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Mathematical Treasure: 1833 Bulgarian Arithmetic

Frank J. Swetz (The Pennsylvania State University)

The Bulgarian state as an ethnic entity can be traced back to the year 681 CE; however, in 1396, it was absorbed into the Ottoman Empire. Eventually, by the nineteenth century, it emerged again, this time as a nation. In this era of nationalist and ethnic fervor, the use of the Bulgarian language was once again promoted. The first mathematics book to be published in this era was Arithmetika (The Study of Numbers) in 1833. The text was intended for commercial use but soon became a standard schoolbook. Its author was Khristaki Pavlovich (1804-1848), an Orthodox monk and teacher. The book was actually published in Serbia due to existing restrictions in Bulgaria.

The instruction on page 11, below, concerns simple multiplication, followed by a discussion on page 12 concerning the multiplication of two multi-digit numbers. The algorithm employed is the standard “downward method”; note the inclusion of zero place-holders to help preserve place-values in the partial products.

Page 18 provides two examples of downward division with fractional remainders.

These images are obtained through the courtesy of the World Digital Library. The book itself is held by the Central Library of the Bulgarian Academy of Sciences.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: 1833 Bulgarian Arithmetic," Convergence (June 2017)