(related to Subsection: Common Notions (all Books))
And if equal things are added to equal things then the wholes are equal.
see^{1} addition of real numbers is cancellative.
In modern mathematics, the Euclidean space \(\mathbb R^n\) constitutes a normed vector space. In Euclid's "Elements", the set of real numbers is represented by the measures of geometrical objects like the lengths of segments, the magnitudes of angles, the areas of plane figures, the volumes of solids, etc. ↩