翻译成拉丁文，从而为欧洲数学家所利用，而一些顶尖阿拉伯数学家如阿布·瓦法的著作则未被翻译成拉丁文。

关于Jabir ibn Aflah的生平，可获得的资料很少。他来自塞维利亚，这一点有两个来源。首先，在包含其论著的抄本中，他被描述为“al-Ishbili”；这意味着“来自塞维利亚”。另一个来源不仅提供了他来自塞维利亚的信息，还对他生活的时期给出了很好的估计。这一信息来自Maimonides。

摩西·迈蒙尼德，其阿拉伯名字是Abu 'Imran Musa ibn Maymun ibn 'Ubayd Allah，是一位犹太哲学家、法学家和医生，1135年出生于科尔多瓦。在许多重要著作中，他用阿拉伯语写了The Guide of the Perplexed，其中他写道：-

……塞维利亚的ibn Aflah，我见过他的儿子……

Jabir ibn Aflah 发明了一种称为 torquetum 的观测仪器，这是一种在球坐标系之间进行变换的机械装置（更多细节见 [3]）。他还使自己的名字与球面三角学中的一个定理联系在一起，他对 克劳狄乌斯·托勒密 的 Almagest Ⓣ（主要论题：来自阿拉伯语 'al-majisti'——希腊语 'Mathematike Syntaxis' 的阿拉伯语译本，后来译为拉丁语 'Magna Syntaxis'）的批评广为人知。这些批评出现在 Jabir ibn Aflah 最著名的著作 Islah al-Majisti Ⓣ（《天文学大成》的修正）中。人们看到，ibn Aflah 甚至把关于 克劳狄乌斯·托勒密 所犯错误的论证放进了这部著作的标题中。在 [4] 中，Lorch 解释了 Jabir ibn Aflah 最著名的批评，即 克劳狄乌斯·托勒密 把金星和水星置于太阳之下。克劳狄乌斯·托勒密 声称这些行星绝不可能位于地球上观测者与太阳之间的连线上，但 ibn Aflah 指出这是一个错误，金星和水星在太阳之上。

要确定Correction of the Almagest的原创性确切程度有点困难。当然，其总体方法与阿布·瓦法的著作有相当大的相似性，但它可能并非基于阿布·瓦法的著作。两者可能都基于塔比·伊本·库拉的著作，或者ibn Aflah、阿布·瓦法和塔比·伊本·库拉的著作可能都基于某个仍未知的来源。

ibn Aflah的影响相当显著。在[4]中，研究了他对东西方天文学家的影响。特别是，作者考察了他对波斯天文学家Qutb al-Din al-Shirazi的影响，后者是Nasir al-Din纳西尔丁·图西的学生；对西班牙-阿拉伯哲学家ibn Rushd的影响，后者通常被称为Averroes，1126年出生于科尔多瓦，融合了伊斯兰传统和希腊思想；以及对莱维·本·热尔松（有时被称为莱维·本·热尔松）的影响。ibn Aflah较为臭名昭著的影响之一是对约翰·缪勒的影响，后者在其出版物De triangulis第四卷中抄袭了ibn Aflah著作的大部分内容。约翰·缪勒没有承认ibn Aflah是这些材料的来源，这导致吉罗拉莫·卡尔达诺强烈批评约翰·缪勒。

Jabir ibn Aflah is often known by the Latinised form of his name, namely Geber. Although not he was not in the first rank of Arabic mathematicians, he is important in the development of mathematics since his works were translated into Latin, and so became available to European mathematicians, whereas the work of some of the top rank Arabic mathematicians such as Abu'l-Wafa were not translated into Latin.

Very little information is available regarding Jabir ibn Aflah's life. That he came from Seville is known from two sources. Firstly he is described as "al-Ishbili" in manuscripts containing his treatises; this means "from Seville". The other source gives us not only the information that he came from Seville, but also a good estimate for the period in which he lived. The information comes from Maimonides.

Moses Maimonides, whose Arabic name was Abu 'Imran Musa ibn Maymun ibn 'Ubayd Allah, was a Jewish philosopher, jurist, and physician who was born in Córdoba in 1135. Among many important works he wrote The Guide of the Perplexed in Arabic in which he writes of:-

... ibn Aflah of Seville, whose son I have met ...

Jabir ibn Aflah invented an observational instrument known as the torquetum, a mechanical device to transform between spherical coordinate systems (see [3] for further details). He also gave his name to a theorem in spherical trigonometry, and his criticisms of Ptolemy's Almagest Ⓣ are well known. These criticisms appears in Jabir ibn Aflah's most famous work Islah al-Majisti Ⓣ. One sees that ibn Aflah even puts his argument regarding errors made by Ptolemy into the title of the work. In [4] Lorch explains Jabir ibn Aflah's most famous criticism, namely Ptolemy's placement of Venus and Mercury below the Sun. Ptolemy claimed that these planets could never be on a line between an observer on Earth and the sun., but ibn Aflah states that this is an error, and that Venus and Mercury are above the Sun.

It is a little difficult to establish the exact degree of originality of Correction of the Almagest. Certainly its general approach bears considerable similarity to the work of Abu'l-Wafa, but it may not be based on Abu'l-Wafa's work. Both may be based on the work of Thabit ibn Qurra, or the work of ibn Aflah, Abu'l-Wafa, and Thabit ibn Qurra may all be based on some still unknown source.

The influence of ibn Aflah is quite remarkable. In [4] his influence on astronomers in both the East and West is studied. In particular the author looks at his influence on the Persian astronomer Qutb al-Din al-Shirazi, who was a pupil of Nasir al-Din al-Tusi; on the Hispano-Arabian philosopher ibn Rushd, who is often known as Averroes, was born in Córdoba in 1126 and integrated Islamic traditions and Greek thought; and on Levi ben Gerson (sometimes known as Gersonides). One of ibn Aflah's more infamous influences was on Regiomontanus who copied large parts of ibn Aflah's work in the fourth book of his publication De triangulis. Regiomontanus did not acknowledge that ibn Aflah was the source of the material and this caused Cardan to strongly criticise Regiomontanus.