| Isaac Barrow | |
 Isaac Barrow (1630-1677)
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| Born | October 1630 London, England |
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| Died | 4 May 1677 (aged 46) London, England |
| Nationality | United Kingdom |
| Fields | Mathematics |
| Institutions | University of Cambridge |
| Alma mater | University of Cambridge |
| Academic advisors | James Duport |
| Notable students | Isaac Newton |
| Known for | Geometry and optics |
| Influences | Gilles Personne de Roberval Vincenzio Viviani |
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Notes
His mentor was James Duport who was a classicist, but Barrow really learned his mathematics by working under Gilles Personne de Roberval in Paris and Vincenzio Viviani in Florence. October events and holidays Children's Book Week ( England) - First Week of October National Day ( China People's Republic London ( ˈlʌndən is the capital and largest urban area in the United Kingdom. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland Events 1256 - The Augustinian monastic order is constituted at the Lecceto Monastery when Pope Alexander IV London ( ˈlʌndən is the capital and largest urban area in the United Kingdom. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the James Duport (1606 Cambridge &ndash 17 July 1679, Peterborough) was an English Classical scholar. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Gilles Personne de Roberval ( August 10, 1602 - October 27 1675) French Mathematician, was born at Roberval near Vincenzo Viviani ( April 5, 1622 - September 22, 1703) was an Italian Mathematician and Scientist. James Duport (1606 Cambridge &ndash 17 July 1679, Peterborough) was an English Classical scholar. Gilles Personne de Roberval ( August 10, 1602 - October 27 1675) French Mathematician, was born at Roberval near Vincenzo Viviani ( April 5, 1622 - September 22, 1703) was an Italian Mathematician and Scientist. |
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Isaac Barrow (October 1630 – May 4, 1677) was an English scholar and mathematician who is generally given credit for his early role in the development of calculus; in particular, for the discovery of the fundamental theorem of calculus. Events 1256 - The Augustinian monastic order is constituted at the Lecceto Monastery when Pope Alexander IV The Kingdom of England was a State (927-1707 located in Western Europe dating from the ninth or tenth century to the early eighteenth century when it was legally A mathematician is a person whose primary area of study and research is the field of Mathematics. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives The fundamental theorem of calculus specifies the relationship between the two central operations of Calculus, differentiation and integration. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. In Geometry, the kappa curve or Gutschoven's curve is a two-dimensional Algebraic curve resembling the Greek letter &kappa (kappa Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Lunar crater Barrow is named after him. This is a list of craters on the Moon. The large majority of these features are Impact craters The crater nomenclature is governed by the International Barrow is an old lunar crater that is located near the northern limb of the Moon.
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Biography
Barrow was born in London. London ( ˈlʌndən is the capital and largest urban area in the United Kingdom. He went to school first at Charterhouse (where he was so turbulent and pugnacious that his father was heard to pray that if it pleased God to take any of his children he could best spare Isaac), and subsequently to Felstead. Charterhouse, originally Sutton's Hospital in Charterhouse, is a prominent boys independent or public school as they're known in Britain between Felsted School is a public school situated in the beautiful village of Felsted, England. He completed his education at Trinity College, Cambridge; his uncle and namesake, afterwards Bishop of St Asaph, was a Fellow of Peterhouse. Trinity College is a constituent college of the University of Cambridge in Cambridge, England. Isaac Barrow ( 1613 - 24 June 1680) was an English clergyman and Bishop consecutively of Sodor and Man and St Asaph, as well as serving The Bishop of St Asaph heads the Church in Wales Diocese of St Asaph. Peterhouse is the oldest college in the University of Cambridge. He took to hard study, distinguishing himself in classics and mathematics; after taking his degree in 1648, he was elected to a fellowship in 1649; Barrow received an MA from Cambridge in 1652 as a student of James Duport; he then resided for a few years in college, and became candidate for the Greek Professorship at Cambridge, but in 1655 he was driven out by the persecution of the Independents. James Duport (1606 Cambridge &ndash 17 July 1679, Peterborough) was an English Classical scholar. He spent the next four years travelling across France, Italy and even Constantinople, and after many adventures returned to England in 1659.
He is described as "low in stature, lean, and of a pale complexion," slovenly in his dress, and an inveterate smoker. He was noted for his strength and courage, and once when travelling in the East he saved the ship by his own prowess from capture by pirates. Piracy is Robbery committed at sea or sometimes on shore without a commission from a sovereign Nation (as distinct from Privateering A ready and caustic wit made him a favourite of Charles II, and induced the courtiers to respect even if they did not appreciate him. Charles II (Charles Stuart 29 May 1630 – 6 February 1685 was the King of England, Scotland, and Ireland. He wrote with a sustained and somewhat stately eloquence, and with his blameless life and scrupulous conscientiousness was an impressive personage of the time.
