Abraham bar Hiyya Savasorda

Abraham bar Hiyya是一位西班牙犹太数学家和天文学家。在他那个时代的希伯来语中，“Ha-Nasi”意为“领袖”，但他也以拉丁名字Savasorda而闻名，这个名字来自他的“职位描述”，表明他在巴塞罗那的行政机构中担任官方职务。

Abraham bar Hiyya以其著作Hibbur ha-Meshihah ve-ha-Tishboret（《测量与计算论》）而闻名，该书由蒂沃利的柏拉图于1145年译为拉丁文，题为Liber embadorum。这本书是欧洲最早的阿拉伯代数著作。它包含了一般quadratic的完整解法，是欧洲第一部给出此类解法的文本。然而颇为奇怪的是，1145年也是花拉子米的代数书由切斯特的罗伯特译出的一年，因此Abraham bar Hiyya的著作很快便有了第二部给出一般二次方程完整解法的文本相伴。

考察马克斯·亚伯拉罕所熟悉的数学领域和数学家是很有意思的。他当然通过欧几里得的著作了解几何学，但他也了解其他希腊文本对几何学的贡献，如比提尼亚的狄奥多西的三卷本Sphaerics、奥托里库斯关于球面几何的著作On the Moving Sphere、阿波罗尼奥斯的圆锥曲线，以及后来亚历山大里亚的海伦和亚历山大里亚的梅涅劳斯的贡献。亚伯拉罕还研习过阿拉伯数学家在代数方面的一些重要著作，特别是花拉子米和卡拉吉。

Abraham bar Hiyya所写的其他文本中包括Yesod ha-Tebunah u-Migdal ha-Emunah（《理解之基与信仰之塔》）。这部著作是一部涵盖数学、天文学、光学和音乐的百科全书。它是第一部希伯来语百科全书。

亚伯拉罕还写了许多关于天文学的文本，特别是关于地球的形状以及恒星在天球上的路径计算。他的书Tables of the Prince引用了巴塔尼的表格，而亚伯拉罕写于1122-23年的论著Sefer ha-Ibbur（《置闰之书》）则是第一部专门研究历法的希伯来语著作。

在哲学论著Hegyon ha-Nefesh ha-Azuva（《忧伤灵魂的沉思》）中，亚伯拉罕讨论了善与恶的本质以及伦理学。Megillat ha-Megalleh（《启示者之卷》）概述了亚伯拉罕基于占星术的历史观。它声称能预言弥赛亚的未来。

也许Abraham bar Hiyya工作最重要的特点之一是，它似乎激发了对阿拉伯数学的兴趣，并且与阿伯拉罕·伊本·埃兹拉的工作一起，标志着希伯来学术数学研究的开端。正如[5]的作者所写：-

希伯来语数学“经典”的主要部分是在十三世纪第二个三分之一到十四世纪第一个三分之一期间，在西地中海北部沿岸从阿拉伯语翻译过来的。这一运动发生在Abraham bar Hiyya和阿伯拉罕·伊本·埃兹拉的原创著作为广大读者所获得之后。

很难将Abraham bar Hiyya置于数学发展之中，因为在大多数方面他并不完全适合一种文化，而是跨越了几种文化。也许正是因为这个原因，他才重要，因为他促成了这些文化之间思想的交叉融合。正如[6]的作者Levey在[1]中所写，亚伯拉罕：-

... 并不明确地属于某一个数学群体。他一生大部分时间在巴塞罗那度过，那是一个阿拉伯和基督教学术并存的地区，他积极翻译阿拉伯科学的杰作。... 他痛惜普罗旺斯人民缺乏对阿拉伯科学和语言的了解。他用希伯来语写自己的著作，但他帮助将...著作翻译成拉丁语。...

Abraham bar Hiyya was a Spanish Jewish mathematician and astronomer. In the Hebrew of his time 'Ha-Nasi' meant 'the leader' but he is also known by the Latin name Savasorda which comes from his 'job description' showing that he held an official position in the administration in Barcelona.

Abraham bar Hiyya is famed for his book Hibbur ha-Meshihah ve-ha-Tishboret (Treatise on Measurement and Calculation), translated into Latin by Plato of Tivoli as Liber embadorum in 1145. This book is the earliest Arab algebra written in Europe. It contains the complete solution of the general quadratic and is the first text in Europe to give such a solution. Rather strangely, however, 1145 was also the year that al-Khwarizmi's algebra book was translated by Robert of Chester so Abraham bar Hiyya's work was rapidly joined by a second text giving the complete solution to the general quadratic equation.

It is interesting to see the areas of mathematics and the mathematicians with which Abraham was familiar. Of course he knew geometry through the works of Euclid, but he also knew the contributions to geometry from other Greek texts such as Theodosius's Sphaerics in three books, On the Moving Sphere which is a work on the geometry of the sphere by Autolycus, Apollonius's Conics, and the later contributions by Heron of Alexandria and Menelaus of Alexandria. Abraham had also studied some of the important works on algebra by Arab mathematicians, in particular al-Khwarizmi and al-Karaji.

Among other texts written by Abraham bar Hiyya was Yesod ha-Tebunah u-Migdal ha-Emunah (The Foundation of Understanding and the Tower of Faith). This work is an encyclopaedia of mathematics, astronomy, optics and music. It is the first encyclopaedia in the Hebrew language.

Abraham also wrote a number of texts on astronomy; in particular he wrote on the form of the Earth and the calculation of the paths of the stars on the celestial sphere. His book Tables of the Prince refers to the tables of al-Battani while Abraham's treatise Sefer ha-Ibbur (Book of Intercalation), written in 1122-23, is the first Hebrew work devoted exclusively to a study of the calendar.

In the philosophical treatise Hegyon ha-Nefesh ha-Azuva (Meditation of the Sad Soul) Abraham deals with the nature of good and evil and ethics. Megillat ha-Megalleh (Scroll of the Revealer) outlines Abraham's view of history based on astrology. It claims to forecast the messianic future.

Perhaps one of the most important features of Abraham bar Hiyya's work is the fact that it appears to have stimulated an interest in Arabic mathematics and, together with the work of Abraham ibn Ezra, marks the beginning of Hebrew scholarly study of mathematics. As the author of [5] writes:-

The major part of the mathematical 'classics' in Hebrew were translated from Arabic between the second third of the thirteenth century and the first third of the fourteenth century, within the northern littoral of the western Mediterranean. This movement occurred after the original works by Abraham bar Hiyya and Abraham ibn Ezra became available to a wide readership.

It is rather difficult to place Abraham bar Hiyya in the development of mathematics since in most respects he did not fit nicely into one culture but spanned several. It may indeed be for just that reason that he is important since he produced a cross-fertilisation of ideas between these cultures. As Levey, the author of [6], writes in [1], Abraham:-

... did not definitely belong definitely to one mathematical group. He spent most of his life in Barcelona, an area of both Arab and Christian learning, and was active in translating the masterpieces of Arab science. ... he deplored the lack of knowledge of Arab science and language among the people of Provence. He wrote his own works in Hebrew, but he helped translate ... works into Latin....