So I was reading Hamilton's paper on quaternions. http://www.emis.de/classics/Hamilton/OnQuat.pdf. On page 2, I'm having trouble following how QQ' and equations A,B,C lead to equation D. My main question is in the original expression for QQ', we have terms like iwx' and jyw'. Basically, I don't see how those i's and j's disappeared in equation D, and why logically we arrange all the terms like that.
Thanks
They don't disappear; what you see is components of the new quaternion $$ Q''=w''+ix''+iy''+iz''=QQ' $$