Diophantus looked at 3 different types of quadratic equations, because he did not have any notion for zero and he avoided negative coefficients. An example of this is found in problem 16, book i of the arithmetica, and it reads. Thus, we believe to have all of books ivii and three of the. Co 480 lecture 3 diophantus of alexandria, arithmetica and. For example, the first seven problems of the second book fit.
Problem 2 to split a given number 60 in two parts having a given ratio 3. Diophantus and pappus ca 300 represent a shortlived revival of greek mathematics in a society that did not value math as the greeks had done 500750 years earlier. In 1986 three mathematicians, ramachandran balasubramanian of india and jeanmarc deshouillers and francois dress. Diophantus wrote a seminal series of books called the arithmetica, and is regarded by many as being the father of. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Diophantus main claim to fame rests on his book arithmetika, which. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations. Full text of first course in algebra internet archive. Alexandrian algebra according to diophantus math department. Arithmetica is the major work of diophantus and the most prominent work on algebra in greek mathematics. Diophantus lived in alexandria in times of roman domination ca 250 a. In warings problem diophantus of alexandrias publication of arithmetica.
In book 3, diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. Diophantus is aware of the fact that his method produces many more solutions. Find two square numbers whose di erence is a given number, say 60. Problem 3 to split a given number 80 in two parts, the larger of which has a given ratio 3. And if diophantus states a necessary condition for dividing a number into two or three squares as in the previous case of v. The eighth problem of the second book of diophantuss arithmetica is to divide a square into a sum of two squares. Josephus account of the early divided monarchy aj 8,212. Of the original thirteen books of which arithmetica consisted only six have survived. The general assertion concerning fn was proved by the german mathematician david hilbert in 1909.
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