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William Gardiner (died 1752) was an English mathematician. [1] His logarithmic tables of sines and tangents (Tables of logarithms, 1742) had various reprints and saw use by scientists and other mathematicians.
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 × 10 × 10 = 103, the "logarithm base 10" of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.
In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Jean-Charles, chevalier de Borda was a French mathematician, physicist, and Navy officer.
Henry Briggs was an English mathematician notable for changing the original logarithms invented by John Napier into common logarithms, which are sometimes known as Briggsian logarithms in his honour. The specific algorithm for long division in modern use was introduced by Briggs c. 1600 AD.
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Tables of trigonometric functions were used in ancient Greece and India for applications to astronomy and celestial navigation. They continued to be widely used until electronic calculators became cheap and plentiful, in order to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks, and specialized tables were published for numerous applications.
In trigonometry, the law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.
The Douay–Rheims Bible, also known as the Rheims–Douai Bible or Douai Bible, and abbreviated as D–R and DRB, is a translation of the Bible from the Latin Vulgate into English made by members of the English College, Douai, in the service of the Catholic Church. The New Testament portion was published in Reims, France, in 1582, in one volume with extensive commentary and notes. The Old Testament portion was published in two volumes twenty-seven years later in 1609 and 1610 by the University of Douai. The first volume, covering Genesis through Job, was published in 1609; the second, covering Psalms to 2 Machabees plus the three apocrypha books of the Vulgate appendix following the Old Testament was published in 1610. Marginal notes took up the bulk of the volumes and had a strong polemical and patristic character. They offered insights on issues of translation, and on the Hebrew and Greek source texts of the Vulgate.
The versine or versed sine is a trigonometric function found in some of the earliest trigonometric tables. The versine of an angle is 1 minus its cosine.
The exsecant and excosecant are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astronomy, and spherical trigonometry and could help improve accuracy, but are rarely used today except to simplify some calculations.
Jost Bürgi, active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.
Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally applicable way of approximating products quickly. Its name comes from the Greek prosthesis (πρόσθεσις) and aphaeresis (ἀφαίρεσις), meaning addition and subtraction, two steps in the process.
Leonty Filippovich Magnitsky, born Telyatin, was a Russian mathematician and educator.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics and reaching its modern form with Leonhard Euler (1748).
The history of logarithms is the story of a correspondence between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer. The Napierian logarithms were published first in 1614. Henry Briggs introduced common logarithms, which were easier to use. Tables of logarithms were published in many forms over four centuries. The idea of logarithms was also used to construct the slide rule, which became ubiquitous in science and engineering until the 1970s. A breakthrough generating the natural logarithm was the result of a search for an expression of area against a rectangular hyperbola, and required the assimilation of a new function into standard mathematics.
Florimond de Beaune was a French jurist and mathematician, and an early follower of René Descartes. R. Taton calls him "a typical example of the erudite amateurs" active in 17th-century science.
The Ohio and Mississippi Railway, abbreviated O&M, was a railroad operating between Cincinnati, Ohio, and East St. Louis, Illinois, from 1857 to 1893.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.
John Speidell was an English mathematician. He is known for his early work on the calculation of logarithms.
John Caulfield Hannyngton was a British military commander, actuary and mathematician. He is remembered as inventor of a slide rule of previously unattainable precision.
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