Why did Descartes describe extension in three dimensions as the essential feature of matter?

In Cartesianism, René Descartes established an ontological dualism that strictly separated reality into two distinct finite substances: mind and matter.123

Descartes defined the essence of mind as self-conscious thinking, while he identified the essence of matter as extension in three dimensions. This characterization was central to his rejection of Scholastic Aristotelianism, which attributed internal purposes, "souls," or vital forces to physical objects. By defining matter solely through its spatial extension, Descartes sought to strip away "occult" or teleological qualities—such as color, smell, or inherent goals—and treat the physical world as a purely mechanistic system.1234

In this framework, physical phenomena are explained exclusively through the primary qualities of shape, size, motion, and position within space. Because matter is essentially extended, it can be understood through mathematics and geometry, allowing scientists to describe the movement of bodies as passive, deterministic interactions governed by mechanical laws rather than internal "natures".324