Equations in the book are presently called diophantine equations. Diophantus of alexandria arithmetica book i joseph. The eighth problem of the second book of diophantuss arithmetica is to divide a square into a sum of two squares. Books iv to vii of diophantus arithmetica springerlink. 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. Diophantus, often known as the father of algebra, is best known for his. 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. From aristarchus to diophantus dover books on mathematics book 2 sir thomas heath. In modern terms, for example, a determinate problem could be 5x 10, so x 2, and an. For example, the first seven problems of the second book fit. Diophantus is aware of the fact that his method produces many more solutions. Heath d 2 furthermore, wilbur knorr concluded diophantus dates to be. In it he introduced algebraic manipulations on equations including.
In book iii, diophantus solves problems of finding values which make two linear. This book features a host of problems, the most significant of which have come to be called diophantine equations. Diophantus of alexandria was an alexandrian hellenistic mathematician, who was the author. Diophantus of alexandria, arithmetica and diophantine equations. Heath argues that diophantus is contemporary to anatolius, who was the bishop of laodicea around 280ce. Problem 2 to split a given number 60 in two parts having a given ratio 3. Diophantuss arithmetica1 is a list of about 128 algebraic problems with so lutions.
Diophantus about 200 about 284 mactutor history of mathematics. For example, book ii, problem 8, seeks to express a given square number as the sum of two square numbers here read more. Alexandrian algebra according to diophantus mathematics. It is not clear whether these results were part of another. In book 3, diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. Diophantus looked at 3 different types of quadratic equations. Most of the arithmetica problems lead to quadratic equations. Introduction the works of the mathematician diophantus have often struck readers as idiosyncratic. Sesiano found 4 more books bringing the total to 10 books found. This work brings to the audience diophantus problems of first degree in a literal. However, bombelli borrowed many of the problems for his own book algebra.