NEWTON 1761

Description

Arithmetica universalis; sive de compositione et resolutione arithmetica liber, auctore Is. Newton, Cum commentario Johannis Castillionei, Amstelodami, Apud . Marcum Michaele Rey, 1761

2 vols. and supplement, bound in 2 vols. First edition of Castillon’s “useful commentary on Newton’s ‘Arithmetica universalis'” (DSB). Illustrated with 37 engraved folding plates. The supplement includes additional treatises by Halley, Colson, DeMoivre, Maclaurin, Campbell, Baermann and Kaestner; this edition also includes new material by R. G. Boscovich. – Mild browning and some foxing or spotting, somewhat stronger in places. Slight waterstaining to lower inner margins, stronger to first and last leaves. Minor traces of mildew to last leaves at dampstaining in vol. 1. Errata leaf of vol. 1 bound in the end of vol. 2. Library and deaccession stamps to fly leaf of vol. 1. Bound in repaired contemporary calf, somewhat worn, corners, joints and the 2 heads and 1 tail of spine repaired and covered by leather stripes, frontpapers renewed by using old paper.

References: Riccardi I/1, 298 (dat. 1760); Babson 205; Wallis 281; DSB III, 119.

 

Arithmetica Universalis (“Universal Arithmetic”) is a mathematics text by Isaac Newton. Written in Latin, it was edited and published by William Whiston (1667-1752), Newton’s successor as Lucasian Professor of Mathematics at the University of Cambridge. The Arithmetica was based on lecture notes by Newton for the period 1673 to 1683. There is no record of the lectures ever being presented. Whiston’s original edition was published in 1707. It was translated into English by Joseph Raphson, who published it in 1720 as the Universal Arithmetic. John Machin (1680-1751) published a second Latin edition in 1722. Seven more editions were printed in the 18th century, including Leyden, Paris, Amsterdam, and Milan.

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.

In this work, Newton covers the essentials of algebra: notation, addition, subtraction, multiplication, division, extraction of roots, reduction of fractions, reduction of geometrical questions to equations, and the resolution of equations.

In addition, Newton extended Descartes’ rule of signs to imaginary roots. He also formulated a rule to determine the number of imaginary roots of any equation. The rule was complicated and offered without proof. Some idea of its originality is shown by the fact that it took another 180 years before the rule was proven by rigorous analysis.

 

Isaac Newton was born on Christmas Day, 25 December 1642  at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. His father, also named Isaac Newton, had died three months before.

From the age of about twelve until he was seventeen, Newton was educated at The King’s School in Grantham, which taught Latin and Ancient Greek.

In June 1661, Newton was admitted to Trinity College at the University of Cambridge. At the time, Cambridge’s teachings were based on those of Aristotle, whom Newton read along with then more modern philosophers, including Descartes and astronomers such as Galileo Galilei and Thomas Street. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton obtained his BA degree at Cambridge in August 1665, the university temporarily closed as a precaution against the Great Plague. In April 1667, Newton returned to the University of Cambridge, and in October he was elected as a fellow of Trinity. His academic work impressed the Lucasian professor Isaac Barrow, who was anxious to develop his own religious and administrative potential (he became master of Trinity College two years later); in 1669, Newton succeeded him, only one year after receiving his MA.

Calculus

Newton’s work has been said “to distinctly advance every branch of mathematics then studied”. His work on the subject, usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newton’s mathematical papers. His work De analysi per aequationes numero terminorum infinitas, sent by Isaac Barrow to John Collins in June 1669, was identified by Barrow in a letter sent to Collins that August as the work “of an extraordinary genius and proficiency in these things”. Newton later became involved in a dispute with Leibniz over priority in the development of calculus (the Leibniz–Newton calculus controversy). Most modern historians believe that Newton and Leibniz developed calculus independently, although with very different mathematical notations. However, it is established that Newton came to develop calculus much earlier than Leibniz. Leibniz’s notation and “differential Method”, nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians.

Gravity

Newton’s own copy of Principia with Newton’s hand-written corrections for the second edition, now housed at Wren Library at Trinity College, Cambridge

Newton had been developing his theory of gravitation as far back as 1665. In 1679, Newton returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler’s laws of planetary motion. This followed stimulation by a brief exchange of letters in 1679–80 with Hooke, who had been appointed to manage the Royal Society’s correspondence, and who opened a correspondence intended to elicit contributions from Newton to Royal Society transactions.[64] Newton’s reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed. After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum, a tract written on about nine sheets which was copied into the Royal Society’s Register Book in December 1684. This tract contained the nucleus that Newton developed and expanded to form the Principia. The Principia was published on 5 July 1687 with encouragement and financial help from Halley. In this work, Newton stated the three universal laws of motion.

Newton died in his sleep in London on 20 March 1727. He was given a ceremonial funeral, attended by nobles, scientists, and philosophers, and was buried in Westminster Abbey among kings and queens. He was the first scientist to be buried in the abbey.

Works

Published in his lifetime

• De analysi per aequationes numero terminorum infinitas (1669, published 1711)
• Of Natures Obvious Laws & Processes in Vegetation (unpublished, c. 1671–75)
• De motu corporum in gyrum (1684)
• Philosophiæ Naturalis Principia Mathematica (1687)
• Scala graduum Caloris. Calorum Descriptiones & signa (1701)
• Opticks (1704)
• Reports as Master of the Mint (1701–1725)
• Arithmetica Universalis (1707)

Published posthumously

• De mundi systemate (The System of the World) (1728)
• Optical Lectures (1728)
• The Chronology of Ancient Kingdoms Amended (1728)
• Observations on Daniel and The Apocalypse of St. John (1733)
• Method of Fluxions (1671, published 1736)
• An Historical Account of Two Notable Corruptions of Scripture (1754)