How was the practice of arithmetic developed and spread during the transition between the Middle Ages and the Modern Period? We know a lot about the evolution of mathematical theory and its diffusion in Latin, but little about the way in which arithmetic knowledge spread in the vernaculars in the 15^th and early 16^th centuries. Translation and adaptation of arithmetic treatises and manuals provided access to mathematical knowledge for new groups of people, shaped the practices of reckoning, and opened new ways of teaching arithmetic skills to persons without higher education. These efforts also endowed European vernaculars with new linguistic forms of abstraction and thus enhanced their potential to serve as a tool in the modern scientific revolution.

ARITHMETIC will study handwritten German arithmetic treatises from their first appearance around 1400 until the time when printed reckoning-books became easily available at the beginning of the 16^th century. These texts have not been studied before, although they are important witnesses of the vernacularization of mathematical knowledge, of the interdependence of vernacular and Latin pragmatic literacy and of the links between mathematics, sciences, and commerce.

The treatises will be transcribed, digitally edited, and analyzed from a historic, literary, and linguistic perspective. An “Assertive Edition” relying on Semantic Enrichment will be one product of ARITHMETIC. A detailed linguistic analysis focusing on semantics, syntax, the vocabulary, and the transmission context will lead to the reconstruction of an arithmetic discourse, give information on the orality underlying didactic texts and allow tracing writers/compilers and users and their educational and social background. This research aims at a new understanding of how arithmetical knowledge and practices of calculation were transformed in Late Medieval Europe, and how an abstract and scientific language emerged in the German vernacular.