3min chapter

In Our Time: Science cover image

Euclid's Elements

In Our Time: Science

CHAPTER

The Problem With Euclid's Fifth Postulate

The fifth postulate says you can always draw a line through that point, which is parallel to the up surface. But in 19th century mathematicians discover new geometries that don't seem to satisfy this axiom. This doesn't invalidate anything that Euclid is - it just expands our horizon.

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