The Optical Mouse (1981) [pdf]
bitsavers.trailing-edge.com
bitsavers.trailing-edge.com
The alleged "turn it 45 degrees, making it easy to see" rationale is only in surrounding modern text (at these blog posts and the StackExchange answer). It might be right, but if so, it's not supported in the linked 1981 document.
From ArsTechnica's article. Though it doesn't say WHY either. http://arstechnica.com/features/2005/05/gui/3/
At least for me when I'm pointing at a regular computer monitor my hand is tilted not strait up and down.