What is the "parameter on the squares of the ordinates" w.r.t. a parabola?

Question

I'm going through some constructions and derivations in the English Translation of On Burning Mirrors - Diocles, Pg 44 but I'm unable to understand a particular statement w.r.t. to the construction below:

Here is the explanation of the construction:

What exactly is $BH$ and how does one draw it? The statement "...let half the parameter of the squares on the ordinates be line $BH$" is a bit confusing. What's the modern equivalent translation?

(Background context: Discovery of the focus/directrix property)

Answer 1

The parameter of the ordinates, also called "latus rectum", is that length $BH$ such that, for any point $\Theta$ of the parabola, $\Theta G^2=BH\cdot BG$.

In modern terms, if $y=ax^2$ is the equation of the parabola, then $BH=1/a$. Traditionally, the latus rectum was drawn starting from the vertex of the parabola, perpendicular to its axis. See Prop. I 11 in Apollonius (Proposition 1 in Heath's translation).

EDIT.

Notice, however, that the Diocles' defines $BH$ as "half the parameter of the ordinates", hence the semi-latus rectum. We have then $\Theta G^2=2BH\cdot BG$. This approach was common before Apollonius' treatise.