The following document gives an account of the process carried out by the author in the development of the research project. Analyzing the concept of construction and accuracy; in mathematics, Greek, making a review of some issues raised in the proposal by Euclid elements work as well as reviewing these two concepts in the early modern age in the geometry text written by Descartes. This document makes an approach to the problem the trisection of the angle and the change of conception that notion of construction and accuracy was analysed.
