Numbers couldn’t be trusted anymore. They were inadequate as a foundation for mathematics. To describe continuous quantities and reason about them, the ancient Greek mathematicians realized they needed to invent something more powerful than whole numbers. So they developed a system based on shapes and their proportions. It relied on measures of geometrical objects: lengths of lines, areas of squares, volumes of cubes. All of these they called magnitudes. They thought of them as distinct from numbers and superior to them.
