Lincoln studied Euclid's Elements as a traveling lawyer because he wanted to understand exactly what it meant to formally "demonstrate" an argument in court.

Euclid built his entire geometric system upon five basic axioms, or postulates, which were accepted as true without proof to establish a logical baseline.

After centuries of failing to prove Euclid's fifth postulate, 19th-century mathematicians replaced it to study geometry on curved surfaces rather than flat planes.

The final book of Elements culminates by constructing the five regular polyhedra, mathematically proving that no other perfect solid shapes can exist.