1

By motion Descartes meant what we now call the momentum, mv. He believed that Σmv retained a constant value, where E indicates summation over all the moving bodies. Leibniz introduced the concept of energy at a later date, describing it as force (vis viva, equal to mv²), and found that Σmv² retained a constant value. He also discovered the constancy of the momenta Σmv, etc. in the separate directions in space. Descartes wanted his animal spirits to change the direction of motion while keeping Σmv constant. Leibniz’s objection was that this would change Σmv; energy did not come into the question at all.

2

By ‘force’ Leibniz here means energy or vis viva.

3

We need not discuss the possibility of space having inherent in itself a curvature on a universe-wide scale; such curvature, if it exists, is unimportant for our present discussion.