Can motion be drawn as a picture?

That time, that place

Nicole Oresme of the University of Paris was a theologian and an adviser to the king. He translated Aristotle into French and wrote on money and the economy.

Why this question

Motion is hard to handle because it keeps changing. How far does a body travel in a given time if it is speeding up throughout?

A number captures one instant. You cannot write down with a single number a thing that differs at every moment.

What was found

Oresme turned it into a picture. Lay time along a horizontal line and stand each moment's speed above it as a vertical bar. Constant speed gives a rectangle; steady acceleration gives a triangle.

Then comes the decisive step: the area of that figure is the distance traveled. What was changing at every instant becomes one fixed quantity.

With this picture he proved that a body accelerating steadily covers the same distance as one traveling throughout at its middle speed — exactly the result Galileo would use on falling bodies three centuries later.

Terms on this card

Limit