A Point Is That Which Has

Euclid's Elements (c. 300 BC) opens with a sequence of definitions that establish the objects of geometry from first principles. Definition 1 — "A point is that which has no part" — defines a geometric point as having no dimension: no length, breadth, or depth. This radical abstraction, defining objects by what they lack rather than what they are, established the axiomatic method that Isaac Newton, René Descartes, and later mathematicians would follow.