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"From what I have already described, and from many other ingenious Devices of the like Nature, which I have seen, I shall conclude with this general Observation, that the knowledge and use of Symbols, (or of sensible and arbitrary Signs of intellectual Ideas) is of the greatest Importance and Extent in all Parts of the Mathematics." John Colson

John Colson (1680--1760), the fifth Lucasian Professor of Mathematics at Cambridge University, is a relative unknown in the history of the field. He followed in the wake of Newton's revolution, assuming the Chair twelve years after Newton's death and fifty-two years after the publication of the Principia. While Colson's original contributions were minor, his translation works had some value. His life was that of an educator more than a scholar. There was some speculation that Cambridge had expected more of him.¹

Before Colson came to Cambridge, he had been the master at a mathematical school at Rochester. He was first educated at Christ Church Oxford, but never graduated. In 1713 he was elected to the Royal Society. In the later years of his life he was also the rector of Lokington in Yorkshire.

Colson was invited to Cambridge to read lectures in mathematics at Sydney College. Eventually he moved to Emmanuel College, Cambridge, where he received his M.A. in 1728, when he was forty-eight years old. He was elected to the Lucasian Chair in May 1739 which he occupied until his death in 1760.

Three published papers comprise Colson's mathematical contributions plus one explanatory essay published in Nicolas Saunderson's Elements of Algebra , that explains in detail the blind mathematician's system for performing calculations. The topics of the three papers include a Latin version of a method for solving quadratic and biquadratic equations, ² an English paper demonstrating negativo-affirmative arithmetic, and the last, in English, a solution to the problem of map making involving conversion between a flat surface and a spherical surface.

The paper discussing negativo-affirmative is quite interesting in what it proposes and what it does. The objective was to simplify arithmetic calculation which, of course, was done by hand. When numbers containing 10 or more digits are multiplied by numbers of similar size, the calculation takes time. Since science was developing the need for such calculations, any method to speed up the process was welcome. There is no obvious evidence however that this method was used by anyone else. At the end of the paper, Colson promised to show more of the method and mentioned an instrument he had contrived, called a counting-table to aid in using this new method of arithmetic. No follow up paper appeared, however.

The method of negativo-affirmative arithmetic is still interesting. Colson found a way to mix negative and positive digits to make up a number. He devised a set of rules to create a negativo-affirmative number and another set of rules to return the number to a common one. There are sets of rules for performing the arithmetic as well. Once learned, the method does, in fact, speed up the multiplication of large numbers.

Besides mathematics, Colson was fluent in Latin, Italian and French. His own work was published in both Latin and English, and he did a number of translations in many other areas. When Saunderson's Elements of Algebra was translated into French, Colson's essay on him was translated as well. ³

His first translations were publications for the sea faring community, The mariners magazine and The mariners new kalendar. They contained such topics as geometry, trigonometry, navigation by the heavens, day and night, and sailing by Mercator's principles. He commented on and explained much of the material that he translated. From the French, he translated a work of experimental philosophy⁴ and a dictionary of the Bible.⁵ He translated a work from Latin by a Dutch author⁶ in natural philosophy and a book on linear perspective.⁷

His most notable translation is probably that of Newton's work. In 1736, he published an English version of Newton's Method of Fluxions and Infinite Series originally written in Latin.⁸ In the same year he also published the English edition of Geometrica Analytica by Newton.⁹ Each of these translations contained substantial commentary by Colson. In 1761, an edition of Newton's Arithmetica universalis was published in Latin with Colson's commentary, also in Latin.

Colson showed himself to be ahead of his times by his translation of Analyitical Institutions written originally in Italian by Donna Maria Agnesi, a professor of mathematics and philosophy at the University of Bolgna. It was the first book on calculus written by a woman, and Colson intended the translation to make calculus more accessible to women.¹⁰ His manuscript was not published until 1801, forty-one years after his death. He had also prepared a manuscript, with the same idea in mind, called The Plan of the Lady's System of Analytics, which still remains in the Cambridge Library.

Footnotes

1. Dictionary of National Biography.
2. Colson 1707.
3. Saunderson 1756.
4. Abbe Jean Nollet, Lectures in experimental philosophy (London: J.J. Wren, 1792).
5. Augustin Calmet, An historical, critical, geographical, chronological, and etymological dictionary of the Holy Bible (London: J.J. and P. Knapton, 1732).
6. Petrus van Musschenbroek, The elements of natural philosophy Chiefly intended for the use of students in universities (London: John J. Nourse, 1744)
7. Brook Taylor, New principles of linear perspective (London: John Ward, 1749).
8. Howard Eves, An Introduction to the History of Mathematics (New York: Holt, Rinehart and Winston 1969), 334.
9. H.W. Turnbull, ed., The Mathematical Discoveries of Newton (London: Blackie and Son, 1945), 64.
10. Florian Cajori, A History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodhouse (Chicago: Open Court Press, 1919), 248.