Napierian logarithms explained by Pietro Mengoli

At its meeting of 15 July 1912, the Council of the Royal Society of Edinburgh resolved to commemorate the tercentenary of the publication in 1614 of Napier's Mirifici Logarithmorum Canonis Descriptio. From Saturday 25 July 1914 to Monday 27 July 1914 the Royal Society of Edinburgh held a Congress in Edinburgh to honour the Tercentenary. A fine volume was published in the following year C G Knott (ed.), Napier Memorial Volume (Royal Society of Edinburgh, London, 1915). Knott writes in the Preface:-

As regards the Congress itself it is pleasant to recall the goodwill and friendliness which characterised its meetings, attended though these were by men and women whose nationalities were fated to be in the grip of war before a week had passed.

Our library in St Andrews contains at least two copies of this Napier Memorial Volume , one of which still retains many uncut pages.

A number of interesting articles in this volume are difficult to obtain elsewhere. We produce below one by Giovanni Vacca. When he wrote the article Vacca was Professore incarito of Chinese in the Royal University of Rome. The article makes an interesting comment on Pietro Mengoli. We give an extract below:-


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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