John Collins (mathematician)

John Collins (mathematician)

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John Collins was an English
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...

 mathematician. He is most known for his extensive correspondence with leading scientists and mathematicians such as Giovanni Alfonso Borelli
Giovanni Alfonso Borelli
Giovanni Alfonso Borelli was a Renaissance Italian physiologist, physicist, and mathematician. He contributed to the modern principle of scientific investigation by continuing Galileo's custom of testing hypotheses against observation...

, Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

, and John Wallis. His correspondence provides details of many of the discoveries and developments made in his time, and shows his activity as an 'intelligencer'.


He was the son of a nonconformist minister, and was born at Wood Eaton
Woodeaton or Wood Eaton is a village and civil parish about northeast of Oxford.-Archaeology:There was a Romano-Celtic temple north of where the parish church now stands, and probably a Romano-British settlement and shrine as well. The shrine was used successively by Roman pagans and Christians...

 in Oxfordshire
Oxfordshire is a county in the South East region of England, bordering on Warwickshire and Northamptonshire , Buckinghamshire , Berkshire , Wiltshire and Gloucestershire ....

, 5 March 1625. Apprenticed at the age of sixteen to Thomas Allam, a bookseller, living outside the Turl Gate of Oxford
The city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...

, he was driven to quit the trade by the troubles of the time, and accepted a clerkship in the employment of John Marr, clerk of the kitchen to the Prince of Wales
Charles II of England
Charles II was monarch of the three kingdoms of England, Scotland, and Ireland.Charles II's father, King Charles I, was executed at Whitehall on 30 January 1649, at the climax of the English Civil War...

. From him he derived some instruction in mathematics, but the outbreak of the First English Civil War
First English Civil War
The First English Civil War began the series of three wars known as the English Civil War . "The English Civil War" was a series of armed conflicts and political machinations that took place between Parliamentarians and Royalists from 1642 until 1651, and includes the Second English Civil War and...

 drove him to sea for seven years, 1642-9, most of which time he spent on board an English merchantman, engaged by the Venetians
Republic of Venice
The Republic of Venice or Venetian Republic was a state originating from the city of Venice in Northeastern Italy. It existed for over a millennium, from the late 7th century until 1797. It was formally known as the Most Serene Republic of Venice and is often referred to as La Serenissima, in...

 as a ship of war in their defence of Candia
-Places:* The old Venetian name for Heraklion, Crete* Kingdom of Candia, colony of the Republic of Venice * Candia Canavese, Italy* Candia Lomellina, Italy...

 against the Turks.

He devoted his leisure to the study of mathematics and merchants' accounts, and on leaving the service set up in London as a teacher. In 1652 he published An Introduction to Merchants' Accounts, originally drawn up for the use of his scholars. Reprinted in 1665, the major part of the impression perished in the great fire of London
Great Fire of London
The Great Fire of London was a major conflagration that swept through the central parts of the English city of London, from Sunday, 2 September to Wednesday, 5 September 1666. The fire gutted the medieval City of London inside the old Roman City Wall...

, but was replaced in 1674 by a new and amplified folio edition. He next wrote The Sector on a Quadrant, or a Treatise containing the Description and Use of three several Quadrants. Also an appendix touching Reflected Dyalling, from a Glass however posited (London, 1658); and The Description and Uses of a general Quadrant, with the Horizontal Projection upon it Inverted (1658). In 1659 appeared his Geometricall Dyalling, or Dyalling performed by a Line of Chords only, and The Mariner's Plain Scale new Plained, a treatise on navigation for the East India Company
East India Company
The East India Company was an early English joint-stock company that was formed initially for pursuing trade with the East Indies, but that ended up trading mainly with the Indian subcontinent and China...

's navy. It was well received, and became a class-book with the students of navigation at Christ Church Hospital.

After the Restoration
English Restoration
The Restoration of the English monarchy began in 1660 when the English, Scottish and Irish monarchies were all restored under Charles II after the Interregnum that followed the Wars of the Three Kingdoms...

, Collins was appointed successively accountant to the excise office, accountant in chancery, and secretary to the council of plantations, exchanging the last post in 1672 for that of manager of the farthing office. With this employment went a house in Fenchurch Street
Fenchurch Street
Fenchurch Street is a street in the City of London home to a number of shops, pubs and offices. It links Aldgate at its eastern end with Lombard Street and Gracechurch Street to the west. To the south of Fenchurch Street and towards its eastern end is Fenchurch Street railway station...

, where he had thoughts of setting up a stationer's shop, and hoped 'to fall into the printing of books,' including some he himself designed to write, 'particularly one of the modern advancement of mathematical sciences, and an account of the best authors of that kind'. He did not, however, succeed in carrying the plan into effect. With the failure of his arguments against the issue of tin farthings his office ceased, and he was glad subsequently to accept a small post as accountant to the Royal Fishery Company.

