I know the Google Books API, but if for whatever reason I can't access it, how do I check whether a book is in the public domain?
For whatever reason, Google doesn't think this is an information worth of the information pages or of the advanced book search.
Google doesn't guarantee copyright status etc. etc., but in the HTML of the book description you can find a lot of information enclosed in a script tag, for example:
<script>_OC_addFlags(... {"volume_id":"qyi8-5g8dzAC","is_ebook":true,"volumeresult": ... ,"sample_url": ... ,"is_browsable":true,"is_public_domain":true}, ...);</script>
Checking for is_public_domain should be ok.
Of course you're really supposed to use the API, in the example:
"accessInfo": {
"country": "IT",
"viewability": "ALL_PAGES",
"embeddable": true,
"publicDomain": true,
"textToSpeechPermission": "ALLOWED",
"epub": {
"isAvailable": false
},