Why is "orthographic size" defined as it is?

It’s a weird question, but I’ve always wondered why the “orthographic size” (or “ortho size”) is defined as half the vertical size of the viewing volume. Is there some reason it’s defined this way instead of half the horizontal size or something?

Or is it just an arbitrary decision? Is it based off of some mathematical precedent? It always confuses me since the term “ortho size” is so ambiguous (it would be much better served with a name like “height of viewing volume”, in my opinion).

Strictly speaking, its an arbitrary decision, since either one of the vertical or horizontal could easily allow you to obtain the other (along with aspect ratio).

However, having said that, generally a gradient is defined as “rise-over-run”, so its the ratio between the vertical and horizontal, with the vertical being the numerator. Its more natural to expect to have the numerator, and have to discover the denominator.

Finally, and most logically, the main reason the vertical value is chosen is that given the aspect ratio, its just a matter of multiplication to get the horizontal value out. If you had the horizontal dimension and aspect ratio, it would take a few more (mathematical) steps to get the vertical dimension.