With a horse entirely ignorant of leaping, the best way is to take him
by the leading rein, which hangs loose, and to get across the trench
yourself first, and then to pull tight on the leading-rein, to induce
him to leap across. If he refuses, some one with a whip or switch
should apply it smartly. The result will be that the horse will clear
at a bound, not the distance merely, but a far larger space than
requisite; and for the future there will be no need for an actual
blow, the mere sight of some one coming up behind will suffice to make
him leap. As soon as he is accustomed to leap in this way you may
mount him and put him first at smaller and then at larger trenches. At
the moment of the spring be ready to apply the spur; and so too, when
training him to leap up and leap down, you should touch him with the
spur at the critical instant. In the effort to perform any of these
actions with the whole body, the horse will certainly perform them
with more safety to himself and to his rider than he will, if his
hind-quarters lag, in taking a ditch or fence, or in making an upward
spring or downward jump.[4]

[4] Lit. "in making these jumps, springs, and leaps across or up or
down."

To face a steep incline, you must first teach him on soft ground, and
finally, when he is accustomed to that, he will much prefer the
downward to the upward slope for a fast pace. And as to the
apprehension, which some people entertain, that a horse may dislocate
the shoulder in galloping down an incline, it should encourage them to
learn that the Persians and Odrysians all run races down precipitous
slopes;[5] and their horses are every bit as sound as our own.[6]

[5] Cf. "Anab." IV. viii. 28; and so the Georgians to this day