That wiki page needs some work. The section you linked to describes the eccentricity as a ratio, however the top of the page describes 0 as perfectly circular and 1 as an escape trajectory.
If it were a ratio then 0 would be escape and 1 would be circular.
The "Examples" section doesn't seem to talk about ratios, do you mean the end of the prior "Calculation" section? If so part is just saying you can calculate the ratio of r_a to r_p given you know e and run it through the equation, not that e itself = r_a / r_p (the formula to calculate e from r_a and r_p is higher up in the section).
If not that section, apologies for missing what you're trying to point out - I'm just trying to see what needs to be cleaned up so I can make an edit if needed.
If it were a ratio then 0 would be escape and 1 would be circular.