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's definition of it is worthless, but his axioms remain basically sound. His successors in mathematics have extended his ideas to the curved line and a clearer concept of length ...

The European Space Agency's (ESA) Euclid mission released its first batch of survey data on Wednesday (March 19), including a preview of its deep fields revealing hundreds of thousands of galaxies ...

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 ...