TITLE: History of the orientation of Cartesian coordinates in drawing
QUESTION [5 upvotes]: Is there any actual historical example in which a Cartesian plane with all four quadrants has been used, but with all axes marked with positive numbers? [Please see Sawyer's paper below for a "made-up" example] 
I am writing the result of a research the point of which was to teach children negative numbers in an algebraic context. There were many interesting similarities between their conceptions and difficulties and the so-called historical ones. For the one in the question (suggested by one of the children) I have claimed that "It has an interesting historical counterpart". Has it? Or, I have to delete my claim?  
Added: In this nice paper of Warwick Sawyer, The Importance of the Unbelievable, he writes"without negative numbers the equation of a line would depend upon which quarter it was in." The question is whether this possibility has ever been practiced in history or Sawyer just made it up for educational purposes? 
PS. Following Todd's comments, I changed the wording of the question. I hope it is now clearer.

REPLY [3 votes]: A very detailed historical account of the debates about clarifying the concept of negative numbers can be found in the book http://link.springer.com/book/10.1007%2F0-387-28273-4 (Conflicts between Generalization, Rigor, and Intuition, by Gert Schubring). It is stated in the book (p. 82) that "Reyneau (1736) was probably the first to explicitly introduce the four quadrants in the coordinate system of the plane, a novelty that appears self-evident to us today" and that (p. 289) in De Prony's lectures (1795) Cours d'Analyse appliquée à la mécanique "for the first time in France the four quadrants of a coordinate system are explicitly assigned to the respective positive and negative values of the x– and y–axes in the plane".