Isaac Barrow

Isaac Barrow
Born	October, 1630 London, England
Died	May 4, 1677 London, England
Residence	England
Nationality	English
Field	Mathematician
Institution	University of Cambridge
Alma Mater	University of Cambridge
Doctoral Advisor	James Duport
Doctoral Students	Isaac Newton
Known for	Geometry and optics
Note that PhDs in Cambridge did not exist until 1919. Barrow received an MA from Cambridge in 1652, and was a student of James Duport who played the the equivalent mentorship role as a doctoral advisor. Duport was a classicist, and Barrow really learned his mathematics by working under Gilles Personne de Roberval in Paris and Vincenzio Viviani in Florence.

Isaac Barrow (October 1630 - May 4, 1677) was an English divine, scholar and mathematician who is generally given minor credit for his role in the development of modern calculus; in particular, for his work regarding the tangent; for example, Barrow is given credit for being the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's. Lunar crater Barrow is named after him. Download high resolution version (529x631, 88 KB)In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Look up October in Wiktionary, the free dictionary. ... Events February 22 - Native American Quadequine introduces Popcorn to English colonists. ... London (pronounced ) is the capital city of England and the United Kingdom. ... 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Motto: (French for God and my right) Anthem: Multiple unofficial anthems Capital London Largest city London Official language(s) English (de facto) Unification    - by Athelstan AD 927  Area    - Total 130,395 km² (1st in UK)   50,346 sq mi  Population    - 2005 est. ... Image File history File links Flag_of_England_(bordered). ... Motto: (French for God and my right) Anthem: Multiple unofficial anthems Capital London Largest city London Official language(s) English (de facto) Unification    - by Athelstan AD 927  Area    - Total 130,395 km² (1st in UK)   50,346 sq mi  Population    - 2005 est. ... Image File history File links Flag_of_England_(bordered). ... Motto: (French for God and my right) Anthem: Multiple unofficial anthems Capital London Largest city London Official language(s) English (de facto) Unification    - by Athelstan AD 927  Area    - Total 130,395 km² (1st in UK)   50,346 sq mi  Population    - 2005 est. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ... The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ... James Duport (1606, Cambridge - July 17th 1679, Peterborough) was an English classical scholar. ... Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ... Table of Geometry, from the 1728 Cyclopaedia. ... Table of Opticks, 1728 Cyclopaedia Optics ( appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ... James Duport (1606, Cambridge - July 17th 1679, Peterborough) was an English classical scholar. ... Gilles Personne de Roberval (August 10, 1602 - October 27, 1675), French mathematician, was born at Roberval, near Beauvais, France. ... Vincenzo Viviani. ... Events February 22 - Native American Quadequine introduces Popcorn to English colonists. ... May 4 is the 124th day of the year in the Gregorian calendar (125th in leap years). ... Events First performance of Racines tragedy, Phèdre Sarah Churchill marries John Churchill, 1st Duke of Marlborough Battle of Cassel, Philippe I of Orléans defeats William of Orange Mary II of England marries William of Orange English Statute of frauds is passed into law Battle of Landskrona Elias... Motto: (French for God and my right) Anthem: Multiple unofficial anthems Capital London Largest city London Official language(s) English (de facto) Unification    - by Athelstan AD 927  Area    - Total 130,395 km² (1st in UK)   50,346 sq mi  Population    - 2005 est. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Calculus is the current Good Article Collaboration of the week! Please help to improve this article to the highest of standards. ... In mathematics, the word tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry. ... The kappa curve has two vertical asymptotes. ... Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ... Wikipedia does not yet have an article with this exact name. ... Barrow is an old lunar crater that is located near the northern limb of the Moon. ...

Youth, education, and description

Barrow was born in London. 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. He completed his education at Trinity College, Cambridge, where his uncle and namesake, afterwards Bishop of St Asaph, was a Fellow. 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; 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. He spent the next four years traveling across France, Italy and even Constantinople, and after many adventures returned to England in 1659. London (pronounced ) is the capital city of England and the United Kingdom. ... Charterhouse School is an English public school, located in Godalming in the county of Surrey. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names Kings Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street... The Bishop of Saint Asaph is the Ordinary of the Church in Wales Diocese of Saint Asaph. ... // Events January 17 - Englands Long Parliament passes the Vote of No Address, breaking off negotiations with King Charles I and thereby setting the scene for the second phase of the English Civil War. ... // Events January 30 - King Charles I of England, Scotland and Ireland is beheaded. ... Events March 25 - Saturns largest moon, Titan, is discovered by Christian Huygens. ... // Events May 25 - Richard Cromwell resigns as Lord Protector of England following the restoration of the Long Parliament, beginning a second brief period of the republican government called the Commonwealth. ...

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. 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. He wrote with a sustained and somewhat stately eloquence, and with his blameless life and scrupulous conscientiousness was an impressive personage of the time. Look up pirate and piracy in Wiktionary, the free dictionary. ... Charles II (29 May 1630 – 6 February 1685) was the King of England, King of Scots, and King of Ireland from 30 January 1649 (de jure) or 29 May 1660 (de facto) until his death. ...

