What is tangent to a curve by Descartes?

In the context of Descartes' work, a tangent to a curve is a straight line that touches the curve at a single point without crossing it at that point. This concept is fundamental in understanding how curves behave locally, as the tangent line represents the instantaneous direction of the curve at that point. Descartes used geometric methods to explore tangents, which laid the groundwork for later developments in calculus and the study of derivatives.