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This paper analyzes from a cultural history perspective the role of Sylvestre Lacroix's algebra textbook (1757-1833) in the Royal Military Academy of Rio de Janeiro mathematics teaching. By documentary analysis of sources - such as the Royal Charter which founded the Military Academy, newspaper issues, official letters, programs and minutes of meetings, etc. - clues of the algebra teaching at the Academy were searched for. Throughout the mathematics course, which lasted for four years, the teaching of algebra began in the first year and comprised from the fundamental notions and notations up to equations of the third and fourth degrees, followed, the next year, by the teaching of higher algebra equation solving. This research considers the way controversial concepts - such as the one of zero, infinite, negative numbers and imaginary numbers - were addressed in the Lacroix's textbook adopted by this institution. It analyzes this author's work by looking for characteristics which endorsed its recommendation for such a long period in the royal Military Academy.