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Mathematical Treasure: Valentin Heins’s Tyrocinium mercatorio-arithmeticum

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Valentin Heins (1637–1704) was a German Rechenmeister who specialized in the teaching of commercial arithmetic. From 1663 to 1672, he served as accountant for the Guinean African Company. Most of his career, though, was spent teaching mathematics in Hamburg. He published several textbooks, the most popular being Tyrocinium mercatorio-arithmeticum (1684), which went through twenty-four editions. The author claimed his book would supply to students:

An ordinary basic grounding in commercial accounts: about which the dear youth, for a firm learning of the same, adequate means and ways are shown faithfully and in the most correct method, so that the students, during the instruction, will not have not much trouble, as the discipline of learning will have special attention. Out of love for all boys (next to the true godliness) of the old arithmetic art, but especially for our Hamburg school youth, who inevitably seek to establish themselves, after the current fashion, in trade and exchange as well as managing domestic and foreign accounts.

Here is the title page from a 1726 seventh edition:

Title page from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

A proud owner identifies his possession in 1733.

Owner's signature in a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

The first few pages carry the expected definitions and examples:

Early page from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

Page 2 from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum. Page 3 from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

Later in the text is an extensive section on monetary exchange. What is particularly interesting to a modern reader is the lengthy list of trading regions and cities that require exchange rates.

Page 144 from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

Page 162 from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum. Page 163 from a 1726 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

The twenty-first edition of 1785 adds a frontispiece and has a different title page layout.

Title page from a 1785 edition of Valentin Heins's Tyrocinium mercatorio-arithmeticum.

Perhaps the center of the illustration carries a moral: a building is planned, constructed, and then collapses as the contractor runs away with the money.

The first eight images are presented courtesy of the John Carter Brown Library, Brown University. The last was retrieved from Wikimedia Commons. The full 1726 seventh edition may be read here.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Valentin Heins’s Tyrocinium mercatorio-arithmeticum," Convergence (September 2020)

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