History and Technology: Allied in solving equations of the first grade teaching learning of analytical geometry

This article integrates the doctoral research on the use of the History of Mathematics and GeoGebra for the teaching of analytical geometry with emphasis on the study of REAMEC doctoral studies. Which sought an alternative methodology for the resolution of algebraic equations of the second degree. We adopted the book "the geometry" of Descartes, as an original source allied to the use of technology with GeoGebra dynamic geometry software. The bibliographies of Boero, Pedemonte, and Robotti, as well as the semiotic representations of Duval, have developed a connection between the past and the present, in order to construct a dialogue of new re-signified concepts of the past and the present, based on behavior, technology and socio-cultural conceptions. However, the research points to the diversification of methodologies in mathematics teaching, as well as the multiplicity of strategies that can be realized integrating the history of mathematics and technologies