According to the document, the "partials" are done bottom up.
By partials I mean
restricting the range of motion to just under 1/2 of a complete rep.
Always touch the floor with your chest (when possible) and come up
almost half-way then back down.
Failure means when you fail to be able to do the exercise, you're done.
Position three is a "wide" pushup. Your hands are even with your shoulders, and out at 90 degrees. If you make a 90 degree bend in your elbow and keep your hands at shoulder level, you'll have it. Or another way to visualize it is the standard hand position for the bench press.
In theory, there is no difference between theory and practice.
In practice, there is.