Publishing an article after a book? If I first publish an article, afterward I may publish a book containing materials from the article.
What's about the reverse: If I first publish a book does it make sense to publish its fragment as an article AFTERWARD?

To add to the previous answers, it's very important to realize that unless you self-publish a book or article, it is almost always the case that the publisher will hold the copyright. That will be part of the contract you sign with the publisher. That means that you can't legally extract any part of the first work for publishing elsewhere, even though you wrote it. To avoid being sued for copyright infringement in a case like this you must obtain permission from the publisher (to whom you signed over the copyright). 
In my experience, book publishers are generally happy to give you permission to extract part of your book for publishing elsewhere, as long as they don't see any negative impact on the sales of the original. It's not quite as straightforward for journal publishers: they can often be quite difficult when it comes to using your article as part of a compilation.
