''Arithmetica Universalis'' ("Universal Arithmetic") is a

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

text by

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

. Written in

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

, it was edited and published by

William Whiston William Whiston (9 December 166722 August 1752) was an English theologian, historian, natural philosopher, and mathematician, a leading figure in the popularisation of the ideas of Isaac Newton. He is now probably best known for helping to inst ...

, Newton's successor as

Lucasian Professor of Mathematics The Lucasian Chair of Mathematics () is a mathematics professorship in the University of Cambridge, England; its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas (politician), Henry Lucas, who was Cambridge U ...

at the University of Cambridge. The ''Arithmetica'' was based on Newton's lecture notes.

Publication history

Whiston's original edition was published in 1707. It was translated into English by

Joseph Raphson Joseph Raphson (c. 1668 – c. 1715) was an England, English mathematician and intellectual known best for the Newton–Raphson method. Biography Very little is known about Raphson's life. Connor and Robertson give his date of birth as 1668 bas ...

, who published it in 1720 as the ''Universal Arithmetick''. John Machin published a second Latin edition in 1722.

Lack of credit for the writer

None of these editions credit 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.

Content

The ''Arithmetica'' touches on algebraic notation, arithmetic, the relationship between

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

and

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, 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. A rigorous proof of Newton's counting formula for equations up to and including the fifth degree was published by

James Joseph Sylvester James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership ...

in 1864.

References

The ''Arithmetica Universalis'' from the Grace K. Babson Collection, including links to PDFs of English and Latin versions of the ''Arithmetica''Centre College Library information on Newton's works

External links

''Arithmetica Universalis''
(1707), first edition
''Universal Arithmetick''
(1720), English translation by Joseph Raphson
''Arithmetica Universalis''
(1722), second edition {{Authority control 1707 non-fiction books 1720 non-fiction books Mathematics books Books by Isaac Newton 18th-century books in Latin