Geometry is not easy reading. An edition appeared subsequently with no — La Géométrie

"The Latin term for "ordinate," used by Descartes comes from the expression lineœ ordinatœ, employed by Roman surveyors for parallel lines. The term abscissa occurs for the first time in a Latin work of 1659, written by ..."

"It is evident from Descartes explanation of his method that he had an intuitive grasp of the elusive concepts of variable and function, both of which are basic in analysis. Moreover, he intuited continuous variation."

"Descartes recognized that the points of intersection of two curves are given by solving their equations simultaneously. The last implies... a major advance over all who had previously used coordinates: Descartes saw that an infinity of distinct curves can be referred to one system of coordinates. In this... he was far ahead of Fermat..."

"Descartes separated all curves into two classes, the "geometrical" and the "mechanical" ...according as (in our terminology) dy/dx is an algebraic or a transcendental function. ...this classification was abandoned long ago... The current definition... [a curve] which intersects some straight line in an infinity of points was given by Newton in his work on cubics."

"The gradual evolution of calculus was considerably stimulated by the publication of Descartes "Géométrie"... which brought the whole field of classical geometry within the scope of algebraists."

"If... we wish to solve any problem, we first suppose the solution already affected, and give names to all the lines that seem needful for its construction,—to those that are unknown as well as to those that are known. Then, making no distinction between the known and unknown lines, we must unravel the difficulty in a way that shows most naturally the relations between these lines, until we find it possible to express a single quantity in two ways. This will constitute an equation, since the terms of one of these two expressions are together equal to the terms of the other."