fourteenth century. In a century that saw one third of the population of Europe die from the plague known as the

Black Death, and the century that saw the beginning of the Hundred Years’ War, there were not many

opportunities for creativity; but Oresme was an exception. Besides being a college professor, Oresme later

became a bishop in the Church.

Oresme wrote five mathematical works and also translated some of the works of Aristotle. His works show an

originality that was unsurpassed since the days of the Greeks, and contain many ideas that foreshadowed those

of later famous mathematicians including Cardano, Descartes, Galileo, and Johann Bernoulli.

In one of his tracts,

and also gave rules for combining proportions that are equivalent to the laws of exponents we use today, such

as x^m * x^n = x^(m+n) and (x^m)^n = x^mn. He even hinted at the possibility of irrational proportions. In a second

work called

proportion to geometrical problems.

Oresme’s most significant contribution to mathematics was a tract called

representation of a function, foreshadowing Descartes by nearly three hundred years. (Descartes was probably

influenced by this work of Oresme when he applied the ideas, combined with algebraic symbolism.)

For example, in the above diagram Oresme drew a velocity-time graph for an object starting from rest and moving

with constant acceleration. Along a horizontal axis (which he called longitudo) he marked points representing

instants of time. For each instant he drew a perpendicular line (which he called latitudo). The above diagram has

sixteen latitudo.

Oresme observed that the velocity half way through the time period (dotted line) was equal to half the final

velocity, and that the distance covered in the second half of the time period was three times the distance covered

in the second half of the time period.

So Oresme not only foreshadowed Descartes, but also gave hints of Galileo’s law for a falling body

Oresme died in 1382.

..

**A contribution of Oresme to mathematics**

Another of Oresme’s works was his *Quaestiones super Geometriam Euclidis* (c1350) in which he effectively gave a

proof that the harmonic series diverges to infinity. He did not use modern algebraic notation, but what follows is the

gist of Oresme’s argument.

First of all, what is the harmonic series?

with constant acceleration. Along a horizontal axis (which he called longitudo) he marked points representing

instants of time. For each instant he drew a perpendicular line (which he called latitudo). The above diagram has

sixteen latitudo.

Oresme observed that the velocity half way through the time period (dotted line) was equal to half the final

velocity, and that the distance covered in the second half of the time period was three times the distance covered

in the second half of the time period.

So Oresme not only foreshadowed Descartes, but also gave hints of Galileo’s law for a falling body

Oresme died in 1382.

..

proof that the harmonic series diverges to infinity. He did not use modern algebraic notation, but what follows is the

gist of Oresme’s argument.

First of all, what is the harmonic series?

Since there are an infinite number of brackets, there will be an infinite number of halves, and so the series

diverges (gets bigger and bigger as you add more and more terms) to infinity.

Oresme’s proof was given two hundred years before that of Cardano, and more than three hundred years before

that of Johann Bernoulli.

diverges (gets bigger and bigger as you add more and more terms) to infinity.

Oresme’s proof was given two hundred years before that of Cardano, and more than three hundred years before

that of Johann Bernoulli.