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Mathematical Treasure: Gaspar Nicolas’s Tratado da Prática D'arismetyca

Author(s): 
Pedro Jorge Freitas (University of Lisbon) and Jorge Nuno Silva (University of Lisbon)

The 1519 Tratado da Prática D'arismetyca by Gaspar Nicolas was the first book on mathematics printed in Portugal. It is a manual of arithmetic and geometry, especially concerned with practical concerns relating to commerce and investments, which, by that time, were starting to play a much greater role than in the medieval era. Tratado comes in the tradition of Italian abacus schools, established as teaching institutions for these kinds of purposes. The title page and final page appear below.

Title page of Nicolas's 1519 Tratado da Prática D'arismetyca.

Final page from Gaspar Nicolas's 1519 Tratado da Prática D'arismetyca.

The text is heavily influenced by Luca Pacioli’s work, namely his 1494 Summa de arithmetica, geometria, proportioni et proportionalita, which is explicitly mentioned in the text, although other sources were also used. Many of the problems are classics of recreational mathematics of the time, some going back even to Alcuin of York (c. 735–804).

The book also contains a great number of exercises in proportions, in which the rule of three is extensively used. Additionally, it also contains a large list of recreational problems, some of which could be solved with known techniques, while others were meant to be intellectual challenges, to be solved “by fantasy”, to use the author’s expression. Several pages with arithmetic and geometric problems are shown below; note that one problem considers two birds, flying from the top of two towers down to a fountain.

Folio 7 from Gaspar Nicolas's 1519 Tratado da Prática D'arismetyca.

Folio 27 from Gaspar Nicolas's 1519 Tratado da Prática D'arismetyca.

Folio 83 from Gaspar Nicolas's 1519 Tratado da Prática D'arismetyca.

Folio 87 from Gaspar Nicolas's 1519 Tratado da Prática D'arismetyca.

Folio 92 from Gaspar Nicolas's 1519 Tratado da Prática D'arismetyca.

A full digitization of the book by the Old Fund of the Faculty of Sciences of the University of Porto can be found here.

Index to Mathematical Treasures

Pedro Jorge Freitas (University of Lisbon) and Jorge Nuno Silva (University of Lisbon), "Mathematical Treasure: Gaspar Nicolas’s Tratado da Prática D'arismetyca ," Convergence (July 2021)