| 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
X.11 | |
| 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. | ||
| Q.E.D. | ||
