I'm curious as to the origins of thinking of displacement as the area under a v/t curve.
I assume that Newton (and/or Leibniz) was already familiar with the concept and knew that calculating the area was simple for linear curves, but developed his new "calculus" in order to calculate areas for more complex curves.
I am also aware of the Merton rule, developed a few centuries before Newton, which proved more-or-less that the average velocity for an object experiencing constant acceleration would be exactly halfway between the initial and final velocities. I am not sure as to the methods used to prove the Merton rule.
I think that the concept of "area under the curve" couldn't really come about until coordinate plane graphing was invented, which I believe started with Descartes.
So what is the first reference to calculating areas under curves? What was the context of this first use? What is the first reference to doing so on a v/t graph specifically to calculate displacement?