Dear Eckard,
A) For the history of negative numbers:
1) http://nrich.maths.org/public/viewer.php?obj_id=5961
2) http://uncyclopedia.wikia.com/wiki/Negative_Numbers
3) "...Lazare Carnot (1753-1823), member of the Academy of Science and famous mathematician:
" to really obtain an isolated negative quantity, it would be necessary to cut off an effective quantity from zero, to remove something of nothing: impossible operation. How thus to conceive an isolated negative quantity? "; Geometry of position, 1803.
... The numbers can be only positive; it is the quantities that can be negative or positive. A negative quantity is defined by an opposition to a positive quantity: a path in a direction, a path in the contrary direction; a profit, a debt... ";http://www.gobiernodecanarias.org/educacion/3/Usrn/penelope/uk_confboye.htm#elements
Negative numbers seem to "work" when the final result is positive but when the result is negative (