Rectangle Contained by Medial Straight Lines Commensurable in Length is Medial

Proof
Let $x$ and $\lambda x$ be two medials such that:
 * $x \frown \lambda x$

where $\frown$ denotes that $x$ and $\lambda x$ are commensurable in length.

By Areas of Triangles and Parallelograms Proportional to Base:
 * $x^2 : x \cdot \lambda x = x : \lambda x$

From Commensurability of Elements of Proportional Magnitudes:
 * $x^2 \frown x \cdot \lambda x$

From Medial is Irrational we have that $x^2$ is medial.

Therefore by Straight Line Commensurable with Medial Straight Line is Medial: Porism:
 * $x \cdot \lambda x$ is medial.