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And there is all the demonstration of the theorem and the solution of the problem!

Every horse, however, has one side which is more supple than the other; and it is better to begin practice in changing lead by shifting from the less supple to the more supple side.

Suppose, for example, that the more flexible side is the left. My horse being straight, I start it galloping to the right, by the method given above, and keep it going straight. I then reverse all my effects. If the horse changes lead, I stop it as soon as may be, and recompense its obedience. When it is completely calm, I begin again, galloping to the right. After several steps, I again change; and again recompense.

When the horse understands the change of lead from right to left, I proceed in the same way to teach the change from left to right. At first, I ask the change only after the horse has galloped ten or fifteen steps on the same foot. When the horse manages this, I reduce the interval progressively, first to six or eight steps, then to four, and finally to only two. I need not say that this training takes time that cannot be measured by days or lessons. I progress slowly, ask very little, rest my horse a great deal, and keep calm. I do not, under any circumstances, permit my horse to choose the lead for itself, nor to change foot on its own initiative. It is essential that the rider always impose his mastership upon the horse's intelligence. The rules are: short lessons, precision helped by moderation,