James Gregory (astronomer and mathematician)
Encyclopedia
James Gregory FRS (November 1638 – October 1675) was a Scottish
mathematician
and astronomer
. He described an early practical design for the reflecting telescope
– the Gregorian telescope
– and made advances in trigonometry
, discovering infinite series representations for several trigonometric functions.
at Drumoak
, Aberdeenshire
, and was initially educated at home by his mother, Janet Anderson. It was his mother who endowed Gregory with his appetite for geometry
, her brother – Alexander Anderson
– having been a pupil and editor of Viète. After his father's death in 1651 his elder brother David took over responsibility for his education. He was sent to Aberdeen Grammar School
, and then to Marischal College
, graduating in 1657.
In 1663 he went to London, meeting John Collins
and fellow Scot Robert Moray
, the first President of the Royal Society
. In 1664 he departed for the University of Padua
, in the Venetian Republic, passing through Flanders
, Paris
and Rome
on his way. At Padua he lived in the house of his countryman James Caddenhead, the professor of philosophy, and he was taught by Stefano Angeli.
Upon his return to London in 1668 he was elected a member of the Royal Society
, before travelling to St Andrews
in late 1668 to take up his post as the first Regius Chair of Mathematics, a position created for him by Charles II
, probably upon the request of Robert Moray.
He was successively professor
at the University of St Andrews
and the University of Edinburgh
.
He had married Mary, daughter of George Jameson
, painter, and widow of Peter Burnet of Elrick, Aberdeen; their son James was Professor of Physics at King's College Aberdeen. He was the grandfather of John Gregory
(FRS 1756); uncle of David Gregorie (FRS 1692) and brother of David Gregory (1627–1720), an inventor.
About a year after assuming the Chair of Mathematics at Edinburgh
, James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36.
, the "Gregorian telescope
". He also described the method for using the transit of Venus to measure the distance of the Earth from the Sun, which was later advocated by Edmund Halley and adopted as the basis of the first effective measurement of the Astronomical Unit
.
and hyperbola
could be obtained in the form of infinite convergent series. This work contains a remarkable geometrical proposition to the effect that the ratio
of the area of any arbitrary sector of a circle to that of the inscribed or circumscribed regular polygon
s is not expressible by a finite number of terms. Hence he inferred that the quadrature of the circle was impossible; this was accepted by Montucla
, but it is not conclusive, for it is conceivable that some particular sector might be squared, and this particular sector might be the whole circle. Nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed transcendental numbers. In addition the first proof of the fundamental theorem of calculus
and the discovery of the Taylor series
can both be attributed to him.
The book also contains series expansions of sin
(x), cos(x), arcsin(x) and arccos(x). (The earliest enunciations of these expansions were made by Madhava
in India
in the 14th century). It was reprinted in 1668 with an appendix, Geometriae Pars, in which Gregory explained how the volumes of solids of revolution could be determined.
with a parabolic mirror
would correct spherical aberration
as well as the chromatic aberration
seen in refracting telescope
s. According to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one.
The telescope design attracted the attention of several people in the scientific establishment such as Robert Hooke
, the Oxford physicist who eventually built the telescope 10 years later, and Sir Robert Moray
, polymath
and founding member of the Royal Society
.
The Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are also used in radio telescopes such as Arecibo
, which features a "Gregorian dome".
,
the result being true only if θ lie between −(1/4)π and (1/4)π.
This formula was later used to calculate digits of π
, although more efficient formulas were later discovered.
James Gregory discovered the diffraction grating
by passing sunlight
through a bird feather
and observing the diffraction pattern produced. In particular he observed the splitting of sunlight into its component colours – this occurred a year after Newton had done the same with a prism
and the phenomenon was still highly controversial.
Gregory, an enthusiastic supporter of Newton, later had much friendly correspondence with him and incorporated his ideas into his own teaching, ideas which at that time were controversial and considered quite revolutionary.
The crater Gregory
on the Moon is named after him. He was the uncle of mathematician David Gregory.
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
. He described an early practical design for the reflecting telescope
Reflecting telescope
A reflecting telescope is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from...
– the Gregorian telescope
Gregorian telescope
The Gregorian telescope is a type of reflecting telescope designed by Scottish mathematician and astronomer James Gregory in the 17th century, and first built in 1673 by Robert Hooke...
– and made advances in trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
, discovering infinite series representations for several trigonometric functions.
Biography
The youngest of the 3 children of John Gregory, an Episcopalian Church of Scotland minister, James was born in the manseManse
A manse is a house inhabited by, or formerly inhabited by, a minister, usually used in the context of a Presbyterian, Methodist, Baptist or United Church...
at Drumoak
Drumoak
Drumoak is a village situated between Peterculter and Banchory in North Deeside, Aberdeenshire, Scotland...
