Parallelograms which are on the same base and in the same parallels are equal to one another.
在同一底边、同两条平行线之间的平行四边形彼此相等。
平行四边形 ABCD 与 EBCF 同底 BC，顶边在直线 AF 上（A、D、E、F 依次排开）；G 为 BE 与 CD 的交点。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
Let ABCD, EBCF be parallelograms on the same base BC and in the same parallels AF, BC; I say that ABCD is equal to the parallelogram EBCF. For, since ABCD is a parallelogram, AD is equal to BC.
两个平行四边形在同一底边、同两条平行线之间。
[I. 34] For the same reason also EF is equal to BC, so that AD is also equal to EF; [C.N. 1] and DE is common; therefore the whole AE is equal to the whole DF. [C.N. 2] But AB is also equal to DC; [I. 34] therefore the two sides EA, AB are equal to the two sides FD, DC respectively, and the angle FDC is equal to the angle EAB, the exterior to the interior; [I. 29] therefore the base EB is equal to the base FC, and the triangle EAB will be equal to the triangle FDC.
连接相应顶点，利用平行线性质得到外侧三角形相等。
[I. 4] Let DGE be subtracted from each; therefore the trapezium ABGD which remains is equal to the trapezium EGCF which remains. [C.N. 3] Let the triangle GBC be added to each; therefore the whole parallelogram ABCD is equal to the whole parallelogram EBCF.
从同一大图形中减去相等三角形。
[C.N. 2] Therefore etc.
余下的两个平行四边形相等。