How did Frans van Schooten help spread Descartes's ideas about analytic geometry?

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Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated. — analytic geometry The conic sections result from intersecting a plane with a double cone, as shown in the figure. There are three distinct families of conic sections: the ellipse (including the circle), the parabola (with one branch), and the hyperbola (with two branches).

Frans van Schooten played a pivotal role in disseminating René Descartes’s ideas by establishing a prominent school of mathematical research in Leiden. He was instrumental in making Descartes's work accessible to the broader mathematical community through his editorial efforts.

Specifically, Van Schooten edited and published a Latin translation of Descartes’s La Géométrie in 1649. He later published a more extensive two-volume edition between 1659 and 1661. These editions were highly significant because they included mathematical appendixes written by his disciples—Johan de Witt, Johan Hudde, and Hendrick van Heuraet—which helped further the development of Cartesian geometry. Along with other mathematicians such as Christiaan Huygens, this Leiden group was largely responsible for the rapid advancement and spread of analytic geometry during the mid-17th century.1