Is it legal to use the eagle from the Great Seal of the United States (as shown on the dollar bill) as part of a commercial design in a book? I am also changing the "e pluribus unum" to a slogan.
Use of the Great Seal of the United States is governed by Public Law 91-651, Title 18 of the United States Code. This is a criminal statute with penal provisions, prohibiting certain uses of the Great Seal that would convey or reasonably be calculated to convey a false impression of sponsorship or approval by the Government of the United States or any department, agency, or instrumentality thereof.
You can ultimately be fined and imprisoned for up to 6 months for use of the seal without written permission. You can read the details of the legislation here:
If your intended use can in any way be reasonably confused with an official endorsement or use by the Government of the United States then I would stay clear. Ultimately it is a decision you need to make but I would be careful either way and only use it if you can be certain it will not be confused as "Official".
Note: I am not a lawyer, this is not legal advice. If you require legal advice, contact a legal professional.
As per the copyright notes on the Wikimedia commons image of the Seal, it is Public Domain, but heavily restricted in use. Which is common for a seal, coat of arms, flag or insignia.
There are laws that allow use in parody, though I can't say how those interact with the stated limitations.
Finally, your answer heavily depends on what jurisdiction you are in yourself.
disclaimer: I am not a lawyer, nor an American citizen. This answer does not constitute legal advice, nor does it aspire to.
18 U.S. Code Section 713(a) in summary says that displaying a reproduction or likeness of the Great Seal of the U.S. or the seals of the President, Vice-President, Senate, House of Representations or Congress is a federal crime if you convey a "false impression of sponsorship or approval" by the Government of the U.S. or any of its departments, agencies or instrumentalities. Violators will be fined and/or punished by no more than six months in prison.
Section 713(b) forbids reproducing, selling or purchasing for resale any likeness of the seals of the President or Vice-President, other than for government use. The criminal penalty is the same as noted above. Exceptions to this rule are provided in regulations submitted by the President. President Nixon promulgated such regulations in Executive Order #11649 dated 1972.
Sections 713(c)-(e) apply the language of (b) above to seals of the Senate, Representatives and Congress.
Section 713(f) states that violators may be enjoined in litigation filed by the Attorney General at the request of specified representatives of the aggrieved parties.
You mention that it is part of a commercial design in a book. That might be the deal breaker. It might not.
You do not need a lawyer but do your homework.
You will have to visit or consult the US Department of the Treasury for their ruling (which can be appealed). The agents will tell you directly. Either way, yes or no, ask for the ruling in writing. Nothing verbal is binding or conclusive, however, regardless of the decision be it in your favour or against. They will also advise you if you are in a grey area. They try to be very helpful. If you are found in violation of counterfeit law, your artwork will be confiscated. You can appeal this too. If you go voluntarily, you will be "in compliance" in spirit and even if you are in violation, that you asked prior to use will be considered.
Get everything in writing. You can appeal anything.
There are different aspects to this question which involve different legal specialties. One is Intellectual Property and the other is US Federal Trade Law, probably more.