Die Große Arithmetik aus dem Codex Vind. phil. gr. 65

The anonymous Cod. Vind. phil. gr. 65 is one of the numerous Greek manuscripts bought by Augerius von Busbeck, a Habsburgian ambassador, in Constantinople in the middle of the 16th century. Since then, the codex has been kept in the Hofbibliothek of Vienna (today Österreichische Nationalbibliothek). Although it constitutes one of the most important mathematical manuscripts from the later Byzantine period, the two first chapters were transcribed by J. L. Heiberg only in the year 1899. In 1963 an expert edition of the so-called Aufgabensammlung (collection of problems), the smaller part of the manuscript, followed by H. Hunger and K. Vogel. A reliable edition of the greater part written by another scribe in the year 1436 and containing arithmetics, algebra, and geometry, is still lacking. The author presents hereby an edition of the extensive arithmetical text – called “first book” by the scribe – with complete reproduction of the numerous diagrams, philological analyses and indexes, conveniently selected partial translations, and a comprehensive mathematical and historical comment understandable also for readers without profound mathematical background. As template for the manuscript an unknown trattato d’abbaco has to be supposed because the Italian influences dominate. However, the scribe introduces the decimal position system with the Greek alphabetic numerals completed by a special sign (ɥ) for the empty position (0). In addition decimal fractions and calculation appear here for the first time in Europe, an achievement from the Islamic culture.