"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""). The book contained fifty-seven pages of explanatory matter and ninety pages of tables related to natural logarithms. The English mathematician Henry Briggs visited Napier in 1615, and proposed a re-scaling of Napier's logarithms to form what is now known as the common or base-10 logarithms. Napier delegated to Briggs the computation of a revised table, and they later published, in 1617, ""Logarithmorum Chilias Prima"" (""The First Thousand Logarithms""), which gave a brief account of"
"commonly used in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors: provided that , and are all positive and . The present-day notion of logarithms comes from Leonhard Euler, who connected them to"
"William Oughtred William Oughtred ( ; 5 March 1574 – 30 June 1660) was an English mathematician and Anglican clergyman. After John Napier invented logarithms and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, Oughtred was the first to use two such scales sliding by one another to perform direct multiplication and division. He is credited with inventing the slide rule in about 1622. He also introduced the ""×"" symbol for multiplication and the abbreviations ""sin"" and ""cos"" for the sine and cosine functions. Oughtred was born at Eton in Buckinghamshire (now part"
"Edward Sang Prof Edward Sang FRSE FRSSA LLD (30 January 1805 – 23 December 1890) was a Scottish mathematician and civil engineer, best known for having computed large tables of logarithms, with the help of two of his daughters. These tables went beyond the tables of Henry Briggs, Adriaan Vlacq, and Gaspard de Prony. Sang was born in Kirkcaldy on 30 January 1805, the son of Jean Nicol and Edward Sang, Provost of Kirkcaldy. He attended the Subscription School in Kirkcaldy and from there went on to study at the University of Edinburgh. In the 1830s he is listed as"
"John Napier of Merchiston the hint which led to his discovery of logarithms. Anthony à Wood states that This story may not be independently verifiable. Napier himself informed Tycho Brahe, via Craig, of his discovery, some twenty years before it was made public. John Craig (physician) John Craig M.D. (died 1620) was a Scottish physician, known also as an astronomer. He was physician to James VI of Scotland, and accompanied him to England. He also corresponded with Tycho Brahe, and associated with John Napier. He was born in Scotland, the son of an Edinburgh tailor and merchant Robert Craig and"
"logarithms of all numbers 1-1000. Along with William Oughtred and Richard Norwood, Speidell helped push toward the abbreviations of trigonometric functions. Speidel published a number of work about mathematics, including ""An Arithmeticall Extraction"" in 1628. John Speidell John Speidell (fl. 1600–1634) was an English mathematician. He is known for his early work on the calculation of logarithms. Speidell was a mathematics teacher in London and one of the early followers of the work John Napier had previously done on natural logarithms. In 1619 Speidell published a table entitled ""New Logarithmes"" in which he calculated the natural logarithms of sines, tangents,"
"John Speidell John Speidell (fl. 1600–1634) was an English mathematician. He is known for his early work on the calculation of logarithms. Speidell was a mathematics teacher in London and one of the early followers of the work John Napier had previously done on natural logarithms. In 1619 Speidell published a table entitled ""New Logarithmes"" in which he calculated the natural logarithms of sines, tangents, and secants. He then diverged from Napier's methods in order to ensure all of the logarithms were positive. A new edition of ""New Logarithmes"" was published in 1622 and contained an appendix with the natural"
"Common logarithm In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as ""standard logarithm"". Historically, it was known as ""logarithmus decimalis"" or ""logarithmus decadis"". It is indicated by log(""x""), or sometimes Log(""x"") with a capital ""L"" (however, this notation is ambiguous since it can also mean the complex natural logarithmic multi-valued function). On calculators, it is usually ""log"", but mathematicians usually mean natural logarithm (logarithm with"
"in 1547. The most famous of the name was John Napier the seventeenth Laird of Merchiston who developed the system of Logarithm. In 1617 he was succeeded by his son, Archibald Napier, 1st Lord Napier who accompanied James VI and I to claim his new throne in England. Napier married the daughter of the fourth Earl of Montrose and sister of James Graham, 1st Marquess of Montrose. As the brother-in-law of the king's captain the Napiers supported the king throughout the Scottish Civil War. Lord Napier died in 1645 and his only son, Archibald Napier, 2nd Lord Napier, was forced"
