"Seeing there is nothing that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers. [...] I began therefore to consider in my mind by what certain and ready art I might remove those hindrances." (John Napier, "Mirifici logarithmorum canonis descriptio", 1614)
"They seem to have been called logarithms by their illustrious inventor because they exhibit to us numbers which always preserve the same ratio to one another." (Henry Briggs, "Arithmetica Logarithmica", 1624)
"These Exponents they call Logarithms, which are Artificial Numbers, so answering to the Natural Numbers, as that the addition and Subtraction of these, answers to the Multiplication and Division of the Natural Numbers. By this means, (the Tables being once made) the Work of Multiplication and Division is performed by Addition and Subtraction; and consequently that of Squaring and Cubing, by Duplication and Triplication; and that of Extracting the Square and Cubic Root, by Bisection and Trisection; and the like in the higher Powers." (John Wallis, "Of Logarithms, Their Invention and Use", 1685)
"I have finally discovered the true solution: in the same way that to one sine there correspond an infinite number of different angles I have found that it is the same with logarithms, and each number has an infinity of different logarithms, all of them imaginary unless the number is real and positive; there is only one logarithm which is real, and we regard it as its unique logarithm." (Leonhard Euler, [letter to Cramer] 1746)
"The science of calculation [...] is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence." (Thomas Jefferson, [letter to William G Munford] 1799)
"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, "The Construction of the Wonderful Canon of Logarithms", 1889)
"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, "The Construction of the Wonderful Canon of Logarithms", 1889)
"Any desired geometrical mean between two sines has for its Logarithm the corresponding arithmetical mean between the Logarithms of the sines." (John Napier, "The Construction of the Wonderful Canon of Logarithms", 1889)
"To decrease geometrically is this, that in equal times, first the whole quantity then each of its successive remainders is diminished, always by a like proportional part." (John Napier, "The Construction of the Wonderful Canon of Logarithms", 1889)
"Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skillful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures."(Johann F Herbart, 1890)
"The miraculous powers of modern calculation are due to three inventions: the Arabic Notation, Decimal Fractions, and Logarithms." (Florian Cajori, "A History of Mathematics", 1894)
"Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm [ln(-1)]; secondly that a negative quantity has no square root [√-1]; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter [π]." (Augustus De Morgan) [attributed]
"[logarithms] by shortening the labours doubled the life of the astronomer." (Pierre Simon Laplace, [in Howard Eves' "Mathematical Circles", 1969])
"As nature puts forth its wonders, most of us are oblivious to the massive calculations and mathematical work needed to explain something that i5 very routine to nature. For example, the Orb spider's web is a simple, but elegant natural creation. When this beautiful structure is analyzed, the mathematical ideas that appear in the web are indeed complicated and surprising - radii, chords, parallel segments, triangles, congruent corresponding angles, the logarithmic spiral, the catenary curve and the transcendental number e. Yet even with all our mathematical forces at work - including chaos and complexity theories - many natural phenomena, such as earthquake and weather predictions, still elude precise mathematical description. The profound study of nature is the most fertile source of mathematical discoveries." (Joseph Fourier)
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