## Napierian logarithms explained by Pietro Mengoli

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The Italian mathematician, Pietro Mengoli, the last disciple of Bonaventura Cavalieri in Bologna, has not yet received the just appreciation he merits.

I have vindicated his discoveries in two lectures read in the Universities of Genoa and Rome, in 1910 and 1911; and recently, in an accurate article in his *Bibliotheca Mathematica*, G Eneström has deduced the same conclusion from the analysis of the works of Mengoli.

The *Geometria Speciosa* of Pietro Mengoli, published in 1659 in Bologna, contains an elementary, purely arithmetical, and rigorous theory of Napierian logarithms.

This theory has also the great advantage of, being direct, that is, does not depend on the complicated theory of powers of numbers with irrational exponents.

The theory of Mengoli is explained in pages 69-75 of his *Geometria Speciosa*. But his style and notation are difficult. I shall therefore expound it in modern language, with the hope that it may be introduced into elementary mathematics ... .

JOC/EFR March 2006

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