How did 'take in stride' originally signify 'without change of gait'?

[ Etymonline :] To take (something) in stride (1832), i.e. "without change of gait," originally is of horses leaping hedges in the hunting-field; figurative sense attested from 1902.

to take in stride: to accept advances or setbacks as normal, to be dealt with as they arise. The image is of a person walking along without stopping for distractions.

TAKE STH IN YOUR STRIDE | meaning in the Cambridge English Dictionary

to deal with a problem or difficulty calmly and not to allow it to influence what you are doing:

I know nothing of equestrianism. Horses obviously stride, but why was 'take in' adopted to signify 'horses leaping hedges in the hunting-field' and then 'without change of gait'?

The idiom "take in stride" derives from taking, or adjusting to or accepting something, "in stride," meaning, during the course of a stride or while/whilst striding. The word "in" means "in the course of the" [stride], so it is not "take + in," but to take, in [a] stride. This would suggest that the hazard or barrier was negotiated without having to change the gait, or occurring "in" the course of the stride of the horse. I hope that explains it.