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Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of
infinitesimal calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of ari ...
; in particular, for proof of the
fundamental theorem of calculus The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each time) with the concept of integrating a function (calculating the area under its graph, ...
. His work centered on the properties of the
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
; 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 . The kappa curve was first studied by Gérard van Gutschoven around 1662. In the history of mathematics, it is remembered as one o ...
. He is also notable for being the inaugural holder of the prestigious Lucasian Professorship of Mathematics, a post later held by his student,
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
.


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. 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.


Early career

Isaac 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
Felsted School (Keep your Faith) , established = , closed = , type = Public school Independent day and boarding , religion = Church of England , president = , head_label = Headmaster , head = Chris Townsend , r_head ...
, where he settled and learned under the brilliant
puritan The Puritans were English Protestants in the 16th and 17th centuries who sought to purify the Church of England of Roman Catholic practices, maintaining that the Church of England had not been fully reformed and should become more Protestant. ...
Headmaster Martin Holbeach who ten years previously had educated John Wallis. Having learnt Greek, Hebrew, Latin and logic at Felsted, in preparation for university studies, he continued his education at
Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...
; he enrolled there because of an offer of support from an unspecified member of the Walpole family, "an offer that was perhaps prompted by the Walpoles' sympathy for Barrow's adherence to the
Royalist A royalist supports a particular monarch as head of state for a particular kingdom, or of a particular dynastic claim. In the abstract, this position is royalism. It is distinct from monarchism, which advocates a monarchical system of gov ...
cause." His uncle and namesake Isaac Barrow, afterwards
Bishop of St Asaph The Bishop of St Asaph heads the Church in Wales diocese of St Asaph. The diocese covers the counties of Conwy and Flintshire, Wrexham county borough, the eastern part of Merioneth in Gwynedd and part of northern Powys. The Episcopal seat is loca ...
, was a Fellow of Peterhouse. 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 having refused to sign the Engagement to uphold the Commonwealth, he obtained travel grants to go abroad.


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
pirate Piracy is an act of robbery or criminal violence by ship or boat-borne attackers upon another ship or a coastal area, typically with the goal of stealing cargo and other valuable goods. Those who conduct acts of piracy are called pirates, v ...
s. He is described as "low in stature, lean, and of a pale complexion," slovenly in his dress, and having a committed and long-standing habit of tobacco use (an '' inveterate smoker''). In respect to his courtly activities his aptitude to wit earned him favour with Charles II, and the respect of his fellow courtiers. In his writings one might find accordingly, a sustained and somewhat stately eloquence. He was an altogether impressive personage of the time, having lived a blameless life in which he exercised his conduct with due care and conscientiousness.


Later career


Work

On the Restoration in 1660, he was ordained and appointed to the
Regius Professorship A Regius Professor is a university professor who has, or originally had, royal patronage or appointment. They are a unique feature of academia in the United Kingdom and Ireland. The first Regius Professorship was in the field of medicine, and ...
of Greek at the
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
. In 1662, he was made professor of
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
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 his professorship in favour of
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
. About this time, Barrow 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 or the divine are things that are either related to, devoted to, or proceeding from a deity.divine< ...
. He was made a
Doctor of Divinity A Doctor of Divinity (D.D. or DDiv; la, Doctor Divinitatis) is the holder of an advanced academic degree in divinity. In the United Kingdom, it is considered an advanced doctoral degree. At the University of Oxford, doctors of divinity are ran ...
by Royal mandate in 1670, and two years later Master of
Trinity College Trinity College may refer to: Australia * Trinity Anglican College, an Anglican coeducational primary and secondary school in , New South Wales * Trinity Catholic College, Auburn, a coeducational school in the inner-western suburbs of Sydney, New ...
(1672), where he founded the library, and held the post until his death. His earliest work was a complete edition of the ''Elements'' of
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
, 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 Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
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 Apollonius of Perga ( grc-gre, Ἀπολλώνιος ὁ Περγαῖος, Apollṓnios ho Pergaîos; la, Apollonius Pergaeus; ) was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributio ...
, 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

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 46, and was buried at
Westminster Abbey Westminster Abbey, formally titled the Collegiate Church of Saint Peter at Westminster, is an historic, mainly Gothic church in the City of Westminster, London, England, just to the west of the Palace of Westminster. It is one of the United ...
. John Aubrey, in the Brief Lives, attributes his death to an opium addiction acquired during his residence in Turkey.


