Euclidean geometry
Branch · c. 300 BC onward, Alexandria · Mathematics, stage 2: Map the branches
Euclid's Elements collected the geometry known to the Greeks and arranged it as a single deductive structure: a list of definitions, five postulates, and common notions, followed by hundreds of propositions each proved from what came before. The content was largely not new; the arrangement was, and it fixed the form of mathematical writing for the next two thousand years. Hilbert returned to it in 1899 and supplied the assumptions Euclid had used without stating them.
What it claims
- All of plane and solid geometry can be derived from a short list of stated assumptions.
- A claim counts as established only when it has been proved from those assumptions, not when it has been measured or drawn.
- Through a point not on a given line there passes exactly one parallel line.
Key ideas
People
Sources
- Euclidean geometry Wikipedia
- Euclidean geometry Encyclopaedia Britannica
