It is also addressed in the slightly more user friendly AdSense FAQ:
You can only place one set of ads (one copy of the AdSense HTML ad code) on each page. Otherwise, ads may be double-served. In an effort to maintain the quality of our program, Google does not support double-serving. Please select the one ad placement best suited for each of your pages.
You can read the full FAQ here: https://www.google.com/adsense/faq
And the technical FAQ here: https://www.google.com/adsense/faq-tech