  Leibniz’s conservation of progress is closely related to the  Cartesian law of conservation of quantity of motion (and the more  familiar law of the conservation of momentum). As Leibniz is at pains to emphasize, however, his law differs from the Cartesian law at  least in that it traffics in “signed” velocities rather  than scalar speeds. Leibniz is thus able to maintain that although  “it will be found that the total progress is conserved, or that there is as much progress in the same direction before or after the  impact” nonetheless the quantity of motion, as measured simply  by speed times mass is not conserved (GM VI.217/Langley 658). 