From Euclid's theory of proportions to Mengoli's quasi proportions

What is it about?

This article analyses the original new theory of "quasi proportions" developed by Mengoli, based in Euclid’s theory of proportions. The idea of "ratio quasi a number" suggests, although in an imprecise way, the first ideas on the modern concept of limit. His highly innovative numerical theory, which incorporates the new idea of quasi ratio, made it possible to calculate limits and then to do quadratures.

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Why is it important?

This is important because in order to develop this theory of quasi proportions, we show the original and useful construction involving summations of powers of integers. Indeed, Mengoli proofs the rules for the sums of powers of integers and calculates 37 results.

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