Short answer: you don't need it because you have the word "all."
All of these sentences are correct as they are written without the addition of the definite article. Adding "the" wouldn't be incorrect, but it is unnecessary and sounds a very awkward.
The purpose of the definite article is to identify a specific example of whatever you're talking about. In all of your examples, there is no specific example being pointed to, because you're talking about all of them. "The" could replace "all" in some cases. "The 26 people on board the plane were killed," is correct and means the same thing as "all 26 people."
It wouldn't work that way with your other two sentences, and the reasons it wouldn't might just create more confusion.
For #3, you could write "all of the chapters." In #1, "all of the" would make it sound like there may have been more than 26 people. It doesn't work in #2 because "all corners" is sort of a figure of speech that just means "all over." To say "all of the corners" changes the meaning to indicate that you're specifically talking about the corners, and only the corners, which Africa doesn't literally have.
In #1, If you were talking about specific ones out of the entire group, you would need to use "the." For example, if only some of the people were killed on the plane and some were not, you could use "the" to talk about the ones who were killed. "The 26 people who were killed on the plane were all sitting on the left side. Everyone seated on the right side survived."
In #2, If you were talking about specific corners, you could say, "the death trail touched the northern corners of Africa."
#3) "There are summaries at the beginning of the first three chapters"