Chronicles of Discoveries First I'd like to bring an example to make myself more clear. 
I know what the Jacobian matrix is and where, how and why it is used (some examples, at least) . But still I can't get it's geometrical interpretation. And I don't understand how and why it works. 
I wonder how Jacobian matrix was discovered. What theoretical issues laid behind this discovery? What mathematical problems of the time did it solve? 
Generally, is are there any books that describe the history of various mathematical discoveries, not [auto]biographies of the author, but rather chronicles of the discovery itself, but the demands of the time, the difficulties, approaches that didn't work, and eventually the discovery? 

At Alain Lascoux's web page you can find .pdf files of Thomas Muir's encyclopedic history of determinants. Look at the citations for Jacobian on p. 391 of the file "History, Index (pdf)" and track down those citations in Muir's work.
I'm sure there are some historical survey papers on what you're asking about, but off-hand I don't know of any. However, Muir does something that may be unique in mathematical historical writing by providing detailed summaries of virtually every paper written in a certain area of mathematics up to a certain time.
