Isaac Barrow
Isaac Barrow | |
---|---|
Born | October 1630 London, England |
Died | 4 May 1677 London, England | (aged 46)
Nationality | English |
Education | Felsted School, Trinity College, Cambridge |
Known for | Fundamental theorem of calculus Optics |
Scientific career | |
Fields | Mathematics |
Institutions | Trinity College, Cambridge, Gresham College |
Academic advisors | James Duport |
Notable students | Isaac Newton |
Notes | |
His mentor was Gilles Personne de Roberval in Paris and Vincenzo Viviani in Florence. |
Isaac Barrow (October 1630 – 4 May 1677) was an English
Life
Early life and education
Barrow was born in London. He was the son of Thomas Barrow, a linen draper by trade. In 1624, Thomas married Ann, daughter of William Buggin of North Cray, Kent and their son Isaac was born in 1630. It appears that Barrow was the only child of this union—certainly the only child to survive infancy. Ann died around 1634, and the widowed father sent the lad to his grandfather, Isaac, the Cambridgeshire J.P., who resided at Spinney Abbey.[2] Within two years, however, Thomas remarried; the new wife was Katherine Oxinden, sister of Henry Oxinden of Maydekin, Kent. From this marriage, he had at least one daughter, Elizabeth (born 1641), and a son, Thomas, who apprenticed to Edward Miller, skinner, and won his release in 1647, emigrating to Barbados in 1680.[3]
Early career
Isaac went to school first at
Travel
He spent the next four years travelling across France, Italy, Smyrna and Constantinople, and after many adventures returned to England in 1659. He was known for his courageousness. Particularly noted is the occasion of his having saved the ship he was upon, by the merits of his own prowess, from capture by
Later career
Work
On the
His earliest work was a complete edition of the Elements of Euclid, which he issued in Latin in 1655, and in English in 1660; in 1657 he published an edition of the Data. His lectures, delivered in 1664, 1665, and 1666, were published in 1683 under the title Lectiones Mathematicae; these are mostly on the metaphysical basis for mathematical truths. His lectures for 1667 were published in the same year, and suggest the analysis by which Archimedes was led to his chief results. In 1669 he issued his Lectiones Opticae et Geometricae. It is said in the preface that Newton revised and corrected these lectures, adding matter of his own, but it seems probable from Newton's remarks in the fluxional controversy that the additions were confined to the parts which dealt with optics. This, which is his most important work in mathematics, was republished with a few minor alterations in 1674. In 1675 he published an edition with numerous comments of the first four books of the On Conic Sections of Apollonius of Perga, and of the extant works of Archimedes and Theodosius of Bithynia.
In the optical lectures many problems connected with the reflection and refraction of light are treated with ingenuity. The geometrical focus of a point seen by reflection or refraction is defined; and it is explained that the image of an object is the locus of the geometrical foci of every point on it. Barrow also worked out a few of the easier properties of thin lenses, and considerably simplified the Cartesian explanation of the rainbow.
Barrow was the first to find the integral of the secant function in closed form, thereby proving a conjecture that was well-known at the time.
Death and legacy
Barrow died unmarried in London at the early age of 46, and was buried at Westminster Abbey. John Aubrey, in the Brief Lives, attributes his death to an opium addiction acquired during his residence in Turkey.
Besides the works above mentioned, he wrote other important treatises on mathematics, but in literature his place is chiefly supported by his sermons,[11] which are masterpieces of argumentative eloquence, while his Treatise on the Pope's Supremacy is regarded as one of the most perfect specimens of controversy in existence. Barrow's character as a man was in all respects worthy of his great talents, though he had a strong vein of eccentricity.
Calculating tangents
The geometrical lectures contain some new ways of determining the areas and
Fermat had observed that the tangent at a point P on a curve was determined if one other point besides P on it were known; hence, if the length of the subtangent MT could be found (thus determining the point T), then the line TP would be the required tangent. Now Barrow remarked that if the abscissa and ordinate at a point Q adjacent to P were drawn, he got a small triangle PQR (which he called the differential triangle, because its sides QR and RP were the differences of the abscissae and ordinates of P and Q), so that K
- TM : MP = QR : RP.
To find QR : RP he supposed that x, y were the co-ordinates of P, and x − e, y − a those of Q (Barrow actually used p for x and m for y, but this article uses the standard modern notation). Substituting the co-ordinates of Q in the equation of the curve, and neglecting the squares and higher powers of e and a as compared with their first powers, he obtained e : a. The ratio a/e was subsequently (in accordance with a suggestion made by Sluze) termed the angular coefficient of the tangent at the point.
Barrow applied this method to the curves
- x2 (x2 + y2) = r2y2, the kappa curve;
- x3 + y3 = r3;
- x3 + y3 = rxy, called la galande;
- y = (r − x) tan πx/2r, the quadratrix; and
- y = r tan πx/2r.
It will be sufficient here to take as an illustration the simpler case of the parabola y2 = px. Using the notation given above, we have for the point P, y2 = px; and for the point Q:
- (y − a)2 = p(x − e).
Subtracting we get
- 2ay − a2 = pe.
