Parallelograms which are on equal bases and in the same parallels are equal to one another.
在相等底边、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 EFGH 在相等底 BC、FG 上，且夹在两条相同的平行线之间。连接 BE、CH，使两组面积相等。
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Let ABCD, EFGH be parallelograms which are on equal bases BC, FG and in the same parallels AH, BG; I say that the parallelogram ABCD is equal to EFGH. For let BE, CH be joined.
把两个相等底边放在同两条平行线之间。
Then, since BC is equal to FG while FG is equal to EH, BC is also equal to EH. [C.N. 1] But they are also parallel.
连接端点，可用 euclid-elements/book1-prop-033 得到连接线段相等且平行。
And EB, HC join them; but straight lines joining equal and parallel straight lines (at the extremities which are) in the same directions (respectively) are equal and parallel. [I. 33] Therefore EBCH is a parallelogram.
于是形成同底同高意义下可相互转化的平行四边形。
[I. 34] And it is equal to ABCD; for it has the same base BC with it, and is in the same parallels BC, AH with it. [I. 35] For the same reason also EFGH is equal to the same EBCH; [I. 35] so that the parallelogram ABCD is also equal to EFGH.
由 euclid-elements/book1-prop-035，二者相等。