"James Gregory (mathematician) James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer. His surname is sometimes spelled as Gregorie, the original Scottish spelling. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions. In his book ""Geometriae Pars Universalis"" (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of"
"John Napier introduced logarithms as a powerful mathematical tool. With the help of the prominent mathematician Henry Briggs their logarithmic tables embodied a computational advance that made calculations by hand much quicker. His Napier's bones used a set of numbered rods as a multiplication tool using the system of lattice multiplication. The way was opened to later scientific advances, particularly in astronomy and dynamics. At Oxford University, Edmund Gunter built the first analog device to aid computation. The 'Gunter's scale' was a large plane scale, engraved with various scales, or lines. Natural lines, such as the line of chords, the"
"identity. as procedures exist for determining the numerical value for logarithm base ""e"" and logarithm base 2. Common logarithm In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as ""standard logarithm"". Historically, it was known as ""logarithmus decimalis"" or ""logarithmus decadis"". It is indicated by log(""x""), or sometimes Log(""x"") with a capital ""L"" (however, this notation is ambiguous since it can also mean the complex natural"
"him. He was the uncle of mathematician David Gregory. James Gregory (mathematician) James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer. His surname is sometimes spelled as Gregorie, the original Scottish spelling. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions. In his book ""Geometriae Pars Universalis"" (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special"
"Edinburgh University Library. Other manuscripts: These references are given in particular for the purpose of disambiguation. Sang also had a younger brother John (1809–1887), who was civil engineer and invented a planimeter: Edward Sang Prof Edward Sang FRSE FRSSA LLD (30 January 1805 – 23 December 1890) was a Scottish mathematician and civil engineer, best known for having computed large tables of logarithms, with the help of two of his daughters. These tables went beyond the tables of Henry Briggs, Adriaan Vlacq, and Gaspard de Prony. Sang was born in Kirkcaldy on 30 January 1805, the son of Jean Nicol"
"taking its name from John Napier, the inventor of logarithms and the decimal point, who was born in 1550 in the medieval tower house of Merchiston Castle (the site of the University's Merchiston campus). His statue stands in the tower of Merchiston Castle today. An opening ceremony was held on 23 February 1965. In 1966, it was renamed Napier College of Science and Technology. In 1974, it merged with the Sighthill-based Edinburgh College of Commerce to form Napier College of Commerce and Technology, which became a Central Institution in 1985. The college was renamed Napier Polytechnic in 1986 and in"
"as the base of a number system designed to count the grains of sand in the universe. As was noted in 2000: In 1616 Henry Briggs visited Napier at Edinburgh in order to discuss the suggested change to Napier's logarithms. The following year he again visited for a similar purpose. During these conferences the alteration proposed by Briggs was agreed upon; and on his return from his second visit to Edinburgh, in 1617, he published the first chiliad of his logarithms. In 1624 Briggs published his ""Arithmetica Logarithmica"", in folio, a work containing the logarithms of thirty thousand natural numbers"
"the logarithm. Edmund Gunter of Oxford developed a calculating device with a single logarithmic scale; with additional measuring tools it could be used to multiply and divide. The first description of this scale was published in Paris in 1624 by Edmund Wingate (c.1593–1656), an English mathematician, in a book entitled ""L'usage de la reigle de proportion en l'arithmetique & geometrie"". The book contains a double scale, logarithmic on one side, tabular on the other. In 1630, William Oughtred of Cambridge invented a circular slide rule, and in 1632 combined two handheld Gunter rules to make a device that is recognizably"
