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We present, in this article, a selection of problems from the Arithmetica, which have been rewritten for ease of reading, and consider Diophantus's advancements in mathematics and math-ematical notation in the context of ancient Greek mathematics.
Diophantus of Alexandria Arithmetica joseph.muscat@um.edu.mt 21 January 2023 Notation Diophantus’s Arithmetica1 is a list of over 200 algebraic problems with solutions, dating from about ˘250AD. In it he introduced algebraic manipulations on equations including a symbol for one unknown (probably following other authors in Alexandria).
5.A. Some problems from Diophantus’ Arithmetica Our purpose here is to look more closely at several problems from Diophantus’ Arithmetica which are discussed on pages 220{223 of Burton. Book I, Problem 17. The general form of this problem is to nd x;y;z;w which solve the following system, in which A;B;C;D are arbitrary positive rational ...
Diophantus of Alexandria [1] (born c. AD 200 – c. 214; died c. AD 284 – c. 298) was a Greek mathematician, who was the author of two main works: On Polygonal Numbers, which survives incomplete, and the Arithmetica in thirteen books, most of it extant, made up of arithmetical problems that are solved through algebraic equations.
In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form 4 n + 3 {\displaystyle 4n+3} cannot be the sum of two squares.
The Italian Rafael Bombelli was the first to introduce the Arithmetic of Diophantus in the West. In 1572, Bombelli published in his treatise L’Algebra (Bombelli 1572) an Italian translation of a good part of the problems in Diophantus’ work.
As a theme of historical research Diophantus’ work raises two main issues that have been intensely debated among researchers of the period: (i) The proper understanding of Diophantus’ practice; (ii) the recognition of the mathematical tradition to which this practice belongs.
