A quantity can have a shape
Oresme’s figures could show any quality that varies along a line or through time. A uniform quality makes a rectangle; one that changes steadily makes a triangle or a trapezium.
37 / ANTIQUITY TO THE RENAISSANCE
Nicole Oresme
One cart speeds up steadily; another keeps a steady pace. Draw each speed as a line standing on a line of time, and the shape tells you how far each has gone.
Explore the mathematics ↓
01 / SPEED AND AREA
Can a triangle measure a journey?
Run the clock and watch both carts. Oresme’s figure grows beneath them: time along the base, speed standing up from it.
Count the squares under each speed line. Each one is a metre of road.
Turn the triangle’s top corner into its empty corner: the triangle becomes the rectangle of the middle speed.
Journey:
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THE IDEAThe area under a speed line is the distance travelled. A speed that rises steadily covers the same distance as the steady speed it has at the middle instant: distance = speed at the middle instant × time.
The person behind the ideas
- Studied theology at the College of Navarre in Paris from 1348.
- Wrote the Treatise on the Configurations of Qualities and Motions in the 1350s.
- Became Bishop of Lisieux in 1377.
More of the mathematics
An endless sum that grows forever
Oresme also showed that 1 + ½ + ⅓ + ¼ + … grows without limit, by grouping its terms into blocks that are each at least ½.