F two triangles have two sides of the one respectively equal to two sides of the other, (
to and 
to ) and the angles (
and ) contained by those equal sides also equal; then their bases or their sides (
and ) are also equal: and the remaining and their remaining angles opposite to equal sides are respectively equal (
= and 
= ): and the triangles are equal in every respect.
Let the two triangles be conceived, to be so placed, that the vertex of the one of the equal angles, or ; shall fall upon that of the other, and to coincide with , then will coincide with if applied: consequently will coincide with , or two straight lines will enclose a space, which is impossible (ax. 10), therefore = , = and =, and as the triangles 
and coincide, when applied, they are equal in every respect.
