Editing Mathematical table (section)

==Tables of logarithms==
[[File:Logarithmorum Chilias Prima page 0-67.jpg|thumb|A page from [[Henry Briggs (mathematician)|Henry Briggs]]' 1617 ''Logarithmorum Chilias Prima'' showing the base-10 (common) logarithm of the integers 0 to 67 to fourteen decimal places.]]
[[File:Abramowitz&Stegun.page97.agr.jpg|thumb|Part  of a 20th-century table of [[common logarithm]]s in the reference book [[Abramowitz and Stegun]].]]
[[File:APN2002-table3-30deg.tiff|thumb|A page from a table of logarithms of [[trigonometric function]]s from the 2002 [[American Practical Navigator]]. Columns of differences are included to aid [[interpolation]].]]
Tables containing [[common logarithm]]s (base-10) were extensively used in computations prior to the advent of electronic calculators and computers because logarithms convert problems of multiplication and division into much easier addition and subtraction problems. Base-10 logarithms have an additional property that is unique and useful: The common logarithm of numbers greater than one that differ only by a factor of a power of ten all have the same fractional part, known as the ''mantissa''. Tables of common logarithms typically included only the [[significand|mantissas]]; the integer part of the logarithm, known as the ''characteristic'', could easily be determined by counting digits in the original number.  A similar principle allows for the quick calculation of logarithms of positive numbers less than 1.  Thus a single table of common logarithms can be used for the entire range of positive decimal numbers.<ref>E. R. Hedrick, [https://archive.org/details/logarithmictrigo00hedriala Logarithmic and Trigonometric Tables] (Macmillan, New York, 1913).</ref> See [[common logarithm]] for details on the use of characteristics and mantissas.

===History===
{{main|History of logarithms}}
In 1544, [[Michael Stifel]] published ''Arithmetica integra'', which contains a table of integers and powers of 2 that has been considered an early version of a logarithmic table.<ref>{{Citation|first=Michaele|last=Stifelio|publisher=Iohan Petreium|location=London|year=1544|title=Arithmetica Integra|url = https://books.google.com/books?id=fndPsRv08R0C&pg=RA1-PT419}}</ref><ref>
{{springer  | title=Arithmetic  | id= A/a013260 | last=Bukhshtab  | first=A.A.   | last2=Pechaev | first2=V.I.}}</ref><ref>
{{Citation|title = Precalculus mathematics|author = Vivian Shaw Groza and Susanne M. Shelley|publisher = Holt, Rinehart and Winston|location=New York|year=1972|isbn=978-0-03-077670-0|page = 182|url = https://books.google.com/books?id=yM_lSq1eJv8C&q=stifel&pg=PA182}}</ref>

The method of logarithms was publicly propounded by [[John Napier]] in 1614, in a book entitled ''[[Mirifici Logarithmorum Canonis Descriptio]]'' (''Description of the Wonderful Rule of Logarithms'').<ref>{{Citation|author=Ernest William Hobson|title=John Napier and the invention of logarithms, 1614|year=1914|publisher=The University Press|location=Cambridge|url=https://archive.org/details/johnnapierinvent00hobsiala}}</ref> The book contained fifty-seven pages of explanatory matter and ninety pages of tables related to [[natural logarithms]]. The  English mathematician [[Henry Briggs (mathematician)|Henry Briggs]] visited Napier in 1615, and proposed a re-scaling of [[Napier's logarithm]]s to form what is now known as the [[common logarithm|common]] or base-10 logarithms. Napier delegated to Briggs the computation of a revised table.  In 1617, they published ''Logarithmorum Chilias Prima'' ("The First Thousand Logarithms"), which gave a brief account of logarithms and a table for the first 1000 integers calculated to the 14th decimal place. Prior to Napier's invention, there had been other techniques of similar scopes, such as the use of tables of progressions, extensively developed by [[Jost Bürgi]] around 1600.<ref name="folkerts">{{citation | last1 = Folkerts | first1 = Menso | last2 = Launert | first2 = Dieter | last3 = Thom | first3 = Andreas | arxiv = 1510.03180 | doi = 10.1016/j.hm.2016.03.001 | issue = 2 | journal = [[Historia Mathematica]] | mr = 3489006 | pages = 133–147 | title = Jost Bürgi's method for calculating sines | volume = 43 | year = 2016| s2cid = 119326088 }}</ref><ref>{{mactutor|id=Burgi|title=Jost Bürgi (1552 – 1632)}}</ref>

The computational advance available via common logarithms, the converse of powered numbers or [[exponential notation]], was such that it made calculations by hand much quicker.