Antiquity. al Horezmi

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Brahmagupta (VII century) has developed some positions of Ariabhaty. It is necessary to note also the contribution to development of mathematics and astronomy of Varahamihira (VI century), Shridhara (IX-X centuries).

During the period with IX till XV century the world centre of sciences became Central Asia, presented to the world of the numerous scientists writing in the Arabian language as Central Asia was included then into structure Arabian halifata. Their works have rendered a great influence on development of the European science and a science Near and Middle East.

To number of the well-known scientists of that time Mohammed ben belongs to Musa al to Horezmi (787 apprx. 850). He was born in territory of present Uzbekistan, in Khoresm, present Khiva. al Horezmi has spent a considerable part of the life at court of the Baghdad Caliph Al Mamuna, the known patron of sciences. Here Mohammed has written numerous works on astronomy and the mathematician.

al Horezmi has entered Into a world science as ' vtor the treatise on the mathematician ' About numbers and actions with them ', translated in XII century with Arabian on Latin language. Thanks to this transfer the European scientists have got acquainted for the first time with the indijsko-Arabian way of the account, the so-called decimal item: each figure designated number, ten times bolshee, than the next figure on the right. From now on the Arabian figures were included Into the European And world mathematics. (Modern figures (naz. Arabian) are transferred to Europe by I slaves from India and were extended from sulfurs. XV century In narrow

mysle are signs: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.)

The Second treatise - the textbook of mathematics written by it about 830, ' Kitab al-dzhebr val mukabala ', is devoted basically to the decision

ravneny the first and second degree. In this treatise Mohammed ben Musa widely uses examples from an everyday life of that time: gives examples of trading calculations, inheritance divisions etc. The method of the decision of the equation to which uses al Horezmi, consists in two operations. The first, which it names ' ald-zhebr ', that is restoration, consists in an exception of the equation of negative sizes by addition to both members of equation of the expressions opposite to given negative sizes. The second operation - ' val mukabala ', that is opposition, is found to reduction of similar members but so that I do not appear negative sizes. Thanks to the specified operations any equation of the first and second degree it is possible to lead to one of six kinds of the equations:

1) С…1=ah,

2) X2=and,

3) ah=,

4) С…2 + ah=b,

5) С…2 + and=bС…,

6) ah + b=С…2.

Al Horezmi has given descriptive methods of the decision of all six equations; if them to represent by means of modern algebraic symbolics, they give all known formulas of roots of the equations.