Introducing fractions in Magnitskii's Arithmetics in the early 18th century in Russia

Since 2004, we work with my colleague Alex Volkov, on exploring didactical value of mathematics textbooks, old and modern ones. We look at conceptual approaches that authors represent in their books. Our latest publication for the ICME-12 is now awailable online:  http://www.icme12.org/upload/UpFile2/TSG/0703.pdf
We look at fractions in the first Russian arithmetics textbook written by Magnitskii in the beginning of the 18th century. While some authors point at the origins of the book from earlier European medieval texts, others claim original didactical ideas of introducing concept of fraction. The paper belong to the TSG35 on the History of mathematics teaching and learning and there are other interesting contibutions on textbooks development.