Answer:
This quote can be broken down into two parts:
the first :
who does not examine does not believe.
it means that whoever does not check a hypothesis will not believe it
"I have no proof so I do not believe it" if you do not try to check ... it's not going to change.
the second part:
who does not doubt not examine.
he who is persuaded to be right is not even going to be able to make a mistake.
"Why waste my time to check since I'm sure I'm right?"
suddenly the first will never progress since if he doubts everything without ever checking ... he will continue to doubt and that's all
and the second who does not doubt anything (and especially not him) will not progress because he does not consider that things could be otherwise or that he could make a mistake, as small as it is.