Career and works

In 1660, he was ordained and appointed to the Regius Professorship of Greek at Cambridge. 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. 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. 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. 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. // Events January 1 - Colonel George Monck with his regiment crosses from Scotland to England at the village of Coldstream and begins advance towards London in support of English Restoration. ... The Regius Professorship of Greek is one of the oldest and most prestigious of the professorships at the University of Cambridge. ... Shown within Cambridgeshire Geography Status: City (1951) Region: East of England Admin. ... Events February 1 - The Chinese pirate Koxinga seizes the island of Taiwan after a nine-month siege. ... Table of Geometry, from the 1728 Cyclopaedia. ... Gresham College is an unusual institution of higher learning in London which enrolls no students and grants no degrees. ... // Events Prix de Rome scholarship established for students of the arts. ... The incumbent of the Lucasian Chair of Mathematics, the Lucasian Professor is the holder of a mathematical professorship at Cambridge University. ... // Events Samuel Pepys stopped writing his diary. ... Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ... Divinity has a number of related uses in the field of religious belief and study. ... 1670 was a common year beginning on a Saturday in countries using the Julian calendar and a Wednesday in countries using the Gregorian calendar. ... Events England, France, Munster and Cologne invade the United Provinces, therefore this name is know as ´het rampjaar´ (the disaster year) in the Netherlands. ...

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.

Statue of Isaac Barrow in the chapel of Trinity College, Cambridge

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. Download high resolution version (768x1024, 114 KB)Statue of Isaac Barrow in chapel of Trinity College, Cambridge Photograph © Andrew Dunn, 8 September 2004. ... Download high resolution version (768x1024, 114 KB)Statue of Isaac Barrow in chapel of Trinity College, Cambridge Photograph © Andrew Dunn, 8 September 2004. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names Kings Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street... Euclid (also referred to as Euclid of Alexandria) (Greek: ) (c. ... The English language is a West Germanic language that originates in England. ... // Events January 1 - Colonel George Monck with his regiment crosses from Scotland to England at the village of Coldstream and begins advance towards London in support of English Restoration. ... Events January 8 - Miles Sindercombe, would-be-assassin of Oliver Cromwell, and his group are captured in London February - Admiral Robert Blake defeats the Spanish West Indian Fleet in a battle over the seizure of Jamaica. ... Events March 12 - New Jersey becomes a colony of England. ... 1665 (MDCLXV) was a common year starting on Thursday of the Gregorian calendar (or a common year starting on Sunday of the 10-day slower Julian calendar). ... 1666 is often called Annus Mirabilis. ... Events June 6 - The Ashmolean Museum opens as the worlds first university museum. ... // Events January 20 - Poland cedes Kyiv, Smolensk, and eastern Ukraine to Russia in the Treaty of Andrusovo that put a final end to the Deluge, and Poland lost its status as a Central European power. ... Archimedes (Greek: ) (c. ... // Events Samuel Pepys stopped writing his diary. ... Events February 19 - England and the Netherlands sign the Treaty of Westminster. ... Events January 5 - The Battle of Turckeim June 18 - Battle of Fehrbellin August 10 - King Charles II of England places the foundation stone of the Royal Greenwich Observatory in London - construction begins November 11 - Guru Gobind Singh becomes the Tenth Guru of the Sikhs. ... Apollonius of Perga [Pergaeus] (c. ... Theodosius of Bithynia (ca. ...

In the optical lectures many problems connected with the reflexion and refraction of light are treated with ingenuity. The geometrical focus of a point seen by reflexion 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. René Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher, mathematician, and scientist. ... Full featured rainbow in Wrangell-St. ...

New method of 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. ... Johann van Waveren Hudde (April 23, 1628 - April 15, 1704) was a mathematician. ... Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southwestern France, and a mathematician who is given credit for his contribution towards the development of modern calculus. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ...

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 For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...

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 I alter these to agree with modern practice). 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. In number and more generally in algebra, a ratio is the linear relationship between two quantities of the same unit. ...

Barrow applied this method to the curves

1. x² (x² + y²) = r²y²;
2. x³ + y³ = r³;
3. x³ + y³ = rxy, called la galande;
4. y = (r - x) tan πx/2r, the quadratrix; and
5. 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

TP : 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.

References

• This article incorporates public domain text from: Cousin, John William (1910). A Short Biographical Dictionary of English Literature. 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.

The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ... A Short Biographical Dictionary of English Literature is a collection of biographies of writers by John W. Cousin, published around 1910. ... Walter William Rouse Ball (1850 August 14–1925 April 4) was a Brtish mathematician, and a fellow at Trinity College, Cambridge from 1878 to 1905. ...

See also

• list of Gresham Professors of Geometry

The Professor of Geometry at Gresham College is appointed by the City of London Corporation. ...

External links

• O'Connor, John J., and Edmund F. Robertson. "Isaac Barrow". MacTutor History of Mathematics archive.
• Works by Isaac Barrow at Project Gutenberg