, Aberdeenshire
Aberdeenshire (historic)
Aberdeenshire or the County of Aberdeen is a registration county of Scotland. This area is also a lieutenancy area.Until 1975 Aberdeenshire was one of the counties of Scotland, governed by a county council from 1890...
, and was initially educated at home by his mother, Janet Anderson. It was his mother who endowed Gregory with his appetite for geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, her brother – Alexander Anderson
Alexander Anderson (mathematician)
Alexander Anderson was a Scottish mathematician. He was the son of David Anderson of Finshaugh. His sister was Janet Anderson, the mother of the celebrated James Gregory...
– having been a pupil and editor of Viète. After his father's death in 1651 his elder brother David took over responsibility for his education. He was sent to Aberdeen Grammar School
Aberdeen Grammar School
Aberdeen Grammar School, known to students as The Grammar is a state secondary school in the City of Aberdeen, Scotland. It is one of twelve secondary schools run by the Aberdeen City Council educational department...
, and then to Marischal College
Marischal College
Marischal College is a building and former university in the centre of the city of Aberdeen in north-east Scotland. The building is owned by the University of Aberdeen and used for ceremonial events...
, graduating in 1657.
In 1663 he went to London, meeting John Collins
John Collins (mathematician)
John Collins was an English mathematician. He is most known for his extensive correspondence with leading scientists and mathematicians such as Giovanni Alfonso Borelli, Gottfried Leibniz, Isaac Newton, and John Wallis...
and fellow Scot Robert Moray
Robert Moray
Sir Robert Moray was a Scottish soldier, statesman, diplomat, judge, spy, freemason and natural philosopher. He was well known to Charles I and Charles II, and the French cardinals Richelieu and Mazarin...
, the first President of the Royal Society
President of the Royal Society
The president of the Royal Society is the elected director of the Royal Society of London. After informal meetings at Gresham College, the Royal Society was founded officially on 15 July 1662 for the encouragement of ‘philosophical studies’, by a royal charter which nominated William Brouncker as...
. In 1664 he departed for the University of Padua
University of Padua
The University of Padua is a premier Italian university located in the city of Padua, Italy. The University of Padua was founded in 1222 as a school of law and was one of the most prominent universities in early modern Europe. It is among the earliest universities of the world and the second...
, in the Venetian Republic, passing through Flanders
Flanders
Flanders is the community of the Flemings but also one of the institutions in Belgium, and a geographical region located in parts of present-day Belgium, France and the Netherlands. "Flanders" can also refer to the northern part of Belgium that contains Brussels, Bruges, Ghent and Antwerp...
, Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
and Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
on his way. At Padua he lived in the house of his countryman James Caddenhead, the professor of philosophy, and he was taught by Stefano Angeli.
Upon his return to London in 1668 he was elected a member of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, before travelling to St Andrews
St Andrews
St Andrews is a university town and former royal burgh on the east coast of Fife in Scotland. The town is named after Saint Andrew the Apostle.St Andrews has a population of 16,680, making this the fifth largest settlement in Fife....
in late 1668 to take up his post as the first Regius Chair of Mathematics, a position created for him by Charles II
Charles II of England
Charles II was monarch of the three kingdoms of England, Scotland, and Ireland.Charles II's father, King Charles I, was executed at Whitehall on 30 January 1649, at the climax of the English Civil War...
, probably upon the request of Robert Moray.
He was successively professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
at the University of St Andrews
University of St Andrews
The University of St Andrews, informally referred to as "St Andrews", is the oldest university in Scotland and the third oldest in the English-speaking world after Oxford and Cambridge. The university is situated in the town of St Andrews, Fife, on the east coast of Scotland. It was founded between...
and the University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...
.
He had married Mary, daughter of George Jameson
George Jameson
George Jamesone was Scotland's first eminent portrait-painter.-Early years:He was born in Aberdeen, where his father, Andrew Jamesone, was a stonemason. Jamesone attended the grammar school near his home on Schoolhill and is thought to have gone on to further education at Marischal College...
, painter, and widow of Peter Burnet of Elrick, Aberdeen; their son James was Professor of Physics at King's College Aberdeen. He was the grandfather of John Gregory
John Gregory (moralist)
John Gregory , a.k.a. John Gregorie, was an eighteenth-century Scottish physician, medical writer and moralist....
(FRS 1756); uncle of David Gregorie (FRS 1692) and brother of David Gregory (1627–1720), an inventor.
