Arithmetica Universalis

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Arithmetica Title page (1707) Arithmetica.jpg
Arithmetica Title page (1707)
Raphson 's Eng. Tr. (1720) UniversalArithmetick.gif
Raphson 's Eng. Tr. (1720)

Arithmetica Universalis ("Universal Arithmetic") is a mathematics text by Isaac Newton. Written in Latin, it was edited and published by William Whiston, Newton's successor as Lucasian Professor of Mathematics at the University of Cambridge. The Arithmetica was based on Newton's lecture notes.

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.

Isaac Newton Influential British physicist and mathematician

Sir Isaac Newton was an English mathematician, physicist, astronomer, theologian, and author who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

William Whiston theologian, historian, mathematician

William Whiston was an English theologian, historian, and mathematician, a leading figure in the popularisation of the ideas of Isaac Newton. He is now probably best known for helping to instigate the Longitude Act in 1714 and his important translations of the Antiquities of the Jews and other works by Josephus. He was a prominent exponent of Arianism and wrote A New Theory of the Earth.

Whiston's original edition was published in 1707. It was translated into English by Joseph Raphson, who published it in 1720 as the Universal Arithmetick. John Machin published a second Latin edition in 1722.

Joseph Raphson British mathematician

Joseph Raphson was an English mathematician known best for the Newton–Raphson method.

John Machin, a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.

None of these editions credits Newton as author; Newton was unhappy with the publication of the Arithmetica, and so refused to have his name appear. In fact, when Whiston's edition was published, Newton was so upset he considered purchasing all of the copies so he could destroy them.

The Arithmetica touches on algebraic notation, arithmetic, the relationship between geometry and algebra, and the solution of equations. Newton also applied Descartes' rule of signs to imaginary roots. He also offered, without proof, a rule to determine the number of imaginary roots of polynomial equations. Not for another 150 years would a rigorous proof to Newton's counting formula be found (by James Joseph Sylvester, published in 1865).

Geometry Branch of mathematics that studies the shape, size and position of objects

Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

René Descartes 17th-century French philosopher, mathematician, and scientist

René Descartes was a French philosopher, mathematician, and scientist. A native of the Kingdom of France, he spent about 20 years (1629–1649) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. One of the most notable intellectual figures of the Dutch Golden Age, Descartes is also widely regarded as one of the founders of modern philosophy.

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Diophantus Alexandrian Greek mathematician

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History of mathematics aspect of history

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Number theory Branch of pure mathematics

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Galois theory connection between field theory and group theory

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Muhammad ibn Musa al-Khwarizmi Persian mathematician, astronomer and geographer

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<i>Disquisitiones Arithmeticae</i> book

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Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.

In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a1a2, ..., an are real numbers and let denote the kth elementary symmetric function in a1a2, ..., an. Then the elementary symmetric means, given by

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Richard Sault was an English mathematician, editor and translator, one of The Athenian Society. On the strength of his Second Spira he is also now credited as a Christian Cartesian philosopher.

Michael Stifel German mathematician

Michael Stifel or Styfel was a German monk, Protestant reformer and mathematician. He was an Augustinian who became an early supporter of Martin Luther. He was later appointed professor of mathematics at Jena University.

John Radford Young was an English mathematician, professor and author, who was almost entirely self-educated. He was born of humble parents in London. At an early age he became acquainted with Olinthus Gilbert Gregory, who perceived his mathematical ability and assisted him in his studies. In 1823, while working in a private establishment for the deaf, he published An Elementary Treatise on Algebra with a dedication to Gregory. This treatise was followed by a series of elementary works, in which, following in the steps of Robert Woodhouse, Young familiarized English students with continental methods of mathematical analysis.

<i>Summa de arithmetica</i> Renaissance mathematics textbook

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