Can I copy or publish text—from a website—that is in the public domain?
The text was already published as hard cover, in many apps, and as
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I am not a lawyer, but: If the text is in the public domain, then yes, you can use it. Be sure that it really is in the public domain, though—copyright lasts for a very long time. Also bear in mind that if the text is annotated, translated, or altered in any other way, or if it's a collection of public domain works, there may be further complications. If you have any doubts, you'd be best advised to contact an IP/Copyright lawyer.
If it really is public domain you are free to do whatever you want*. You should keep in mind some things:
*Some things may still not be allowed due to the personal right of the authors, but that is another topic.
Both existing answers are mostly correct. To expand a little:
Copyright laws vary by country. For example, Wikisource contains works that are considered public domain by United States law. BUT that site also carries works that are published under Creative Commons licenses.
Then there is Wikilivres, which contains works that are public domain in Canada but not in the United States. If you take a work from Wikilivres and sell it in the US, you will be subject to US law for the copyright violation.
Also, there are works like English translation of Somnium (1608), by Johannes Kepler, which is published on the Frosty Dew website with what seems to be Public Domain or at least CC, but currently all English translations seem to copyrighted.
According to answers on the question As a US citizen is it illegal to access an ebook from a country where it is PD, if it is not PD in the US?, even reading (on your computer) a work that is public domain in another country but not in the US may be illegal.
In summary it is all very confusing, there are about a million ways to get it wrong. Getting it wrong is called Copyright infringement, and you can be fined and/or jailed (depending on the laws of your country) even if you don't make any money doing it.
If there is any doubt Ask a lawyer, before publishing anything you did not write.
Keep in mind that even if a text is freely reusable (like those on Wikipedia) there could be a copyright on it (in that case, you should cite the source and publish your work under the same license)
So: yes, if the original text is in public domain you may package it for a Kindle, and even sell it; but first check thoroughly whether the text is really in public domain.