"Colin Maclaurin Colin Maclaurin (; ; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, is named after him. Owing to changes in orthography since that time (his name was originally rendered as “M‘Laurine”), his surname is alternatively written MacLaurin. Maclaurin was born in Kilmodan, Argyll. His father, Reverend and Minister of Glendaruel John Maclaurin, died when Maclaurin was in infancy, and his mother died before he reached nine years of age. He was then educated under the care of his"
"of logarithms"". The first such table was compiled by Henry Briggs in 1617, immediately after Napier's invention. Subsequently, tables with increasing scope were written. These tables listed the values of and for any number in a certain range, at a certain precision, for a certain base (usually ). For example, Briggs' first table contained the common logarithms of all integers in the range 1–1000, with a precision of 14 digits. As the function is the inverse function of log""x"", it has been called the antilogarithm. The product and quotient of two positive numbers ""c"" and ""d"" were routinely calculated as"
"Adriaan Vlacq Adriaan Vlacq (1600–1667) was a Dutch book publisher and author of mathematical tables. Born in Gouda, Vlacq published a table of logarithms from 1 to 100,000 to 10 decimal places in 1628 in his ""Arithmetica logarithmica"". This table extended Henry Briggs' original tables which only covered the values 1-20,000 and 90,001 to 100,000. The new table was computed by Ezechiel de Decker and Vlacq who calculated and added 70,000 further values to complete the tables. This table was further extended by Jurij Vega in 1794, and by Alexander John Thompson in 1952. A shorter trigonometric table called Canon"
"Logarithmic norm In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for square matrices. It has since been extended to nonlinear operators and unbounded operators as well. The logarithmic norm has a wide range of applications, in particular in matrix theory, differential equations and numerical analysis. In the finite dimensional setting it is also referred to as the matrix measure or the Lozinskiĭ measure. Let formula_1 be a"
"Hume was no mathematical reductionist, like Hobbes. The only 17th-century Scottish philosopher, other than James I, that Hume applauds is John Napier of Merchiston, the inventor of logarithms. However Napier, Newton and James I are criticised for producing eschatological literature predicting the final days. Writings of this sort were a potent factor in the politico-religious ferment of the time. They were calling for a purification in preparation for the new age of the second coming. Of these three alchemists, Hume writes: ""From the grossness of its superstitions, we may infer the ignorance of an age; but never should pronounce concerning"
"Jan Mikołaj Smogulecki Jan Mikołaj Smogulecki (1610–1656), of the Grzymała coat of arms, was a Polish nobleman, politician, missionary, scholar and Jesuit credited with introducing logarithms to China. Smogulecki was born in 1610 in Kraków or Smogulec (sources vary), the son of the ""starosta"" of Bydgoszcz, Maciej Smogulecki, and Zofia Zebrzydowska. He began his education about 1621 at a Jesuit school in Braniewo, then continued it from about 1623 at the Lubrański Academy in Poznań. Later he left the Polish-Lithuanian Commonwealth to gain more education abroad. In the years 1626–29 he studied mathematics and astronomy at Freiburg, philosophy in Rome,"
"a daughter, Martha Sherman Stringham, (March 5, 1891- August 7, 1967). Irving Stringham Washington Irving Stringham (December 10, 1847 – October 5, 1909) was a ""Professor of Mathematics and Sometime Dean in the University of California"" born in Yorkshire, New York. Stringham was the first person to denote the natural logarithm as formula_1 where formula_2 is its argument. The use of formula_1 in place of formula_4 is commonplace in digital calculators today. ""In place of formula_5 we shall henceforth use the shorter symbol formula_6, made up of the initial letters of ""logarithm"" and of ""natural"" or ""Napierian""."" Stringham graduated from"
"James Thomson Bottomley James Thomson Bottomley (10 January 1845 – 18 May 1926) was an Irish-born physicist. He is noted for his work on thermal radiation and on his creation of 4-figure logarithm tables, used to convert long multiplication and division calculations to simpler addition and subtraction before the introduction of fast calculators. He was born in Fort Breda, County Down in Ireland, on 10 January 1845, the son of William Bottomley JP, a merchant in nearby Belfast. His mother, Anna Thomson, was the sister of William Thomson, Lord Kelvin, a connection which served him well throughout his life. He"
