|The rectangle contained by medial straight lines commensurable in length is medial.|
|Let the rectangle AC be contained by the medial straight lines AB and BC which are commensurable in length.
I say that AC is medial.
|Describe the square AD on AB. Then AD is medial.|
|And, since AB is commensurable in length with BC, while AB equals BD, therefore DB is commensurable in length with BC, so that DA is commensurable with AC.||VI.1
|But DA is medial, therefore AC is also medial.||X.23,Cor.|
|Therefore, the rectangle contained by medial straight lines commensurable in length is medial.|
Book X Introduction - Proposition X.23 - Proposition X.25.