This problem became important when fermat, in his copy of diophantus arithmetica edited by bachet, noted that he had this wonderful proof that cubes cant. Is there an english translation of diophantuss arithmetica available. Based on this puzzle diophantus married at the age of 26 and had a son who died at the age of 42, four years before diophantus himself died at the age of 84. Diophantus, byname diophantus of alexandria, flourished c.
Diophantus lived and worked in alexandria in the third century and has been called the father of algebra. Diophantus of alexandria arithmetica book i joseph. In nineteenth century, jacobi and weirstrass connected these efforts with elliptic integrals and elliptic functions. Diophantus 20th problem and fermats last theorem for n4. 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. Thomas heath 1910 made an english translation of bachets version, but. Mathematical treasures bachets arithmetic of diophantus. Like the synagoge, diophantus text was also a mathematical compendium, but its approach was completely different, having more in common stylistically. Of later greek mathematicians, especially noteworthy is diophantus of alexandria flourished c. In a well publicized story, fermat communicated his last theorem but not its proof in the margin of diophantus arithmetica. The most famous latin translation of arithmetica was by bachet inwhich was the first translation of arithmetica available to the public. Alongside bachet s original greek and latin translations were fortyeight observations made by fermat, one of which was to become known as fermats last theorem. For this reason, mathematical historian kurt vogel writes.
Avoiding implicit bias copyright agreement principal investigators manual. Diophantuss arithmetica1 is a list of about 128 algebraic problems with so lutions. Selected problems of second degree from arithmetica. In it he introduced algebraic manipulations on equations. In the arithmetica there is a result that is even harder to. The meaning of plasmatikon in diophantus arithmetica. Boethius was a 6th century roman philosopher who wrote one of the most important texts of the time consolation of philosophy.
Arabic and prebyzantine era who quotes from diophantuss arithmetica. Check out the new look and enjoy easier access to your favorite features. Bachet s translation of diophantuss arithmetica, made a famous. Six of the thirteen books ofarithmetica in greek have come down to us,3 and four more books, in arabic, were discovered in.
For more on the history of the reception of the arithmetica, see 9 and 10. Before considering several of the types of results found in arithmetica it is worth taking a few moments to. The story of mathematics hellenistic mathematics diophantus. Diofantos wikipedia bahasa indonesia, ensiklopedia bebas.
Diophantus was a greek mathematician sometimes known as the father of algebra who is best known for his arithmetica. Arithmetica of diophantus department of mathematical. Diophantus dan karyakaryanya juga telah mempengaruhi matematika arab dan ketenaran besar di antara matematikawan arab. Greek mathematics lacked the notational devices that enable us to think quickly and easily on problems that we conceptualize through the use of algebraic symbols.
Around 400ce hypatia of alexandria wrote a commentary on the first six of these, and the remaining seven were. A common example of this type of problem is the variety of ways of changing a pound using di erent. Iv to vii of diophantus arithmetica in the arabic translation attributed to qusta ibn luqa. In several places in the arithmetica diophantus refers to propositions which he had. Heath declared that tannery misread bachet and that bachet had also concluded that hypatia wrote on diophantus arithmetica. He developed indeterminate diophantine equations, that is, equations with multiple solutions. The author thanks benjamin braun, for whose history of mathematics course this paper was originally written, and an anonymous referee for their guidance and suggestions. Xylender, bachet, fermat, and euler, to name a few, but their focus has always been. Bachet 15911639 translated the arithmetica of diophantus into latin.
The symbolic and mathematical influence of diophantuss. The arithmetica as written by diophantus originally contained thirteen books. It is a collection of algebraic problems giving numerical solutions of determinate equations those with a unique solution and indeterminate equations. Tannery, disagreeing with an earlier editor bachet 1621, who supposed that hypatia must have written on an astronomical work of diophantus, asserted that her commentary must have been on the arithmetica 46. It seems more like a book about diophantuss arithmetica, not the translation of the actual book. Hypatias work on diophantus appalachian state university. Diophantus arithmetica consists of books written in greek in ce the dates vary by years from 70ad to ad. Edisi arithmetica memberikan pengaruh besar pada perkembangan aljabar di eropa pada akhir abad keenam belas dan melalui abad 17 dan 18. Diophantus revisited 3 be written also as a sumof positive rational cubes, again a result which nowadays we would explain in terms of elliptic curves. Diophantus is usually considered to be the father of algebra, and his books consider more than problems most of which have been solved of. Diophantus was the first greek mathematician who recognized fractions as numbers, thus allowed positive rational numbers for the coefficients and solutions. He also considered simultaneous quadratic equations. Books iv to vii of diophantus arithmetica springerlink.
Diophantuss arithmetica1 is a list of about algebraic problems with so like all greeks at the time, diophantus used the extended greek. In addition to philosophy, boethius wrote on other topics including music, geometry, astronomy, and arithmetic. Terkadang disebut bapak algebra, teksteksnya berisi. Mathematics from diophantus to leonardo of pisa part 2. Karya diophantus memiliki pengaruh besar dalam sejarah. Diophantus of alexandria wikisource, the free online library. In it he introduced algebraic manipulations on equations including a symbol for one unknown probably following other authors in alexandria. Claude bachet 15811638 published a latin translation of books ivi of.
He had famously added i have discovered a truly marvelous proof of this, which, however, the margin is not large enough to contain. Where one would writediophantus has to resort to constructions like. Diophantus, pappus and the decline of greek mathematics. Diophantus arithmetica consists of books written originally in greek circa in 270 ce. To divide a given square into a sum of two squares. One of the most famous problems that diophantus treated was writing a square as the sum of two squares book ii, problem 8. Diophantus of alexandria, arithmetica and diophantine.
Theres just an abstract from the books, mostly an abbreviated description of the problems and their solutions which doesnt seem to be a 1. The symbolic and mathematical influence of diophantuss arithmetica. Bachet s translation of diophantuss arithmetica, made a famous marginal note which came to be known as fermats last theorem. Diophantus himself refers to a work which consists of a collection of lemmas called the porisms or porismatabut this book is entirely lost. In 1670 at toulouse he brought out diophantus arithmetica containing observations by p. Diophantus akexandria made advances in mathematical notation and was the first hellenistic mathematician who frankly recognized fractions as numbers.
358 1217 886 509 906 661 291 779 370 1450 282 835 354 922 731 67 1225 65 134 19 998 706 751 643 802 755 200 1247 1083 698 426 1418 831 511 182 397 272 856 381 1162 991 1287 416