Calculating tangents

The geometrical lectures contain some new ways of determining the areas and
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
s 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, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve ...
. 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 A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...
''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 In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
''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 #''x''2 (''x''2 + ''y''2) = ''r''2''y''2, the
kappa curve In geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter . The kappa curve was first studied by Gérard van Gutschoven around 1662. In the history of mathematics, it is remembered as one o ...
; #''x''3 + ''y''3 = ''r''3; #''x''3 + ''y''3 = ''rxy'', called '' la galande''; #''y'' = (''r'' − ''x'') tan π''x''/2''r'', the
quadratrix In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and E. W. Tschirnhaus, which are both related to the circ ...
; and #''y'' = ''r'' tan π''x''/2''r''. It will be sufficient here to take as an illustration the simpler case of the parabola ''y''2 = ''px''. Using the notation given above, we have for the point ''P'', ''y''2 = ''px''; and for the point ''Q'': :(''y'' − ''a'')2 = ''p''(''x'' − ''e''). Subtracting we get :2''ay'' − ''a''2 = ''pe''. But, if ''a'' be an infinitesimal quantity, ''a''2 must be infinitely smaller and therefore may be neglected when compared with the quantities 2''ay'' and ''pe''. Hence :2''ay'' = ''pe'', that is, ''e'' : ''a'' = 2''y'' : ''p''. Therefore, :''TM'' : ''y'' = ''e'' : ''a'' = 2''y'' : ''p''. Hence :TM = 2''y''2/''p'' = 2''x''. 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) n Latin
Euclide's Elements
' (1660)
n English N, or n, is the fourteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History ...
translations of Euclid's ''Elements''
''Lectiones Opticae''
(1669)
''Lectiones Geometricae''
(1670), translated a
''Geometrical Lectures''
(1735) by Edmund Stone, later translated a
''The Geometrical Lectures of Isaac Barrow''
(1916) by James M. Child
''Apollonii Conica''
(1675) translation of '' Conics''
''Archimedis Opera''
(1675) translation of
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
’s works
''Theodosii Sphaerica''
(1675) translation of '' Sphaerics''
''A Treatise on the Pope's Supremacy, To Which Is Added A Discourse Concerning The Unity Of The Church''
(1680)
''Lectiones Mathematicae''
(1683) translated a
''The Usefulness of Mathematical Learning''
(1734) by John Kirkby * ''The works of the learned Isaac Barrow, D.D.'' (1700
Vol. 1Vol. 2–3
* ''The Works of Dr. Isaac Barrow'' (1830)
Vol. 1Vol. 2Vol. 3Vol. 4Vol. 5Vol. 6Vol. 7
ermons and theological essays


See also

* The
lunar crater Lunar craters are impact craters on Earth's Moon. The Moon's surface has many craters, all of which were formed by impacts. The International Astronomical Union currently recognizes 9,137 craters, of which 1,675 have been dated. History The w ...
Barrow is named after him * Gresham Professors of Geometry


References


Further reading

* * W. W. Rouse Ball. ''A Short Account of the History of Mathematics'' (4th edition, 1908) *
Clinton Bennett Clinton Bennett (born 7 October 1955) is a British-American scholar of religions and participant in interfaith dialogue specialising in the study of Islam and Muslim-non-Muslim encounter. An ordained Baptist minister, he was a missionary in Bang ...
, ''Promise, Predicament and Perplexity: Isaac Barrow (1630–1677) on Islam'' ( Gorgias Press, 2022) * * *


External links

* * * * *
The Master of Trinity
at
Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...
* * {{DEFAULTSORT:Barrow, Isaac Alumni of Trinity College, Cambridge English Anglicans 17th-century English mathematicians Lucasian Professors of Mathematics Masters of Trinity College, Cambridge Original Fellows of the Royal Society Professors of Gresham College People educated at Charterhouse School People educated at Felsted School 17th-century Anglicans 1630 births 1677 deaths English Christian theologians Vice-Chancellors of the University of Cambridge Regius Professors of Greek (Cambridge) 17th-century Anglican theologians