Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal.

Euclid started with 35 definitions, a handful of postulates, a dozen or more axioms, a series of postulates, and argued for a set of theorems, all about triangles, lines, angles, squares ...

The company said this is the 12th flight for the stage booster supporting this mission, which previously launched Euclid, Axiom-2, Axiom-3, Cygnus NG-21, SES 24, CRS-30, and five Starlink missions.

How is this possible? The Euclidean Programme conceives of mathematical knowledge as based on watertight deduction from self-evidently true axioms (first principles). We argue that this account is not ...