"book proposes" is a correct and usable phrase in written English.
It can be used to describe the main idea or argument put forth by a book, or to indicate what a book suggests or recommends. Example: In his controversial new book, the author proposes a revolutionary solution to the current political crisis.
But your book proposes other ideas too.
The book proposes that organizations conduct their business in circles.
Mr. Dobson's book proposes that many dictators today may be feeling a similar sort of blues.
But since some employers may balk at this, the book proposes a smaller step: remove some of the penalties that come with borrowing.
Subtitled 'Science and Religion in the Fullness of Life', the book proposes the scientist's theory that science and religious faith can comfortably co-exist.
The book proposes that many of the traditional block patterns for quilts were used to convey secret messages to escaping slaves.
The book proposed that women's adaptive responses to setbacks and sadness were of enormous value — that the improvisational nature of some lives is worth emulating and celebrating.
The book proposed a distinctive middle ground between the conventional positions on the proper role of judges in interpreting the Constitution.
The book proposed taxing companies that emit carbon dioxide, a byproduct of burning fossil fuels that is also a significant component of smog.
Mr. Gores, pointing out that most of the characters are either dead or in prison by the end of the book, proposed a prequel instead, and "Spade & Archer" was published in 2009.
The astronomer Johann Elert Bode, also of Germany, published the law in 1772 in a popular introductory astronomy book, proposing that the missing 3 in the progression might indicate an as-yet-undiscovered planet between Mars and Jupiter.
