How does one determine priority, prominence, and impact with regard to books, rather than articles?
You can still check how widely the book is cited in academic literature (no matter, books, papers, reports, or conference papers) with the use of Google Scholar. 

Warning. Google Scholar may be misleading sometimes because it indexes virtually anything that is claimed to be academic even if it doesn't belong there. Sometimes you may come across academic crooks. See for example this guy. More than a thousand citations. But if you check him in Scopus, you will find that he is only cited 5 (five!) times by papers in journals of some quality. So, be careful.