The aim of this thesis is to make a characterization of the teacher of Mathematics in Brazil since the expulsion of the Jesuits until the last years of the Empire, being covered the period that goes of 1759 up to 1879. The characterization is made from both the analysis of the necessary knowledge to the teacher who taught Mathematics and the legal requirements made by the imperial government for the exercise of primary and secondary teaching at the time detached. The mentioned characterization was based upon documentary analysis of the examinations for selecting teachers of First Letters and of public and private intermediate education, allied to the analysis of the current law in the corresponding years. The main focus of the study was the city of Rio de Janeiro because of its importance in politics, economy and social affairs as it were the center of the imperial government, as well as for its role in public instruction. Finally, as a conclusion, this work proposes to reflect on subjects related to the teacher of Mathematics, considering its professionalization, the prerequisite for the exercise of this profession, admission to the positions of public and private teaching, and the study of corresponding laws and regulations throughout that period.