**1.3 Fermat and Pascal Use Figurate Numbers, Binomials, and ...**

sums of powers by using the following theorem on “natural progressions”: ... +1. Indeed, in his treatise on the arithmetical triangle, Pascal de?nes the numbers in the triangle by starting the process o? witha1inthecorner, and de?nes the rest simply by saying that each number is the sum of the two numbers directly above and directly to the left of it, which corresponds precisely to ...

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