with traditional Greek mathematics since it is divorced from geometric methods, and it is different from Babylonian mathematics in that Diophantus is concerned primarily with exact solutions, both determinate and indeterminate, instead of simple approximations. In Arithmetica, Diophantus is the first to use symbols for unknown numbers as well as abbreviations for powers of numbers, relationships, and operations; thus he used what is now known as . The main difference between Diophantine syncopated algebra and modern algebraic notation is that the former lacked special symbols for operations, relations, and exponentials. So for example, what would be written in modern notation as which can be rewritten as would be written in Diophantus's syncopated notation as where the symbols represent the following: Unlike in modern notation, the coefficients come after the variables and that addition is represented by the juxtaposition of terms. A literal symbol-for-symbol translation of Diophantus's syncopated equation into a modern symbolic equation would be the following: where to clarify, if the modern parentheses and plus are used then the above equation can be rewritten as: Arithmetica is a collection of some 150 solved problems with specific numbers and there is no postulational development nor is a general method explicitly explained, although generality of method may have been intended and there is no attempt to find all of the solutions to the equations. Arithmetica does contain solved problems involving several unknown quantities, which are solved, if possible, by expressing the unknown quantities in terms of only one of them. Arithmetica also makes use of the identities: See also Diophantus II.VIII Muhammad ibn Mūsā al-Khwārizmī Citations References External links Diophantus Alexandrinus, Pierre de Fermat, Claude Gaspard Bachet de Meziriac, Diophanti Alexandrini Arithmeticorum libri 6, et De numeris multangulis liber unus. Cum comm. C(laude) G(aspar) Bacheti et observationibus P(ierre) de Fermat. Acc. doctrinae analyticae inventum novum, coll. ex variis eiu. Tolosae 1670, . 3rd-century books Ancient Greek mathematical works History of algebra