“If a first sine be multiplied into a second producing a third, the Logarithm of the first added to the Logarithm of the second produces the Logarithm of the third. So in division, the Logarithm of the divisor subtracted from the Logarithm of the dividend leaves the Logarithm of the quotient.”

—  John Napier

Appendix, The relations of Logarithms & their natural numbers to each other
The Construction of the Wonderful Canon of Logarithms (1889)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "If a first sine be multiplied into a second producing a third, the Logarithm of the first added to the Logarithm of the…" by John Napier?
John Napier photo
John Napier46
Scottish mathematician 1550–1617

Related quotes

John Napier photo

“And if any number of equals to a first sine be multiplied together producing a second, just so many equals to the Logarithm of the first added together produce the Logarithm of the second.”

John Napier (1550–1617) Scottish mathematician

Appendix, The relations of Logarithms & their natural numbers to each other
The Construction of the Wonderful Canon of Logarithms (1889)

E. W. Hobson photo

“The second part of the book… contains an exposition of the first principles of the theory of complex quantities; hitherto, the very elements of this theory have not been easily accessible to the English student, except recently in Prof. Chrystal's excellent treatise on Algebra. The subject of Analytical Trigonometry has been too frequently presented to the student in the state in which it was left by Euler, before the researches of Cauchy, Abel, Gauss, and others, had placed the use of imaginary quantities, and especially the theory of infinite series and products, where real or complex quantities are involved, on a firm scientific basis. In the Chapter on the exponential theorem and logarithms, I have ventured to introduce the term "generalized logarithm" for the doubly infinite series of values of the logarithm of a quantity.”

E. W. Hobson (1856–1933) British mathematician

A Treatise on Plane Trigonometry https://books.google.com/books?id=_ktLAAAAMAAJ (1891) Preface

James Whitbread Lee Glaisher photo

“The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier’s Descriptio.”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: Encyclopedia Britannica, 9th Edition; Article “Logarithms.”; Reported in Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book, (1914) : On the invention of logarithms

John Napier photo

“A Logarithmic Table is a small table by the use of which we can obtain a knowledge of all geometrical dimensions and motions in space, by a very easy calculation. It is deservedly called very small, because it does not exceed in size a table of sines; very easy, because by it all multiplications, divisions, and the more difficult extractions of roots are avoided; for by only a very few most easy additions, subtractions, and divisions by two, it measures quite generally all figures and motions.”

John Napier (1550–1617) Scottish mathematician

The Construction of the Wonderful Canon of Logarithms (1889)

Paul R. Halmos photo

“André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That's one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.”

Paul R. Halmos (1916–2006) American mathematician

I Want to be a Mathematician: An Automathography (1985)

Jacob Bronowski photo

“Ralegh's own circle, which turned Christopher Marlowe into a rationalist, was dominated by… Thomas Hariot. For navigation is dependent on astronomy; it went hand in hand with the new speculations about the world and the solar system… in turn, the voyages of the great navigators inspired the literature of Elizabethan England. The worlds of art and science and the physical world unfolded then together. It was not by accident that the first table of logarithms was published within a few years of the First Folio.”

Jacob Bronowski (1908–1974) Polish-born British mathematician

"Sense and Sensibility"
The Common Sense of Science (1951)

Francis Place photo

“I taught myself decimals, equations, the square, cube, and biquadrate roots. I got some knowledge of logarithms, and some of algebra. I readily got through a small schoolbook of geometry; and having an odd volume, the first, of Williamson's ' Euclid,' I attacked it vigorously and perseveringly. Williamson's is by no means the best book on the subject, yet I am still of opinion that it is the best book I could have had for the purpose of teaching myself.”

Francis Place (1771–1854) English social reformer

Source: The life of Francis Place, 1771-1854, 1898, p. 18

Jacob Bronowski photo

“[I]magination… is the faculty… the common root from which science and literature… spring and grow and flourish together. …the great ages of science are the great ages of all the arts… [P]owerful minds have taken fire from one another… without asking… to tie their imagination to falling balls or a haunted island. …When Galileo was looking through his telescope at the moon, Shakespeare was writing The Tempest and all Europe was in ferment, from Johannes Kepler to Peter Paul Rubens, and from the first table of logarithms by John Napier to the Authorized version of the Bible.”

Jacob Bronowski (1908–1974) Polish-born British mathematician

"The Reach of Imagination" (1967)

Charles Sanders Peirce photo

“Chance is First, Law is Second, the tendency to take habits is Third. Mind is First, Matter is Second, Evolution is Third.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Architecture of Theories (1891)
Context: The origin of things, considered not as leading to anything, but in itself, contains the idea of First, the end of things that of Second, the process mediating between them that of Third. A philosophy which emphasises the idea of the One, is generally a dualistic philosophy in which the conception of Second receives exaggerated attention: for this One (though of course involving the idea of First) is always the other of a manifold which is not one. The idea of the Many, because variety is arbitrariness and arbitrariness is repudiation of any Secondness, has for its principal component the conception of First. In psychology Feeling is First, Sense of reaction Second, General conception Third, or mediation. In biology, the idea of arbitrary sporting is First, heredity is Second, the process whereby the accidental characters become fixed is Third. Chance is First, Law is Second, the tendency to take habits is Third. Mind is First, Matter is Second, Evolution is Third.

Thomas Fuller (writer) photo

“1006. Boldness in Business is the first, second, and third thing.”

Thomas Fuller (writer) (1654–1734) British physician, preacher, and intellectual

Introductio ad prudentiam: Part II (1727), Gnomologia (1732)

Related topics