The Construction of the Wonderful Canon of Logarithms

The Construction of the Wonderful Canon of Logarithms  (1889) 
by John Napier, translated by William Rae Macdonald

a translation of Mirifici logarithmorum canonis descriptio

THE


CONSTRUCTION OF LOGARITHMS


WITH A

CATALOGUE OF NAPIER’S WORKS


THE CONSTRUCTION

OF THE WONDERFUL CANON OF

LOGARITHMS

BY

JOHN NAPIER

BARON OF MERCHISTON


TRANSLATED FROM LATIN INTO ENGLISH WITH NOTES

AND

A CATALOGUE

OF THE VARIOUS EDITIONS OF NAPIER’S WORKS, BY

WILLIAM RAE MACDONALD, F.F.A.


Construction of the Wonderful Canon Logarithms-009.jpg


WILLIAM BLACKWOOD AND SONS

EDINBURGH AND LONDON

MDCCCLXXXIX


All Rights reserved

To

The Right Honourable


FRANCIS Baron NAPIER and ETTRICK, K.T.

descendant of

John Napier of Merchiston

this Translation of the

Mirifici Logarithmorum Canonis Constructio

is dedicated with much

respect.


CONTENTS.


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xi
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1
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3
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7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
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55
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64
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76


. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83


A CATALOGUE OF THE WORKS OF JOHN NAPIER,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
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103
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109
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148
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166
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Introduction.



John Napier[1] was the eldest son of Archibald Napier and Janet Bothwell. He was born at Merchiston, near Edinburgh, in 1550, when his father could have been little more than sixteen.

Two months previous to the death of his mother, which occurred on 20th December 1563, he matriculated as a student of St Salvator’s College, St Andrews, While there, his mind was specially directed to the study and searching out of the mysteries of the Apocalypse, the result of which appeared thirty years later in his first published work, ‘A plaine discovery of the whole Revelation of St John.’

Had he continued at St Andrews, his name would naturally have appeared in the list of determinants for 1566 and of masters of arts for 1568. It is not, however, found with the names of the students who entered college along with him, so that he is believed to have left the University previous to 1566 in order to complete his studies on the Continent.

He was at home in 1571 when the preliminaries were arranged for his marriage with Elizabeth, daughter of Sir James Stirling of Keir. The marriage took place towards the close of 1572. In 1579 his wife died, leaving him one son, Archibald, who, in 1627, was raised to the peerage by the title of Lord Napier, and also one daughter, Jane.

A few years after the death of his first wife he married Agnes, daughter of Sir James Chisholm of Cromlix, who survived him. The offspring of this marriage were five sons and five daughters, the best known of whom is the second son, Robert, his father’s literary executor.

Leaving for a moment the purely personal incidents of Napier’s life, we may here note the dates of a few of the many exciting public events which occurred during the course of it. In 1560 a Presbyterian form of Church government was established by the Scottish Parliament, On 14th August 1561, Queen Mary, the young widow of Francis II., sailed from Calais, receiving an enthusiastic welcome on her arrival in Edinburgh. Within six years, on 24th July 1567, she was compelled to sign her abdication. The year 1572 was signalised by the Massacre of St Bartholomew, which began on 24th August; exactly three months later, John Knox died. On 8th February 1587 Mary was beheaded at Fotheringay, and in May of the year following the Spanish Armada set sail. The last event we need mention was the death of Queen Elizabeth on 24th March 1603, and the accession of King James to the throne of England.

The threatened invasion of the Spanish Armada led Napier to take an active part in Church politics. In 1588 he was chosen by the Presbytery of Edinburgh one of its commissioners to the General Assembly. In October 1593 he was appointed one of a deputation of six to interview the king regarding the punishment of the “Popish rebels,” prominent among whom was his own father-in-law. On the 29th January following, 15934,[2] the letter which forms the dedication to his first publication, ‘A plaine discovery,’ was written to the king.

Not long after this, in July 1594, we find Napier entering into that mysterious contract with Logan of Restalrig for the discovery of hidden treasure at Fast Castle.

Another interesting document written by Napier bears date 7th June 1596, with the title, ‘Secrett inuentionis, proffitable & necessary in theis dayes for defence of this Iland & withstanding of strangers enemies of Gods truth and relegion.’

The versatility and practical bent of Napier’s mind are further evidenced by his attention to agriculture, which was in a very depressed state, owing to the unsettled condition of the country. The Merchiston system of tillage by manuring the land with salt is described in a very rare tract by his eldest son, Archibald, to whom a monopoly of the system was granted under the privy seal on 22d June 1598. As Archibald Napier was quite a young man at the time, it is most probable the system was the result of experiments made by his father and grandfather.

About 1603, the Lennox, where Napier held large possessions, was devastated in the conflict between the chief of Macgregor and Colquhoun of Luss, known as the raid of Glenfruin. The chief was entrapped by Argyll, tried, and condemned to death. On the jury which condemned him sat John Napier. The Macgregors, driven to desperation, became broken men, and Napier’s lands no doubt suffered from their inroads, as we find him on 24th December 1611 entering into a contract for mutual protection with James Campbell of Lawers, Colin Campbell of Aberuchill, and John Campbell, their brother-german.

To the critical events of 1588 which, as we have already seen, drew Napier into public life, is due the appearance in English of ‘A plaine discovery,’ already mentioned. The treatise was intended to have been written in Latin, but, owing to the events above referred to, he was, as he says, ‘constrained of compassion, leaving the Latin to haste out in English the present work almost unripe.’ It was published in 15934. A revised edition appeared in 1611, wherein he still expressed his intention of rewriting it in Latin, but this was never accomplished.

