''Arithmetica Universalis'' ("Universal Arithmetic") is a mathematics text by

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the grea ...

. Written in

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

, 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, who was Cambridge University's Member of Pa ...

at the University of Cambridge. The ''Arithmetica'' was based on Newton's lecture notes. Whiston's original edition was published in 1707. It was translated into English by

Joseph Raphson Joseph Raphson (c. 1668 – c. 1715) was an 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 based on a 1 ...

, who published it in 1720 as the ''Universal Arithmetick''. John Machin published a second Latin edition in 1722. 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 Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

and

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

, 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.

References

The ''Arithmetica Universalis'' from the Grace K. Babson Collection, including links to PDFs of English and Latin versions of the ''Arithmetica''

''Arithmetica Universalis''
(1720), translated by Joseph Raphson
Centre College Library information on Newton's works
{{Authority control 1707 books 1720 books Mathematics books Books by Isaac Newton 18th-century Latin books