# John Napier : Mirifici Logarithmorum Canonis Descriptio..... & Constructio.....

## translated and annotated byIan Bruce

A modern translation with some notes of Napier's Descriptio , with the Latin version presented last, is presented here. Book I is an introduction to the new science of logarithms; while Book II is devoted to a thorough explanation of the solution of plane and spherical triangles. The original work was translated by Edward Wright in 1616 and both the original and the translation were used by Briggs at Gresham College as part of the education of navigators, for whom the work was intended; astronomers also benefited. This work and its sequel the Constructio should be read before Briggs's Arithmetica is approached. I present here a spreadsheet derivation of Napier's Log Tables : there was a 'slippery mistake' in one of the tables of the Constructio, which together with the rounding that took place, limited the original tables accuracy to only perhaps 5 places ; thus, there cannot be complete agreement with the original tables.. The Constructio in which Napier promised to elaborate on his method then follows; though Napier did not live long enough to see this work in print. This work is the first time the exponential function appears in mathematics, under the guise of a geometric number line. This is a brilliant exercise in lateral thinking to solve an apparently unsolvable problem : the time and labour spent in long calculations. I am much indebted to the translation of this work by William Macdonald (1888) , that has helped me to unravel some of the knots in Napier's Latin and saved much time. An appendix is also given; and one should also mention the existence of another book that was printed before the death of the philosopher, his Rabdologea, in which Napier's other calculating devices that include his bones and promptuary are set out. As an excellent translation by William Frank Richardson has been published in the history of computing series, there is no need to expound on this here. Perhaps I should say that an internet friend of mine, Jim Hanson, has resurrected the Promptuary, and you should visit his website if you want to know how to make one :

>Click here for the Promptuary. See the bottom of the page if you want to contact Jim Hansen.

Contents of the Descriptio

Book I.

Link to the Descriptio Part I by clicking here.

Book IIa.

Link to the Descriptio Part IIa by clicking here.

Book IIb.

Link to the Descriptio Part IIb by clicking here.

An error in labeling the minutes on the even pages on the right hand side of the tables has come to light and been corrected.

Napier's Constructio.

Link to the Constructio by clicking here.

Appendix to Constructio.

De Arte Logistica.

Link to the Mark Napiers (1839) Introduction to De Arte Logistca part one by clicking here.

Link to the De Arte Logistca part one by clicking here.

Link to the De Arte Logistca part two by clicking here.

Jim Hansen. Jim will answer relevant questions if you send him an e-mail here.

Ian Bruce. April 30th, 2012 latest revision. Copyright : I reserve the right to publish this translated work in book form. However, if you are a student, teacher, or just someone with an interest, you can copy part or all of the work for legitimate personal or educational use.