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Pierre de Fermat
Pierre de Fermat was born on August 17, 1601, in southern France. He worked as a lawyer and government official; in his free time he studied mathematics. Fermat did not publish very much, but he did write many letters to other people interested in mathematics.
One of Fermat's projects was an attempt to reconstruct Apollonius' book on plane loci, which was lost sometime during the Middle Ages. As part of this project, Fermat wrote an article called Ad locos planos et solidos isagoge, or Introduction to Plane and Solid Loci. This article contained instructions for graphing simple equations.
Fermat's algebra did not look much like our algebra: he used Latin words where we would use symbols, and he chose different names for variables. But, except for the fact that he did not use negative numbers, his method of graphing was just like ours.
Let's watch Sam graph a line the way Fermat did.
Fermat's equation is "D in A aequetur B in E". The word "in" represents multiplication, and "aequetur" means "equals." (You can see that the words "aequetur" and "equals" look similar.) Fermat used consonants for constants and known quantities, and vowels for variables. Like Descartes, we use letters from the end of the alphabet as variables. So we might write this equation as Dx = By. Let's choose the constants D=6 and B=2; then the equation is 6x = 2y.
First Sam draws a pair of axes. Like Fermat's axes, Sam's are at right angles. Also, like Fermat, Sam does not include space for negative numbers.
Now Sam needs to find some numbers that satisfy this equation. He tries substituting different numbers for x. When x is 0, D*0 = By, so 0 = By and y = 0/B = 0/2 = 0. When x is 1, D*1 = By, so D = By and y = D/B = 6/2 = 3.
Sam graphs the points (0, 0) and (1, 3):
Finally, he draws a line through the two points. Since negative numbers are not included, Sam's line only points one way.
Fermat did not publish his article on graphing. Instead, he sent handwritten copies to his friends in Paris. After he died, one of them decided to publish it; but by then Descartes' geometry was already famous.
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