Antiquity. Geometry

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From all mathematical sciences elliny preferred geometry. Thus, as it is known, many of them were under the influence of Platon's considering geometry by a science philosophy, to be engaged which representatives of intellectual elite of a society are worthy only. In these conditions the geometry has turned to original gymnastics of mind, in art, and its practical application was considered vнизитeльным, profanation of this art. Platon's authority was indisputable in those days. For this reason arithmetics and algebra development as disciplines practical, encountered serious obstacles. Certainly, Greeks had to be engaged and algebra and arithmetics questions, but also in this case it ' gave geometrical forms '. As a relict of such approach in the modern language there were type definitions ' to square ' or ' in a cube '. But simultaneously Greeks promoted introduction in calculations of letter designations and by that - to algebra development. Ancient Greek mathematicians designated points, straight lines and planes capital letters, and figures - lower case.

Fundamental change in Ancient Greek mathematical tradition the outstanding mathematician from Alexandria has made Diofant living in III century d.C. It there was a first scientist who was engaged mainly in algebra. It has transferred to the Greek science of achievement vavilonjan in the field of algebra.

The Main work of Diofanta ' Arithmetics ' (apprx. 250-275) consisted of 13 books from which, unfortunately, has remained only six. But also it is enough of it to judge the contribution of Diofanta to algebra development. The scientist was able to solve the equations to the third degree inclusive, applied more than unknown persons, than it did vavilonjane, and designated unknown persons letters. It used a special symbol for subtraction and has entered into use the reduced words for separate definitions and actions.

Thus, Diofanta can consider as the author of the first algebraic language. For example, the equation 4аг 3mo is 2ar 9то where ' ag ' (reduction from ' arithmos ' - number) - unknown, ' that ' (reduction from ' monas') - unit, ' is' (' isos ') - equals, corresponds to the equation in our tracing: 4х + 3=2х + 9.

From this example it is visible that Diofant instead of the full verbal description of algebraic expressions (rhetorical algebra) has entered the reduced designations (syncopic algebra).