Alexandrian algebra according to diophantus mathematics. If a problem leads to an equation in which certain terms are equal to terms of the same species. This problem became important when fermat, in his copy of diophantus arithmetica edited by bachet, noted that he had this wonderful proof that cubes cant. It consists of a short paragraph from theons commentary on the first book of.
Just in the same manner as in diophantus the multiplication of two species. This book features a host of problems, the most significant of which have come to be called diophantine equations. This book tells the story of abels problem and his proof. In diophantus there is another problem, v, 5, on the same subject2. Nonetheless, restating them algebraically can aid in understanding them. Diophantus of alexandria arithmetica book i joseph. Scribd is the worlds largest social reading and publishing site. A similar problem involves decomposing a given integer into the sum of three squares. Murty,esmonde problems in algebraic number theory summation. In the margin of his copy of diophantus s book on polygonal numbers, he wrote that he had discovered this proposition and called it beautiful and wonderful. On the contrary, it is impossible to divide either a cube into two cubes. Guide to book ii the subject matter of book ii is usually called geometric algebra. For example, book ii, problem 8, seeks to express a given square number as the sum of two square numbers here read more.
Book ii, iii, iv, and v contain indeterminate problems, and book vi contains. Of course, in doing so the geometric flavor of the propositions is lost. Diophantus of alexandria had a great impact in the world of mathematics. Thus the problem has been reduced to a linear equation, which. Diophantuss arithmetica1 is a list of about 128 algebraic problems with so lutions. Abels step ii implies that r 5 is a 2 3 4 rational function of the roots. Find two square numbers whose di erence is a given number, say 60. Immediately preceding book i, diophantus gives the following definitions to solve these simple problems. The problems in book i of the arithmetica are determinate ie, having a unique solution or a. The eighth problem of the second book of diophantus s arithmetica is to divide a square into a sum of two squares. The first ten propositions of book ii can be easily interpreted in modern algebraic notation. In it he introduced algebraic manipulations on equations including a symbol for one unknown probably following other authors in alexandria. To divide a given square into a sum of two squares. The eighth problem of the second book of diophantuss arithmetica is to divide a square into a sum of two squares.