INDIA AND ARABS

Successors of Greeks in a history of mathematics were Indians. Indian mathematics were not engaged in proofs, but they have entered original concepts and a number of effective methods. They have entered zero as cardinal number and as a symbol of absence of units in the corresponding category. Moravia (850 AD) has established rules of operations with zero, believing, however, that division of number into zero leaves number constant. The right answer for a case of division of number on zero has been given by Bharskar (born In 1114 AD -?), he possesses rules of actions above irrational numbers. Indians have entered concept of negative numbers (for a designation of duties). We find their earliest use at Brahmagupta’s (around 630). Ariabhata (born in 476 AD-?) has gone further in use of continuous fractions at the decision of the uncertain equations.

Our modern notation based on an item principle of record of numbers and zero as cardinal number and use of a designation of the empty category, is called Indo-Arabian. On a wall of the temple constructed in India around 250 AD, some figures, reminding on the outlines our modern figures are revealed.

About 800 Indian mathematics has achieved Baghdad. The term "algebra" occurs from the beginning of the name of book Al-Jebr vah-l-mukabala -Completion and opposition (Аль-джебр ва-л-мукабала), written in 830 astronomer and the mathematician Al-Horezmi. In the composition he did justice to merits of the Indian mathematics. The algebra of Al-Horezmi has been based on works of Brahmagupta, but in that work Babylon and Greek math influences are clearly distinct. Other outstanding Arabian mathematician Ibn Al-Haisam (around 965-1039) has developed a way of reception of algebraic solvings of the square and cubic equations. Arabian mathematics, among them and Omar Khayyam, were able to solve some cubic equations with the help of geometrical methods, using conic sections. The Arabian astronomers have entered into trigonometry concept of a tangent and cotangent. Nasyreddin Tusy (1201-1274 AD) in the "Treatise about a full quadrangle” has regularly stated flat and spherical to geometry and the first has considered trigonometry separately from astronomy.

And still the most important contribution of arabs to mathematics of steel their translations and comments to great creations of Greeks. Europe has met these jobs after a gain arabs of Northern Africa and Spain, and later works of Greeks have been translated to Latin.