"logarithms was quickly taken up at Gresham College, and prominent English 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 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 converse of powered numbers or exponential notation,"
"In 1934 he was promoted to Reader in Mathematics and remained in this role until his death in 1946. He died in Edinburgh on 28 March 1946. David Gibb (mathematician) David Gibb FRSE (31 October 1883 – 28 March 1946) was a Scottish mathematician and astronomer. He was the first person to use the term ""numerical integration"". Gibb was born in Methil near Leven, Fife on 31 October 1883, the eldest son of Robert Gibb, a salt manufacturer, and his wife Joanna. He attended Leven Public School then George Watsons College in Edinburgh (1896–99). He studied mathematics and sciences at"
"Irving Stringham Washington Irving Stringham (December 10, 1847 – October 5, 1909) was a ""Professor of Mathematics and Sometime Dean in the University of California"" born in Yorkshire, New York. Stringham was the first person to denote the natural logarithm as formula_1 where formula_2 is its argument. The use of formula_1 in place of formula_4 is commonplace in digital calculators today. ""In place of formula_5 we shall henceforth use the shorter symbol formula_6, made up of the initial letters of ""logarithm"" and of ""natural"" or ""Napierian""."" Stringham graduated from Harvard College in 1877. He earned his PhD from Johns Hopkins"
"1725 the Scott Baronetcy, of Thirlestane in the County of Selkirk, both baronetcies created in the Baronetage of Nova Scotia. The latter one is held till today. Additionally, the tenth Lord was created Baron Ettrick in the Peerage of the United Kingdom in 1872. Lord Napier is the hereditary Clan Chief of Clan Napier. The family seat is Thirlestane Castle, near Ettrick, Selkirkshire. Archibald Napier, son of John Napier, the inventor of logarithms, served as a Gentleman of the Bedchamber to King James VI of Scotland (I of England) and as a Lord of Session. On 2 March 1627 he"
"Napierian logarithm The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this ""natural"" logarithmic function, although it is named after him. However, if it is taken to mean the ""logarithms"" as originally produced by Napier, it is a function given by (in terms of the modern natural logarithm): The Napierian logarithm satisfies identities quite similar to the modern logarithm, such as or Napier's ""logarithm"" is related to the natural logarithm by the relation and to the common logarithm by Note that and Napierian logarithms are essentially"
"Wonderful Rule of Logarithms""). Prior to Napier's invention, there had been other techniques of similar scopes, such as the prosthaphaeresis or the use of tables of progressions, extensively developed by Jost Bürgi around 1600. The common logarithm of a number is the index of that power of ten which equals the number. Speaking of a number as requiring so many figures is a rough allusion to common logarithm, and was referred to by Archimedes as the ""order of a number"". The first real logarithms were heuristic methods to turn multiplication into addition, thus facilitating rapid computation. Some of these methods"
"under the title of ""Trigonometria Britannica""; this work was probably a successor to his 1617 ""Logarithmorum Chilias Prima"" (""The First Thousand Logarithms""), which gave a brief account of logarithms and a long table of the first 1000 integers calculated to the 14th decimal place. In 1649, Alphonse Antonio de Sarasa, a former student of Grégoire de Saint-Vincent, related logarithms to the quadrature of the hyperbola, by pointing out that the area ""A""(""t"") under the hyperbola from to satisfies The natural logarithm was first described by Nicholas Mercator in his work ""Logarithmotechnia"" published in 1668, although the mathematics teacher John Speidell"
"four sons and two daughters. George Chrystal George Chrystal FRSE FRS(8 March 1851 – 3 November 1911) was a Scottish mathematician. He is primarily remembered for his books on algebra and for his studies of seiches (wave patterns in large inland bodies of water) which earned him a Gold Medal from the Royal Society of London (confirmed shortly after his death). He was born in Old Meldrum on 8 March 1851, the son of Margaret (née Burr) and William Chrystal a wealthy farmer and grain merchant. He was educated at Aberdeen Grammar School and the University of Aberdeen, moving in"