If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the parallelogram be double of the triangle, the prisms will be equal.
若两棱柱等高，其一底面为平行四边形，另一底面为三角形，且平行四边形是三角形的两倍，则两棱柱相等。
Let ABCDEF, GHKLMN be two prisms of equal height, let one have the parallelogram AF as base, and the other the triangle GHK, and let the parallelogram AF be double of the triangle GHK; I say that the prism ABCDEF is equal to the prism GHKLMN. For let the solids AO, GP be completed.
设两棱柱ABCDEF与GHKLMN等高，底面AF为平行四边形，底面GHK为三角形，且AF是GHK的两倍。
Since the parallelogram AF is double of the triangle GHK, while the parallelogram HK is also double of the triangle GHK, [I. 34] therefore the parallelogram AF is equal to the parallelogram HK.
补全平行六面体AO和GP。因AF是GHK的两倍，而平行四边形HK也是GHK的两倍（I.34），故AF等于HK。
But parallelepipedal solids which are on equal bases and of the same height are equal to one another; [XI. 31] therefore the solid AO is equal to the solid GP.
等底等高的平行六面体相等（XI.31），因此AO等于GP。
And the prism ABCDEF is half of the solid AO, and the prism GHKLMN is half of the solid GP; [XI. 28] therefore the prism ABCDEF is equal to the prism GHKLMN.
棱柱ABCDEF是AO的一半，棱柱GHKLMN是GP的一半（XI.28），故两棱柱相等。