Career
In 1660, he was ordained and appointed to the Regius Professorship of Greek at Cambridge. The Regius Professorship of Greek is one of the oldest and most prestigious of the professorships at the University of Cambridge. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Gresham College is an unusual institution of higher learning off Holborn in central London. The incumbent of the Lucasian Chair of Mathematics, the Lucasian Professor is the holder of a mathematical Professorship at the University of Cambridge During his tenure of this chair he published two mathematical works of great learning and elegance, the first on Geometry and the second on Optics. In 1669 he resigned in favour of his pupil, Isaac Newton, who was long considered his only superior among English mathematicians. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements About this time also he composed his Expositions of the Creed, The Lord's Prayer, Decalogue, and Sacraments. For the remainder of his life he devoted himself to the study of divinity. Divinity and divine (sometimes 'the Divinity' or 'the Divine' are broadly applied but loosely defined terms used variously within different faiths and belief systems — He was made a D. D. by royal mandate in 1670, and two years later Master of Trinity College (1672), where he founded the library, and held the post until his death.
Besides the works above mentioned, he wrote other important treatises on mathematics, but in literature his place is chiefly supported by his sermons, 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. He died unmarried in London at the early age of 47.
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. Trinity College is a constituent college of the University of Cambridge in Cambridge, England. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States 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. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer 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. Theodosius of Bithynia (ca 160 BC–ca 100 BC was a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere
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. A rainbow is an optical and meteorological phenomenon that causes a spectrum of Light to appear in the Sky when the Sun
Calculating tangents
The geometrical lectures contain some new ways of determining the areas and tangents of curves. The most celebrated of these is the method given for the determination of tangents to curves, and this is sufficiently important to require a detailed notice, because it illustrates the way in which Barrow, Hudde and Sluze were working on the lines suggested by Fermat towards the methods of the differential calculus. In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object Johannes (van Waveren Hudde ( April 23, 1628, Amsterdam - April 15, 1704, Amsterdam was a Burgomaster (mayor of Amsterdam Pierre de Fermat pjɛːʁ dəfɛʁ'ma ( 17 August 1601 or 1607/8 &ndash 12 January 1665) was a French Lawyer at the Differential Calculus, a field in Mathematics, is the study of how functions change when their inputs change
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 PR and PQ were the differences of the abscissae and ordinates of P and Q), so that
- TM : MP = QR : RP. A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line
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. A ratio is an expression which compares quantities relative to each other
Barrow applied this method to the curves
- x² (x² + y²) = r²y²;
- x³ + y³ = r³;
- x³ + y³ = rxy, called la galande;
- y = (r - x) tan πx/2r, the quadratrix; and
- y = r tan πx/2r. In Mathematics, a quadratrix (from the Latin word quadrator squarer is a curve having Ordinates which are a measure of the area (or quadrature
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.
See also
- list of Gresham Professors of Geometry
References
- This article incorporates public domain text from: Cousin, John William (1910). The Professor of Geometry at Gresham College, London gives free educational lectures to the general public The public domain is a range of abstract materials &ndash commonly referred to as Intellectual property &ndash which are not owned or controlled by anyone A Short Biographical Dictionary of English Literature. A Short Biographical Dictionary of English Literature is a collection of biographies of writers by John William Cousin (1849-1910 published in 1910 London, J. M. Dent & sons; New York, E. P. Dutton.
- Adapted from "A Short Account of the History of Mathematics" (4th edition, 1908) by W. W. Rouse Ball. Walter William Rouse Ball ( 14 August 1850 – 4 April 1925) was a British Mathematician, Lawyer and a fellow
External links
- O'Connor, John J. & Robertson, Edmund F. , “Isaac Barrow”, MacTutor History of Mathematics archive
- Works by Isaac Barrow at Project Gutenberg
- The Master of Trinity at Trinity College, Cambridge
| Academic offices | ||
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| Preceded by John Pearson |
Master of Trinity College, Cambridge 1672–1677 |
Succeeded by John North |
| Persondata | |
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| NAME | Barrow, Isaac |
| ALTERNATIVE NAMES | |
| SHORT DESCRIPTION | Mathematician |
| DATE OF BIRTH | October, 1630 |
| PLACE OF BIRTH | London, England |
| DATE OF DEATH | May 4, 1677 |
| PLACE OF DEATH | London, England |
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