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Thomas Harriot College of Arts and Sciences

Thomas Harriot Facts
1. Dates
Born: Oxfordshire, c.1560
Died: London, 2 July 1621
Dateinfo: Birth Uncertain
Lifespan: 61
2. Father
Occupation: Unknown
The only information, in the records at Oxford, is that Harriot's father was a commoner (plebeian).
No information on financial status.
3. Nationality
Birth: English
Career: Englsih
Death: English
4. Education
Schooling: Oxford
Oxford University, St. Mary Hall, 1577-80; B.A., 1580.
5. Religion
Affiliation: Anglican, Heterodox
During his lifetime there were all sorts of stories about Harriot's atheism, centering on the charge that he challenged the universal authority of Scripture. There seems to be no doubt that he held atomistic views, which had the potential at least to be in conflict with orthodoxy. Nevertheless, I list Heterodoxy with grave doubts. Neither I nor anyone else has been able to find solid evidence to support the rumors. The rumors themselves began with a Jesuit diatribe of 1592 against the religious order in England; that hardly increases my confidence in the truth of the rumors.
6. Scientific Disciplines
Primary: Astronomy, Mathematics, Navigation
Subordinate: Physics, Optics, Chemistry
Harriot carried out extensive telescopic observations of the satellites of Jupiter and of sunspots.
He enriched algrebra with a theory of equations and one of interpolation. Artes analyticae praxis, posthumous, 1631, was Harriot's only published scientific work.
Especially early in his career, he worked on navigation for his patron Raleigh, and he continued to be interested in the problems of navigation all his life. He wrote a treatise, Arcticon, which has been lost. He investigated the theory of Mercator's map.
In the early 90's he began to investigate optics; he discovered the sine law and measured the refractive indices of 13 different substances.
He investigated free motion and motion resisted in air, and ballistic curves. He measured the specific gravities of a number of different substances.
In the period 1599-1600 he experimented very assiduously in chemistry, or perhaps alchemy.
Natural history could also be listed, because Harriot did investigate the natural history of Virginia during his year there in Raleigh's colony.
7. Means of Support
Primary: Patronage
Secondary: Schoolmastering
There is no solid evidence of what Harriot did immediately after taking his degree, but there are several good hints (see Batho) that he gave lessons in London. Shirley talks about students throughout his life.
At least by 1584 he was part of the household of Sir Walter Raleigh to whom he acted as a tutor and then steward. At this time at least he had an annual pension from Raleigh. Raleigh apparently gave Harriot a property which he held until 1597. After he returned from Virginia he helped manage Raleigh's vast estate in Ireland; he also received a property there. He continued in Raleigh's service for the rest of Raleigh's life.
In the early 90's he also entered the service of the Earl of Northumberland. Northumberland was Raleigh's friend, and there is no suggestion of conflict between the two services. The first payment to Harriot is recorded in the Northumberland accounts in 1593, and by 1598 at the latest he began to receive an annual pension of £80 (later increased to £100), much the largest pension on the Earl's rolls, and the pension continued until Harriot's death. Apparently Northumberland set him up with a property in Durham in 1595 (held by Harriot until 1515), and he assigned a house to him on the estate at Syon, just west of London along the Thames.
Harriot's relations with Sir William Lower, a member of the Welsh genty and of Parliament, are unclear. I certainly suspect patronage, but I saw no evidence of specific benefits from Lower.
8. Patronage
Types: Gentry, Aristrocrat
See above on Raleigh. Harriot's Brief and True Report (on the Roanoke expedition) was published to defend Raleigh's plans. In his will of 1597 Raleigh left a grant of £100 per annum to Harriot--though I think this was not the will in effect when Raleigh was executed some twenty years later.
Harriot began to receive an annual pension from the Earl of Northumberland in 1598 at the latest. See the other favors above.
9. Technological Involvement
Types: Navigation, Cartography, Instruments, Hydraulics
