Proving that you are the original writer of a certain article that is already published on another website is somewhat difficult. But now Google has introduce a different way to claim your authorship. Google team works very hard to distinguish and identify original articles from those that are ripped off other sites.
Google has ability to crawl on certain or rather finite number of pages at particular time frame. If anyone copy your article or you are the original writer of that article, you can do Digital Millennium Copyright Act notice. So, they has penalties for it if they are lying and stuff disappears off from the other site. So, if someone copied you do always a DMCA notice.
Shared copy of your DCMA take down notice will makes the complaint public, which is a best way to expose the content thieves. Sometime the content are directly copied from your site and sometime content is slightly modified, but at last the final result clearly is based on your original work. But this nature is not always harmful for your site if you want that your original content show only on your site, then you should have removed the duplicate content.