Preferred and Critical Angles for Stairs, Ladders, Ramps and Inclines

Walter E. Durbahn.  Fundamentals of Carpentry.  Volume II.  Practical Construction.
Chicago:  American Technical Society, 1951.

In his absolutely fascinating book, At Home.  A Short History of Private Life (Doubleday Canada, 2010), Bill Bryson has a whole chapter on stairs, their construction and the dangers inherent in poor stair design.  Lots of folks have serious falls because of improper stair construction.