Análisis de la práctica con diagramas en los inicios de las ideas de cálculo propuestas por Isaac Newton

Abstract

The following work is carried out as an innovation research internship, assumes a contribution to the MATTOPO research group and the research project "Diagrams in the constitution of the calculation. Contributions and reflections to teacher training" which is considered that diagrams are cognitive tools in the construction of objects or mathematical theories. The content of the two texts proposed by Isaac Newton in the construction of his calculus will be analyzed. The first, the text Methodus fluxionum et serierum infinitorum (1667), and the second, Philosophiæ naturalis principia mathematica (1687), with the English translation 'mathematical principles of natural philosophy' (2011), in order to analyze about the forms used by Newton to show its development from the use of diagrams and the incidence of these as representational tools in cognitive development. Within the analysis of the texts, the mathematical activities, the objects within the representation, the perspectives of infinity and the look from the variation and covariation that are presented and developed were taken into account. On the other hand, in this text 'Analysis in practice with diagrams at the beginning of the ideas of calculation proposed by Isaac Newton' is evidenced one of the treatments that Newton performs to his diagrams for the understanding of his calculation from tangents, lines and curves. A comparison is shown between the ways of representing the diagrams in the texts mentioned and how the diagrams have an impact on the calculation thinking.