(3)...a. ...depending on the point of center in a given turn, we distinguish turns around the forehand, the backhand and turns in balance (...Wendungen im Gleichgewicht...).
...now the latter is an interesting albeit ambiguous distinction. Fact is, with any change of posture the distribution of the horse's weight changes... Steinbrecht statement implies that no matter what the posture, turns around the center are always in balance...
Ambiguity here enters with the term balance. Balance in a living being can be interpreted in terms of weight distribution or in terms of muscular action and/or fascia health. One may say the horse, as long as it is up on its four legs and able to move, is in balance. However, fact also is only postures with head and neck up are useful for equitation, because neither in the short nor in the long run do they require support from the rider's hand and/or legs.
Steinbrecht, however, makes no mention of another important detail in this context. The horse's body (...unlike the wheels of a car...) rests on four legs. The connection of legs and body in upper arm and hip is made of ball and socket joints. In these joints the horse can distribute and redistribute its body mass... It will do so in turns around the shoulders, the croup and the center according to how the rider, via direct, indirect and/or an elevating rein will requests these turns...
(3)...b. ...further observations and conclusion about the turns mentioned...
(4) + (5) ...more about the point of balance and turning in the free, the untrained and the trained horse...