At the beginning of the 19th century, with the arrival of the Royal family in Brazil, D. Joao VI saw the need to encourage the emergence of an environment conducive to the formation of an elite capable of providing the administrative staff of the new seat of the imperial government and train professionals. To this end, different institutions were created for public administration, such as Banco do Brasil and for education such as military academies, aimed at higher education. In addition to the primary education that worked in “reading, writing and counting” classes and secondary education classes, there were also other classes in Brazil for professional education, such as arts and crafts courses and classes for men who knew how to read, write and calculate, in order to qualify traders in the main commercial plazas in the country. Created in the similarity of the Lisbon class, the Aula de Comercio began to operate in Brazil from 1809 under the jurisdiction of the Junta de Comercio, Agricultura, Fabricas e Navegacao. Commerce classes were created in Rio de Janeiro, Salvador and Recife. Regarding the contents studied, topics of Mathematics, geography, bookkeeping and political economy were present. The main reference for the teaching of mathematics was Bezout's book Elementos de Arithmetica, used in Portugal and Brazil. However, other books began to be written, especially after the 1846 reform. This paper aims to discuss the contents of Arithmetic present in didactic manuals for the instruction of traders who circulated in Rio de Janeiro in the first half of the 19th century. There are two commercial Arithmetic books that circulated at the time, namely Tratado de Arithmetica Commercial by Paulo Perestrello da Câmara and Arithmetica Elementar Commercial de Joao Guilherme Kottinger by Joao Guilherme Kottinger, published respectively in 1846 and 1847, after the reforms in Aula de Comercio in Rio de Janeiro. The knowledge of the contents proposed in the didactic works highlighted in this work, helped to understand the role of Arithmetic in the scope of training of trade professionals in the early 19th century and the use of this knowledge in the practice of traders. We found that many of the contents exposed in the works of Artithmetic have similarities with the commercial Arithmetics published since the Middle Ages. What is perceived is that the contents of these works are closer to the practical contents necessary for commerce than to teaching from Bezout's book. Examples of these contents are simple and compound interest; discounts and rebates; company and league rules; calculation of annuities and amortization; national and foreign weights and measures; exchange rates among others. The rules presented seek to cover the entire system that involves a negotiation: the organization of the company and how profits and dividends are managed in a company; in which currency the commodity is traded; interest or discounts on products; what are the conditions for trading to yield more profit and less loss; the forms of guarantee for the goods to reach their destination, the price to be charged for transportation, among other aspects. Thus, it is expected that, from the study of school manuals, there will be a greater approximation from the historical point of view about the knowledge of Arithmetic and the school culture present in the Commercial Classes, during the first decades of the 19th century.
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