Arithmetica

Arithmetica is een Oudgriekse tekst over wiskunde, geschreven door de wiskundige Diophantus in de 3e eeuw na Christus.[1] Het is een verzameling van 130 algebraïsche problemen met numerieke oplossingen van bepaalde vergelijkingen (met een unieke oplossing) en onbepaalde vergelijkingen.

Samenvatting

De vergelijkingen in het boek worden tegenwoordig diofantische vergelijkingen genoemd. De meeste Arithmetica- problemen leiden tot kwadratische vergelijkingen.

Arithmetica werd oorspronkelijk geschreven in dertien boeken, maar de Griekse manuscripten die de tand des tijds overleefd hebben, bevatten niet meer dan zes boeken.[2] In 1968 vond Fuat Sezgin vier voorheen onbekende boeken van Arithmetica bij het heiligdom van Imam Rezā in de heilige islamitische stad Mashhad in het noordoosten van Iran.[3] De vier boeken zouden door Qusta ibn Luqa (820-912) van het Grieks naar het Arabisch zijn vertaald. Norbert Schappacher schreef hierover:

[De vier ontbrekende boeken] doken rond 1971 op in de Astan Quds-bibliotheek in Meshed (Iran) in een kopie uit 1198 AD. Het werd niet gecatalogiseerd onder de naam Diophantus (maar onder die van Qusta ibn Luqa) omdat de bibliothecaris blijkbaar niet in staat was de hoofdregel van het voorblad te lezen, waar de naam van Diophantus in geometrische Kufi-kalligrafie voorkomt.[4]

Arithmetica werd bekend bij wiskundigen in de islamitische wereld in de tiende eeuw[5] toen Abu'l-Wefa het in het Arabisch vertaalde.[6]

In 1585 voegde Simon Stevin de vragen en de antwoorden van de eerste vier boeken toe aan zijn werk L'arithmètique. Hij maakte een vrije vertaling, zodanig dat dit stilistisch aansloot bij de rest van zijn boek.

Zie ook

Referenties

  1. ↑ Diophantus of Alexandria (Greek mathematician). Encyclopædia Britannica. Gearchiveerd op 28 april 2015. Geraadpleegd op 11 april 2013.
  2. ↑ Dictionary of World Biography. Salem Press (1998), p. 362. ISBN 9781135457396. Gearchiveerd op 15 mei 2014.
  3. ↑ Hogendijk, Jan P., Review of J. Sesiano, Books IV to VII of Diophantus' Arithmetica (1985). Gearchiveerd op 14 juli 2014. Geraadpleegd op 6 juli 2014. “Only six of the thirteen books of the Arithmetica of Diophantus (ca. A.D. 250) are extant in Greek. The remaining books were believed to be lost, until the recent discovery of a medieval Arabic translation of four of the remaining books in a manuscript in the Shrine Library in Meshed in Iran (see the catalogue [Gulchin-i Ma'ani 1971-1972, pp. 235-236]. The manuscript was discovered in 1968 by F. Sezgin).”
  4. ↑ Schappacher, Norbert, Diophantus of Alexandria : a Text and its History (April 2005). Gearchiveerd op 4 maart 2016. Geraadpleegd op 9 oktober 2015.
  5. ↑ Boyer, Carl B. (1991). A History of Mathematics, Second. John Wiley & Sons, Inc., "The Arabic Hegemony", p. 234. ISBN 0-471-54397-7 "Note the omission of Diophantus and Pappus, authors who evidently were not at first known in Arabia, although the Diophantine Arithmetica became familiar before the end of the tenth century."
  6. ↑ Boyer, Carl B. (1991). A History of Mathematics, Second. John Wiley & Sons, Inc., "The Arabic Hegemony", p. 239. ISBN 0-471-54397-7 "Abu'l-Wefa was a capable algebraist as well as a trigonometer. He commented on al-Khwarizmi's Algebra and translated from Greek one of the last great classics, the Arithmetica of Diophantus."
  • Diophantus Alexandrinus, Pierre de Fermat, Claude Gaspard Bachet de Meziriac, Diophanti Alexandrini Arithmeticorum libri 6, en De numeris multangulis liber unus . Cum comm. C (laude) G (aspar) Bacheti et observibus P (ierre) de Fermat. Acc. doctrinae analyticae inventum novum, coll. ex variis eiu. Tolosae 1670, DOI:10.3931/e-rara-9423 .

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