This document shows an analysis of the second book Elementa Curvarum Linearum written by Jan De Witt, published for the first time in the second edition of Geometry [1]. This writing is considered the first analytical geometry textbook. The influence of the work carried out by Apollonius in his conics book is studied, the use and interpretation of diagrams is debated. The development of the analytical method and the generation of curves by means of movement are also studied. Some propositions were renewed versions in terms of eighteenth-century mathematics, they used symbology, algebraic techniques and curves were classified by means of their symbolic representations, in these propositions a work closer to Apollonius is seen, the conic is not generated, it is assumed its existence, its nature is geometric. The study concludes that, although the textbook was published in the second edition of Geometry, the genesis of the curves remains geometric. The conics appear as objects of study in action immersed in the symbolic and algebraic practice characteristic of the time.