But, if a be an infinitesimal quantity, a2 must be infinitely smaller and therefore may be neglected when compared with the quantities 2ay and pe. Hence
- 2ay = pe, that is, e : a = 2y : p.
Therefore,
- TM : y = e : a = 2y : p.
Hence
- TM = 2y2/p = 2x.
This is exactly the procedure of the differential calculus, except that there we have a rule by which we can get the ratio a/e or dy/dx directly without the labour of going through a calculation similar to the above for every separate case.
Publications
- Epitome Fidei et Religionis Turcicae (1658)
- "De Religione Turcica anno 1658" (poem)
- Euclidis Elementorum (1659) [in Latin] Euclide's Elements (1660) [in English] translations of Euclid's Elements
- Lectiones Opticae (1669)
- Lectiones Geometricae (1670), translated as Geometrical Lectures (1735) by Edmund Stone, later translated as The Geometrical Lectures of Isaac Barrow (1916) by James M. Child [12]
- Apollonii Conica (1675) translation of Conics
- Archimedis Opera (1675) translation of Archimedes’s works
- Theodosii Sphaerica (1675) translation of Theodosius' Spherics
- A Treatise on the Pope's Supremacy, to which is Added a Discourse Concerning the Unity of the Church (1680) (1859 edition)
- Lectiones Mathematicae (1683) translated as The Usefulness of Mathematical Learning (1734) by John Kirkby
- Of Contentment, Patience, and Resignation to the Will of God (1685)
- The works of the learned Isaac Barrow, D.D. (1700) Vol. 1, Vol. 2–3
- The Works of Dr. Isaac Barrow (1830), Vol. 1, Vol. 2, Vol. 3, Vol. 4, Vol. 5, Vol. 6, Vol. 7 [sermons and theological essays]
See also
- The lunar crater Barrowis named after him
- Gresham Professors of Geometry
References
- ^ Child, James Mark; Barrow, Isaac (1916). The Geometrical Lectures of Isaac Barrow. Chicago: Open Court Publishing Company.
- ^ 'The Abbey Scientists' Hall, A.R. p12: London; Roger & Robert Nicholson; 1966
- ISBN 1-4120-6700-6.
- ^ Craze, M. R. (1955). A History of Felsted School, 1564–1947. Cowell.
- ^ O'Connor, J. J.; Robertson, E. F. "gap-system". School of Mathematics and Statistics University of St Andrews. Archived from the original on 26 December 2010. Retrieved 1 February 2012.
- ISBN 9780521306942.
- ^ "Barrow, Isaac (BRW643I)". A Cambridge Alumni Database. University of Cambridge.
- ^ Manuel, Frank E. (1968). A Portrait of Isaac Newton. Belknap Press, MA. p. 92.
- Trinity College, Dublin School of Mathematics. Retrieved 1 February 2012
- ^ For a summary of the Barrow–Newton relationship, see Gjersten, Derek (1986). The Newton Handbook. London: Routledge & Kegan Paul. pp. 54–55.
- ^ Isaac Barrow, John Tillotson, Abraham Hill – The works of the learned Isaac Barrow ... Printed by J. Heptinstall, for Brabazon Aylmer, 1700 Published by DR JOHN TILLOTSON THE LORD ARCHBISHOP OF CANTERBURY {&} Isaac Barrow – The theological works of Isaac Barrow, Volume 1 The University Press, 1830 {&} Isaac Barrow, Thomas Smart Hughes 1831 – The Works of Dr. Isaac Barrow: With Some Account of His Life, Summary of Each Discourse, Notes, &c (1831)- Fourth Volume A.J. Valpy. Retrieved 1 February 2012
- (PDF) from the original on 27 April 2014.
Further reading
- "Barrow, Isaac", A Short Biographical Dictionary of English Literature, 1910 – via Wikisource
- W. W. Rouse Ball. A Short Account of the History of Mathematics (4th edition, 1908)
- Clinton Bennett, Promise, Predicament and Perplexity: Isaac Barrow (1630–1677) on Islam (Gorgias Press, 2022)
- Cheesman, Francis W. (2005). Isaac Newton's Teacher. Trafford. ISBN 9781412067003.
- Feingold, Mordechai, ed. (1990). Before Newton: The life and times of Isaac Barrow. Cambridge University Press. ISBN 9780521306942.
- Hill, Abraham (1830) [1683]. "Biographical Memoir of Dr. Isaac Barrow". The Works of Dr. Isaac Barrow. By Barrow, Isaac. Hughes, Thomas Smart (ed.). Vol. 1. A.J. Valpy. pp. ix–xcii.
External links
- Media related to Isaac Barrow at Wikimedia Commons
- O'Connor, John J.; Robertson, Edmund F., "Isaac Barrow", MacTutor History of Mathematics Archive, University of St Andrews
- Isaac Barrow at the Mathematics Genealogy Project
- Works by Isaac Barrow at Project Gutenberg
- Works by or about Isaac Barrow at Internet Archive
- The Master of Trinity at Trinity College, Cambridge
- Correspondence of Scientific Men of the Seventeenth Century at Google Books
- The Usefulness of Mathematical Learning Explained and Demonstrated at Google Books