Parallelepipedal solids which are of the same height are to one another as their bases.
同高的平行六面体体积之比等于其底面积之比。
Let AB, CD be parallelepipedal solids of the same height; I say that the parallelepipedal solids AB, CD are to one another as their bases, that is, that, as the base AE is to the base CF, so is the solid AB to the solid CD. For let FH equal to AE be applied to FG, [I. 45] and on FH as base, and with the same height as that of CD, let the parallelepipedal solid GK be completed.
在直线FG上作平行四边形FH等于AE，并以FH为底、与CD同高作平行六面体GK。
Then the solid AB is equal to the solid GK; for they are on equal bases AE, FH and of the same height.
由于AB与GK等底等高，故AB等于GK。
[XI. 31] And, since the parallelepipedal solid CK is cut by the plane DG which is parallel to opposite planes, therefore, as the base CF is to the base FH, so is the solid CD to the solid DH.
平行六面体CK被平行于相对平面的平面DG所截，因此底CF比FH等于立体CD比DH。
[XI. 25] But the base FH is equal to the base AE, and the solid GK to the solid AB; therefore also, as the base AE is to the base CF, so is the solid AB to the solid CD.
因FH等于AE，GK等于AB，故底AE比CF等于立体AB比CD。