中国、印度和阿拉伯国家应用负数的历史的比较

人类对负数的认识和应用是数系扩充的重大步骤,负数的产生和应用不仅推广了算术的范围,而且为代数学的发展拓宽了道路.中国是世界上最早应用负数的国家,在《算数书》中就出现了负数概念及其加、减法运算,而在《九章算术》的方程章中则明确给出了正负数概念的定义和正负数的加减法则.印度人对负数的应用最早见于婆罗摩笈多的著作,他不仅给出了正负数的加减法则,还建立了正负数的乘除法则.一般认为,阿拉伯人不使用负数,但这似乎不符合东方人对数的概念的发展的认识规律.在20世纪50年代,有学者发现10世纪的艾布·瓦发在他的一种算术手抄本中应用了负数.本文对中国、印度和阿拉伯国家应用负数的历史进行比较分析,指出三者都是在"负债"、"不足"等意义下引入负数概念的,但在应用上却沿着不同的途径发展.文章还对阿拉伯人较少应用负数的原因进行了分析.

Historical Comparison of Applications of Negative Numbers in China,India and Arabia

Human's cognition and application of negative numbers is a important step in expending number system. The creation and application of negative numbers not only exteuded the span of arithmetic, but also widens the way of algebra to develop. China is the first country to use negative numbers. The concept of negative numbers and their rules for addition and subtraction already put forth in the book of A Book on Arithmetic. The definition of positive and negative numbers was definitely advanced in the chapter of equation in "The Mathematics of Nine Chapters",the rules of addition and subtraction of positive and negative numbers were also preseuted. The application of negative numbers in India was originated in the work of Brahmagupta, he established addition and subtraction the rules of positive and negative numbers and the multiplication and division rules. Conventionally Arab is known not to use negative numbers, but this seemed not to conform the eastern's understanding development in the number notion. In 1950's , scholar found that Abul Wefa used negative numbers in one of his algebra hand-written copies. This thesis mainly focuses on comparison of the historical of applications negative numbers in China, India and Arabia. All the countries introduced the concept of negative number under the meaning of \"debt\" and \"insufficiency\", but the application developed in different ways. This thesis also analyses the reason why the Arab seldom used negative numbers.