He had refused in March 1669 a situation offered to him in Ireland by the surveyor-general, Sir James Shaen, and about the same time married one of two daughters of William Austen, head cook to Charles II. As his family increased his means of subsistence became more and more precarious. He undertook accountancy work, spending less time on learned correspondence.

Several of his writings testify to his acquaintance with the course of trade and interest in public matters. He published in 1680 A Plea for the bringing in of Irish Cattel, and keeping out Fish caught by Foreigners, together with an humble Address to the Honourable Members of Parliament of the counties of Cornwall and Devon, about the Advancement of Tin, Fishery, and divers Manufactures; and in 1682 a little treatise entitled Salt and Fishery, in which he dwelt upon the several modes of preparing salt in England and abroad, the catching of fish, the salting and cooking of fish and meat, besides offering proposals for the relief of the salt-workers.

Collins died, 10 November 1683, at his lodging on Garlick Hill, London, of asthma and consumption
Tuberculosis, MTB, or TB is a common, and in many cases lethal, infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis. Tuberculosis usually attacks the lungs but can also affect other parts of the body...

, and was buried in the parish church of St. James.


An enlarged edition of his Doctrine of Decimal Arithmetick, the preparation of which had engaged his attention during about a year before his death, appeared in 1685. It had originally been printed in 1664 on a quarter of a sheet for portability in a letter-case. His Arithmetic in whole Numbers and Fractions, both Vulgar and Decimal, with Tables for the Forbearance and Rebate of Money, &c., was published by Thomas Plant in 1688.

Collins was elected a fellow of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

 24 October 1667, and on 11 November of that year communicated an exposition of a theorem by the Jesuit Jacques de Billy
Jacques de Billy
Jacques de Billy was a French Jesuit mathematician. Born in Compiègne, he subsequently entered the Society of Jesus. From 1629 to 1630, Billy taught mathematics at the Jesuit College at Pontà Mousson. He was still studying theology at this time. From 1631 to 1633, Billy taught mathematics at...

. He contributed further An Account concerning the Resolution of Equations in Numbers, a survey of recent algebra improvements made in England, and A Solution of a Chorographical Problem; while a letter written to John Wallis, 3 October 1682,, was imparted to the society 20 May 1684. This was designed as preliminary to a formal treatise on algebra, never written.

He helped forward many important publications. To him was due the printing of Isaac Barrow
Isaac Barrow
Isaac Barrow was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was...

's Optical and Geometrical Lectures, as well as of his editions of Apollonius
Apollonius of Perga
Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...

 and Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

; of John Kersey
John Kersey the elder
John Kersey the elder was an English mathematician, as well as a textbook writer.-Life:He was son of Anthony Carsaye or Kersey and Alice Fenimore, and was baptised at Bodicote, near Banbury, Oxfordshire, on 23 November 1616. He came to London, and gained a livelihood as a teacher...

's Algebra, Thomas Branker
Thomas Branker
-Life:He was born at Barnstaple in August 1633, the son of another Thomas Brancker, a graduate of Exeter College, Oxford, who was in 1626 a schoolmaster near Ilchester, and about 1630 head-master of the Barnstaple High School. The family originally bore the name of Brouncker. Young Brancker...

's translation of Rhonius's Algebra, and Wallis's History of Algebra. He took an active part in seeing Jeremiah Horrocks
Jeremiah Horrocks
Jeremiah Horrocks , sometimes given as Jeremiah Horrox , was an English astronomer who was the only person to predict, and one of only two people to observe and record, the transit of Venus of 1639.- Life and work :Horrocks was born in Lower Lodge, in...

's Astronomical Remains through the press.


About twenty-five years after Collins's death his books and papers came into the possession of William Jones, F.R.S. They included a voluminous correspondence with Newton, Leibniz, Gregory, Barrow, John Flamsteed
John Flamsteed
Sir John Flamsteed FRS was an English astronomer and the first Astronomer Royal. He catalogued over 3000 stars.- Life :Flamsteed was born in Denby, Derbyshire, England, the only son of Stephen Flamsteed...

, Wallis, Slusius, and others. From it was selected and published in 1712, by order of the Royal Society, the Commercium Epistolicum, of material relevant to Newton's priority over Leibniz in the discovery of the infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...

; specimens of results from the use of the fluxion
Fluxion may refer to:* An alternate spelling of fluxon, a quantum of magnetic flux, such as in a superconductor* Fluxion was Isaac Newton's term for the derivative of a "fluent", or continuous function....

al method were transmitted 20 July 1669 through Barrow to Collins, and by him made widely known.

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