Mathematics, as well as theology, must have occupied Napier’s attention from an early age. What he had done in the way of systematising and developing the sciences of arithmetic and algebra, probably some years before the publication of ‘A plaine discovery,’ appears in the manuscript published in 1839 under the title ‘De Arte Logistica.’ From this work it appears that his investigations in equations had led him to a consideration of imaginary roots, a subject he refers to as a great algebraic secret. He had also discovered a general method for the extraction of roots of all degrees.

The decimal system of numeration and notation had been introduced into Europe in the tenth century. To complete the system, it still remained to extend the notation to fractions. This was proposed, though in a cumbrous form, by Simon Stevin in 1585, but Napier was the first to use the present notation.[3] Towards the end of the sixteenth century, however, the further progress of science was greatly impeded by the continually increasing complexity and labour of numerical calculation. In consequence of this, Napier seems to have laid aside his work on Arithmetic and Algebra before its completion, and deliberately set himself to devise some means of lessening this labour. By 1594 he must have made considerable progress in his undertaking, as in that year, Kepler tells us, Tycho Brahe was led by a Scotch correspondent to entertain hopes of the publication of the Canon or Table of Logarithms. Tycho’s informant is not named, but is generally believed to have been Napier’s friend, Dr Craig. The computation of the Table or Canon, and the preparation of the two works explanatory of it, the Constructio and Descriptio, must, however, have occupied years. The Canon, with the description of its nature and use, made its appearance in 1614. The method of its construction, though written several years before the Descriptio, was not published till 1619.

Napier at the same time devised several mechanical aids to computation, a description of which he published in 1617, ‘for the sake of those who may prefer to work with the natural numbers,’ the most important of these aids being named Rabdologia, or calculation by means of small rods, familiarly called ‘Napier’s bones,’

The invention of logarithms was welcomed by the greatest mathematicians, as giving once for all the long-desired relief from the labour of calculation, and by none more than by Henry Briggs, who thenceforth devoted his life to their computation and improvement. He twice visited Napier at Merchiston, in 1615 and 1616, and was preparing again to visit him in 1617, when he was stopped by the death of the inventor. The strain involved in the computation and perfecting of the Canon had been too great, and Napier did not long survive its completion, his death occurring on the 4th of April 1617. He was buried near the parish church of St Cuthbert’s, outside the West Port of Edinburgh.

It has been stated that Napier dissipated his means on his mathematical pursuits. The very opposite, however, was the case, as at his death he left extensive estates in the Lothians, the Lennox, Menteith, and elsewhere, besides personal property which amounted to a large sum.

For fuller information regarding John Napier, the reader is referred to the Memoirs, published by Mark Napier in 1834, from which the above particulars are. mainly derived.

The ‘Mirifici Logarithmorum Canonis Constructio’ is the most important of all Napier’s works, presenting as it does in a most clear and simple way the original conception of logarithms. It is, however, so rare as to be very little known, many writers on the subject never having seen a copy, and describing its contents from hearsay, as appears to be the case with Baron Maseres in his well-known work, ‘Scriptores Logarithmici,’ which occupies six large quarto volumes.

In view of such facts the present translation was undertaken, which, it is hoped, will be found faithfully to reproduce the original. In its preparation valuable assistance was received from Mr John Holliday and Mr A. M. Laughton, The printing and form of the book follow the original edition of 1619 as closely as a translation will allow, and the head and tail pieces are in exact facsimile. To the work are added a few explanatory notes.

The second part of the volume consists of a Catalogue of the various editions of Napier’s works, giving title-page, full collation, and notes, with the. names of the principal public libraries in the country, as well as of some on the Continent, which possess copies. No similar catalogue has been attempted hitherto, and it is believed it will prove of considerable interest, as showing the diffusion of Napier’s writings in his own time, and their location and comparative rarity now. Appended are notes of a few works by other authors, which are of interest in connection with Napier's writings.

It will be seen from the Catalogue that Napier’s theological work went through numerous editions in English, Dutch, French, and German, a proof of its widespread popularity with the Reformed Churches, both in this country and on the Continent. The particulars now given also show that a statement in the Edinburgh edition of 1611 has been misunderstood. Napier’s reference to Dutch editions was supposed by his biographers to apply to the German translation of Wolffgang Mayer, the Dutch translation by Michiel Panneel, being apparently unknown to them. His arithmetical work, Rabdologia, also seems to have been very popular. It was reprinted in Latin, and translated into Italian and Dutch, abstracts also appearing in several languages.

Rather curiously, his works of greatest scientific interest, the Descriptio and Constructio have been most neglected. The former was reprinted in 1620, and also in Scriptores Logarithmici, besides being translated into English, The latter was reprinted in 1620 only. This neglect is no doubt largely accounted for by the advantage for practical purposes of tables computed to the base 10, an advantage which Napier seems to have been aware of even before he had made public his invention in 1614.

For the completeness of the Catalogue I am very largely indebted to the Librarians of the numerous libraries referred to. I most cordially thank them for their kind assistance, and for the very great amount of trouble they have taken to supply me with the information I was in search of. To Mr Davidson Walker my hearty thanks are also due for assistance in collating works in London libraries.

I have only to add that any communications regarding un-catalogued editions or works relating to Napier will be gladly received.

W. R. MACDONALD.

1 Forres Street, Edinburgh,
December 25, 1888.


Copyright.svg PD-icon.svg This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.
Original:

This work was published before January 1, 1927, and is in the public domain worldwide because the author died at least 100 years ago.

 
Translation:

This work is in the public domain in the United States because it was published before January 1, 1927.


The author died in 1923, so this work is also in the public domain in countries and areas where the copyright term is the author's life plus 95 years or less. This work may also be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.

 
  1. See note, p. 84, as to spelling of name.
  2. 1593 old style, 1594 new Style. Under the old style the year commenced on 25th March.
  3. See note, p. 88.