Background

Cotes was born on July 10, 1682, at Burbage, England, of which place his father, the Reverend Robert Cotes, was rector. Cotes' mother was Grace Farmer, who came from Barwell in Leicestershire. Roger had a brother Anthony one year older than himself, and a sister Susanna who was one year younger.

Education

Cotes was educated first at Leicester School, where he showed such a flair for mathematics that at the age of twelve his uncle, the Reverend John Smith, took him into his home to supervise his studies personally. Cotes later went to St. Paul’s School, London, where he studied mainly classics while keeping up a scientific correspondence with his uncle. He was admitted as a pensioner to Trinity College, Cambridge, in 1699, graduating Bachelor of Arts in 1702 and Master of Arts in 1706. He became a fellow of his college in 1705 and a fellow of the Royal Society in 1711 and was ordained in 1713.

Career

In January 1706, Cotes was named the first Plumian professor of astronomy and natural philosophy at Cambridge on the very strong recommendation of Richard Bentley, master of Trinity. On his appointment as professor, he opened a subscription list in order to provide an observatory for Trinity. This, with living quarters for the professor, was erected on the leads over King’s Gate. Cotes spent the rest of his life here with his cousin Robert Smith, who was his assistant and successor. The observatory was not completed in Cotes’s lifetime and was demolished in 1797.

Concerning his astronomical work, Cotes supplied, in correspondence with Newton, a description of a heliostat telescope furnished with a mirror revolving by clockwork. He recomputed the solar and planetary tables of Flamsteed and J. D. Cassini and had intended to construct of the moon’s motion, based on Newtonian principles. According to Halley (1714), he also observed the total solar eclipse of 22 April 1715, noticing the occultation of three spots.

Cotes formed a school of physical sciences at Trinity in collaboration with William Whiston. The two performed a series of experiments beginning in May 1707, the details of which can be found in a post-humous publication, Hydrostatical, and Pneumatical Lectures by Roger Cotes (1738). These demonstration classes indicate a simple, straightforward style that is both stimulating and thorough. There was no thought of practical work by students at this time.

In 1709 Cotes became heavily involved in the preparation of the second edition of Newton’s great work on universal gravitation, the Philosophiae naturalis principia mathematica. The first edition of 1687 had few copies printed. In 1694 Newton did further work on his lunar and planetary theories, but illness and a dispute with Flamsteed postponed any further publication. Newton subsequently became master of the mint and had virtually retired from scientific work when Bentley persuaded him to prepare a second edition, suggesting Cotes as supervisor of the work.

Newton at first had a rather casual approach to the revision, but Cotes took the work very seriously. Gradually, Newton was coaxed into a similar enthusiasm; and the two collaborated closely on the revision, which took three and a half years to complete. The edition was limited to only 750 copies, and a pirated version printed in Amsterdam met the total demand. Bentley, who had borne the expense of the printing, took the profits and rewarded Cotes with twelve free copies for his labors. Newton wrote a preface, remarking that in this edition the theory of the moon and the precession of the equinoxes had been more fully deduced from the principles, the theory of comets confirmed by several observations, the theory of comets confirmed by several observations, and the orbits of comets computed more accurately. His debt to Cotes for these improvements cannot be estimated.

Cotes’s original contribution to this book was a short preface. He suggested to Newton that he write a description of the scientific methodology used and demonstrate, in particular, the superiority of these principles to the popular idea of vortices presented by Descartes. Cartesian ideas were still vigorous, not only on the Continent but also in England, and continued to be taught at Cambridge until 1730 at least. In particular, Cartesian critics alleged that Newton’s idea of action at a distance required the conception of an unexplained, occult force. Newton and Bentley agreed that Cotes should write a preface defending the Newtonian hypothesis against the theory of vortices and the other objections.

Cote’s major original work was in the field of mathematics, and the decline in British mathematics that followed his untimely death accentuated his being one of the very few British mathematicians capable of following on from Newton’s great work.

His only publication during his life was an article entitled “Logometria” (1714). After his death, his mathematical papers, then in great confusion, were edited by Robert Smith and published as a book, Harmonia mensurarum (1722).

Achievements

• Cotes is best known for working closely with Isaac Newton by proofreading the second edition of his famous book, the Principia, before publication. He also invented the quadrature formulas known as Newton - Cotes formulas and first introduced what is known today as Euler's formula.

Works

More photos

• book

  • The Principia

    (In his monumental 1687 work, Philosophiae Naturalis Princ...)

    1687

Membership

• Royal Society of London , United Kingdom

Connections

Cotes never married.

Father:

Robert Cotes

Mother:

Grace Farmer

Brother:

Anthony Cotes

Sister:

Susanna Cotes

colleague:

Isaac Newton

References

• Dictionary of Scientific Biography Volume 3
  1971
• Correspondence of Sir Isaac Newton and Professor Cotes
  1850
• Roger Cotes - Natural Philosopher Roger Cotes (1682-1716) was the first Plumian Professor of Astronomy and Experimental Philosophy, at Trinity College, Cambridge. One of the most distinguished, and certainly one of the most ardent, of the early Newtonians he did important work in mathematics and astronomy and edited the second edition of Newton's Principia.
  2002
• Newtonian Studies Seven essays which illustrate by means of conceptual analysis the way in which fundamental scientific ideas are at the same time related to the main currents of philosophical thought and yet determined by empirical controls.
  1968