Editing John Napier (section)

===Napier's Bones===
[[File:Bones of Napier (board and rods).png|thumb|[[Napier's bones|Napier's Bones]] ]]

His work ''[[Mirifici Logarithmorum Canonis Descriptio]]'' (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables listing the [[natural logarithm]]s of [[trigonometric function]]s.<ref name="discriptio-trans" />{{rp|Ch. III}} The book also has a discussion of theorems in [[spherical trigonometry]], usually known as Napier's Rules of Circular Parts.

Modern English translations of both Napier's books on logarithms and their description can be found on the web, as well as a discussion of [[Napier's bones]] and [[Promptuary]] (another early calculating device).<ref>{{cite web |url=http://www.17centurymaths.com/ |title=17th Century Maths.com |publisher=17centurymaths.com |date=25 March 2011 |accessdate=3 April 2022 |archive-date=17 May 2011 |archive-url=https://web.archive.org/web/20110517094956/http://www.17centurymaths.com/ |url-status=live }}</ref>

His invention of logarithms was quickly taken up at [[Gresham College]], and prominent English mathematician [[Henry Briggs (mathematician)|Henry Briggs]] visited Napier in 1615. Among the matters they discussed were a re-scaling of Napier's logarithms, in which the presence of the [[e (mathematical constant)|mathematical constant now known as ''e'']] (more accurately, ''e'' times a large power of 10 rounded to an integer) was a practical difficulty. Neither Napier nor Briggs actually discovered the constant ''e''; that discovery was made decades later by [[Jacob Bernoulli]].

Napier delegated to Briggs the computation of a revised table. The computational advance available via logarithms, the inverse of powered numbers or [[exponential notation]], was such that it made calculations by hand much quicker.<ref name = DNB>{{cite DNB|wstitle=Napier, John}}</ref> The way was opened to later scientific advances, in [[astronomy]], [[dynamics (mechanics)|dynamics]], and other areas of [[physics]].

Napier made further contributions. He improved [[Simon Stevin]]'s decimal notation, introducing the [[full stop]] (.) as the delimiter for the fractional part.<ref name=constructionIA>{{cite book|title=[[Commons:File:The_Construction_of_the_Wonderful_Canon_of_Logarithms.djvu|The Construction of the Wonderful Canon of Logarithms]]|first=John|last=Napier|translator-last1=Macdonald|translator-first1= William Rae|date=1889|orig-date=1620|publisher=Blackwood & Sons|publication-place=Edinburgh|via=Internet Archive|quote=In numbers distinguished thus by a period in their midst, whatever is written after the period is a fraction, the denominator of which is unity with as many cyphers after it as there are figures after the period.}}</ref>{{rp|p. 8, archive p. 32)}} [[Lattice multiplication]], used by [[Fibonacci]], was made more convenient by his introduction of [[Napier's bones]], a multiplication tool using a set of numbered rods.

Napier may have worked largely in isolation, but he had contact with [[Tycho Brahe]] who corresponded with his friend [[John Craig (physician)|John Craig]]. Craig certainly announced the discovery of logarithms to Brahe in the 1590s (the name itself came later); there is a story from [[Anthony à Wood]], perhaps not well substantiated, that Napier had a hint from Craig that [[Longomontanus]], a follower of Brahe, was working in a similar direction. Craig had notes on a method of [[Paul Wittich]] that used [[trigonometric identities]] to reduce a multiplication formula for the [[sine function]] to additions.<ref>{{ODNBweb|id=19758|title=Napier, John|first=George|last=Molland}}</ref>