Arithmetica of diophantus book 2 problem 10-1ac

The eighth problem of the second book of diophantuss arithmetica is to divide a square into a sum of two squares. The general assertion concerning f n was proved by the german mathematician david hilbert in diophantus of alexandria c. Diophantus about 200 about 284 mactutor history of mathematics. The six books of the arithmetica present a collection of both determinate and in. Thus the fifth power is relate i, x 1 is relato 2, x 10 is censo di relato i, x is.

It is a collection of algebraic problems giving numerical solutions of determinate equations those with a unique solution and indeterminate equations. Diophantus was a hellenistic greek or possibly egyptian, jewish or even chaldean mathematician who lived in alexandria during the 3rd century ce. In book iii, diophantus solves problems of finding values which make two linear. Diophantus of alexandria arithmetica book i joseph. The number he gives his readers is 100 and the given difference is 40.

The arithmetica is a collection of problems giving numerical solutions of. For example, book ii, problem 8, seeks to express a given square number as the sum of two square numbers here read more. In it he introduced algebraic manipulations on equations including a symbol for one unknown probably following other authors in alexandria. He is sometimes called the father of algebra, and wrote an influential series of books called the arithmetica, a collection of algebraic problems which greatly influenced the subsequent development of number theory. On the other hand, diophantus is quoted around 350ce by theon of alexandria, heath, 2 giving us a possible interval of about five hundred years. This edition of books iv to vii of diophantus arithmetica, which are extant only in a recently discovered arabic translation, is the outgrowth of a doctoral dissertation submitted to the brown university department of the history of mathematics in may 1975. The integers from 1 to 10 were expressed by using the first ten. Diophantuss arithmetica1 is a list of about 128 algebraic problems with so. The place of diophantus m 127 the arithmetica book l 129143 il. Arithmetica work by diophantus arith,etica a history of mathematics second ed. Mathematics, volume 5 issue 1 january 2015, pages 9166.

Diophantus is aware of the fact that his method produces many more solutions. This book features a host of problems, the most significant of which have come to be called diophantine equations. The problem in the very first problem in the very first book of arithmetica diophantus asks his readers to divide a given number into two numbers that have a given difference. The symbolic and mathematical influence of diophantuss arithmetica. Diophantus of alexandria, arithmetica and diophantine equations.