In the elementary propositions concerning the triangles, two such triangles are represented side by side; on the assumption that, of the six parts of each, three in the one triangle are equal to the corresponding three in the other, it is shown that the two triangles are congruent, that is, that in each the remaining three parts are equal to the corresponding remaining three in the other because by virtue of the equality of the first three parts the two triangles cover each other.