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Diophantus Of Alexandria

The first book is anticipated by extensive introduction in which designations used by Diofantom are described. Unknown person Diofant names "number" (ἀριθμός) and designates the letter ς, a square of the unknown person — a symbol δν (reduction from δύναμις — "degree"). Special signs for following degrees of the unknown person are provided, up to the sixth, named a kubo-cube, and for degrees opposite to them. The sign on addition at Diofanta is not present: he simply writes nearby positive members, and in each member degree of the unknown person, and then numerical factor at first registers.Subtracted members also register nearby, and before all their group the special sign in the form of the turned letter Ψ is put. The Equal-sign is designated by two letters ἴσ (reduction from ἴσος — "equal"). The rule of reduction of similar members and an addition or subtraction rule to both members of equation of the same number or expression are formulated: That then at is scarlet-horezmi began be called «as algebra and алмукабалой». The rule of signs is entered: the minus on a minus gives plus; this rule is used at multiplication of two expressions with subtracted members. All it is formulated in a general view, without sending to geometrical interpretations.

The bolshaja part of work is a collection of problems with decisions (in the remained six their books only 189), the general methods skilfully picked up for an illustration. The main problematics of Arithmetics — a finding of positive rational decisions of the uncertain equations. Rational numbers are treated by Diofantom the same as also natural that is not typical for antique mathematicians.

At first Diofant investigates systems of the equations of 2nd order from 2 unknown persons; he specifies a method of a finding of other decisions if one is already known. Then it applies similar methods to the equations of the higher degrees.

In X century Arithmetics has been translated into the Arabian language then mathematics of the countries of Islam (Abu Kamil, etc.) have continued some researches of Diofanta. Interest to Arithmetics has increased In Europe after Raphael Bombelli has found out this composition in the Vatican library and has published 143 problems from it in the Algebra (1572). In 1621 there was the classical, in detail commented Latin translation of Arithmetics executed by Bashe де by Meziriakom. Methods of Diofanta have made huge impact on François Vieta and Pierre Ferma; however, during New time the uncertain equations usually dare in integers, instead of in rational as it was done by Diofant.

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