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MS_M.383_04r-d Fior di Battaglia c1400-1409
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Agrippa 54 circa 1553
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Still capture of Mousse changing from a canter to a walk.
In general, for improved handling, we want the horse to bend their hind limbs and shift their center of gravity backwards. Horses naturally carry their weight a bit forwards and when we add the weight of a rider and equipment, we increase that tendency. It is up to us to teach them how to shift it.
Some positions, such as levade, make this shift obvious as the horse sits and lifts their front legs. More subtle applications include: half halts, where the rider gives a minor application of their slow down aides; downward transitions where the rider changes from a faster gait to a slower one; and backing, where the rider asks the horse to take steps in reverse.
In the image with Mousse, he was performing a canter to walk transition in response to my seat. He bends through his hocks and lowers his haunches dramatically relative to his shoulders.
The written record
Authors as early as Xenophon (Three Essays - On the Duties of a Cavalry General, on Horsemanship, and on Hunting, ~400BC; trans Dakyns, 1897), describe how to use the aids to ask a horse to shift their weight:
...the instant he raises his neck in response in answer to the pull, give him the bit at once;
If the horse is inclined to drop his head, the reins should be held pretty high;
De Reayo ("Doctrina del arte de la cavalleria", 1548; trans Fallows) suggests that men at arm should learn stopping before taking up weapons:
It behooves the man-at-arms firstly to be a horseman and to know how to ride a horse well, to race it and bring it to a halt before have ever takes the lance in his hand, either armed or unarmed.
In "Escuirie de M. de Pavari", de Pavari (1581; trans Tomassini) describes a half halt:
So that when they show such a bad will you must do the opposite and you must give, that is to say to loosen the hand little by little and then to collect it in the same way, so that they will lose that bad will and they will stop.
In "Del Justador", de Chaves (1589-1593; trans Fallows) highlights the idea of shifting the horses weight back when stopping:
It should stop well and not on the forelegs
He further advocates the use of spurs to create a forward halt:
...on setting out, spurs should be put to it one time, and once again in the middle of the course, as if to remind it to run, and once again on stopping, if one wants to stop in double quick time.
Later, Markham (The Compleat Horseman, 1614 from Discourse on Horsemanship, 1593) adds his suggestions in regards to terrain:
Now for helps in these Lessons, the best for stopping is the choice of ground.