Harriot was always concerned with navigation. He instructed Raleigh's captains in the science and composed a book, Arcticon.
Statistical survey in Virginia, 1585. It included technical details, and a survey of the coast line and maps. He helped to map Raleigh's Irish estate, and later he drew a map of the Guiana expedition. In his will he left maps (by implication, manuscript maps that he had drawn) to the Earl of Northumberland. He drew a map of the moon.
Harriot constructed a twelve foot radius astronomicus for observations, especially of the sun for the determination of latitude. Apparently he developed the astronomical telescope independedntly at about the same time as Galileo. He suggested several improved navigational instruments, including what may have been the first backstaff.
His manuscripts seem to show that he worked on the water supply for Syon House and for the residence of the Lord Chamberlain.
Harriot studied ballistic trajectories with the intent of improving artillery performance. Batho speaks of his interest, shared with the Earl of Northumberland, in fortification. However, I found no evidence that any of this went outside his study, and I am not going to list military engineering.
10. Scientific Societies
Memberships: None
Informal Connections: Acquainted with John Dee and Thomas Allen. There is not much documented knowledge of correspondence or personal contact with scientists of his own rank, though he did correspond briefly with Kepler.
Mathematicians in his circle: Nathaniel Torporley, Walter Warner, Robert Hughes, Thomas Aylesburg, and William Lower. A number of Lower's letters to Harriot survive.
  1. John Aubrey, Brief Lives Dictionary of National Biography (repr., London: Oxford University Press, 1949-50), 8, 1321-2. Biographia Britannica, 1st ed. (London, 1747-66), 4, 2539-43.
  2. Muriel Rukeyser, The Traces of Thomas Harriot, (New York, 1971).
  3. Henry Stevens, Thomas Harriot, the Mathematician, the Philosopher, and the Scholar, (London, 1900).
  4. John W. Shirley, Thomas Harriot: A Biography, (Oxford, 1983).
  5. _____, ed., Thomas Harriot. Renaissance Scientist, (Oxford, 1974).
  6. _____, ed., A Source Book for the Study of Thomas Harriot, (New York, 1981). Johannes A. Lohne, "Dokumente zur Revalidierung von Thomas Harriot als Algebraiker," Archive for History of Exact Sciences, 3 (1966), 185-205.
  7. _____, "Harriot on Ballistic Parabolas," ibid., 20 (1979), 230-64.
  8. _____, Harriot's Scientific Writings," ibid., 20 (1979), 265-312.
  9. Jean Jacquot, "Thomas Harriot's Reputation for Impiety," Notes and Records of the Royal Society, 9 (1952), 164-87.
  10. G.R. Batho, Thomas Harriot and the Northumberland Household, (London, 1983)
Not Available and Not Consulted
  1. John J. Roche, "Harriot's Regiment of the Sun and its Background in 16th-Century Navigation," British Journal for the History of Science, 14 (1981), 245-61.
  2. David Beers Quinn, The Roanoke Voyages, 2 vols. (Hakluyt Society Publications, 2nd ser., 104) (London, 1952). J.V. Pepper, "Harriot's Work on the True Sea-Chart," Acts of the XII Congress of the History of Science, 1968, (1971), 4, 135- 8.
  3. Suzanne S. Webb, "Raleigh and Atheism in Elizabethan and Early Stuart England," Albion, 1 (1969), 10-18.
Compiled by:
Richard S. Westfall
Department of History and Philosophy of Science
Indiana University
Source: http://galileo.rice.edu/Catalog/NewFiles/harriot.html


Quadratic Equation

In the years after Cardan's Ars Magna many mathematicians contributed to the solution of cubic and quartic equations. Viète, Harriot, Tschirnhaus, Euler, Bezout and Descartes all devised methods. Tschirnhaus's methods were extended by the Swedish mathematician E S Bring near the end of the 18th Century.

Thomas Harriot made several contributions. One of the most elementary to us, yet showing a marked improvement in understanding, was the observation that if x = b, x = c, x = d are solutions of a cubic then the cubic is

(x - b)(x - c)(x - d) = 0.

Harriot also had a nice method for solving cubics. Consider the cubic

x3 + 3b2x = 2c3

Put x = (e2 - b2)/e. Then

e6 - 2c3e3 = b6

which is a quadratic in e3, and so can be solved for e3 to get

e3 = c3 +√(b6 + c6).


e3(e3 - 2c3) = b6 so that b6/e3 = -c3 +√(b6 + c6).

Now x = e - b2/e and both e and b2/e are cube roots of expressions given above.