I suppose, you don't need the path and the node name. So you can use one of these, supposing, that $books contains the xml:
$books | select-xml -xpath "//edition" | % {$_.Node."#text"}
$books.SelectNodes("//edition") | % { $_."#text"}
$books.book.projects.project."book-editions".edition | % {$_."#text"}
In the later one, you can see, how you could reference the element name containing the hyphen.