And what did the soldiers at the bottom of the wall do to counter that
If the ladder base was far from the wall the defender's stick wouldn't be long enough to push it over, ladders would be pretty heavy with a few people on it, and a defender would be exposed to attack from below. This thread goes a bit more in depth, but these seem to be the main reasons
Assaulting with siege ladders wouldnt be undertaken until the battlemet had been partially cleared of attackers through catapult/trebuchet/arrows. However even if the battlemet was full of men the attackers could easily overwhelm them if enough ladders were used, the first attackers on the ladder would have a rough time but the following waves would break through and create a lodgement. Also siege ladders eventually gave way to siege towers in cases where the defenders could mount a solid defence from the outer wall. With a siege tower all the attackers would be commited at once and success rate was exponentially higher
hooked tops on the ladders made it harder to do this as well