About a year after assuming the Chair of Mathematics at Edinburgh
Edinburgh
Edinburgh is the capital city of Scotland, the second largest city in Scotland, and the eighth most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a rural area...
, James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36.
Optica Promota
In the Optica Promota Gregory described his design for a reflecting telescopeReflecting telescope
A reflecting telescope is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from...
, the "Gregorian telescope
Gregorian telescope
The Gregorian telescope is a type of reflecting telescope designed by Scottish mathematician and astronomer James Gregory in the 17th century, and first built in 1673 by Robert Hooke...
". He also described the method for using the transit of Venus to measure the distance of the Earth from the Sun, which was later advocated by Edmund Halley and adopted as the basis of the first effective measurement of the Astronomical Unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
.
Vera Circuli et Hyperbolae Quadratura
In 1667, Gregory issued his Vera Circuli et Hyperbolae Quadratura, in which he showed how the areas of the circleCircle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
and hyperbola
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
could be obtained in the form of infinite convergent series. This work contains a remarkable geometrical proposition to the effect that the ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
of the area of any arbitrary sector of a circle to that of the inscribed or circumscribed regular polygon
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
s is not expressible by a finite number of terms. Hence he inferred that the quadrature of the circle was impossible; this was accepted by Montucla
Jean-Étienne Montucla
Jean-Étienne Montucla was a French mathematician.-Biography:Montucla was born at Lyon.In 1754 he published an anonymous treatise entitled Histoire des récherches sur la quadrature du cercle, and in 1758 the first part of his great work, Histoire des mathématiques, the first history of mathematics...
, but it is not conclusive, for it is conceivable that some particular sector might be squared, and this particular sector might be the whole circle. Nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed transcendental numbers. In addition the first proof of the fundamental theorem of calculus
Fundamental theorem of calculus
The first part of the theorem, sometimes called the first fundamental theorem of calculus, shows that an indefinite integration can be reversed by a differentiation...
and the discovery of the Taylor series
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
can both be attributed to him.
The book also contains series expansions of sin
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
(x), cos(x), arcsin(x) and arccos(x). (The earliest enunciations of these expansions were made by Madhava
Madhava of Sangamagrama
Mādhava of Sañgamāgrama was a prominent Kerala mathematician-astronomer from the town of Irińńālakkuţa near Cochin, Kerala, India. He is considered the founder of the Kerala School of Astronomy and Mathematics...
in India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
in the 14th century). It was reprinted in 1668 with an appendix, Geometriae Pars, in which Gregory explained how the volumes of solids of revolution could be determined.
Gregorian telescope
In his 1663 Optica Promota, James Gregory described his reflecting telescope which has come to be known by his name, the Gregorian telescope. Gregory pointed out that a reflecting telescopeReflecting telescope
A reflecting telescope is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from...
with a parabolic mirror
Parabolic reflector
A parabolic reflector is a reflective device used to collect or project energy such as light, sound, or radio waves. Its shape is that of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis...
would correct spherical aberration
Spherical aberration
thumb|right|Spherical aberration. A perfect lens focuses all incoming rays to a point on the [[Optical axis|optic axis]]. A real lens with spherical surfaces suffers from spherical aberration: it focuses rays more tightly if they enter it far from the optic axis than if they enter closer to the...
as well as the chromatic aberration
Chromatic aberration
In optics, chromatic aberration is a type of distortion in which there is a failure of a lens to focus all colors to the same convergence point. It occurs because lenses have a different refractive index for different wavelengths of light...
seen in refracting telescope
Refracting telescope
A refracting or refractor telescope is a type of optical telescope that uses a lens as its objective to form an image . The refracting telescope design was originally used in spy glasses and astronomical telescopes but is also used for long focus camera lenses...
s. According to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one.
The telescope design attracted the attention of several people in the scientific establishment such as Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
, the Oxford physicist who eventually built the telescope 10 years later, and Sir Robert Moray
Robert Moray
Sir Robert Moray was a Scottish soldier, statesman, diplomat, judge, spy, freemason and natural philosopher. He was well known to Charles I and Charles II, and the French cardinals Richelieu and Mazarin...
, polymath
Polymath
A polymath is a person whose expertise spans a significant number of different subject areas. In less formal terms, a polymath may simply be someone who is very knowledgeable...
and founding member of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
.
The Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are also used in radio telescopes such as Arecibo
Arecibo Observatory
The Arecibo Observatory is a radio telescope near the city of Arecibo in Puerto Rico. It is operated by SRI International under cooperative agreement with the National Science Foundation...
, which features a "Gregorian dome".
Other work
In 1671, or perhaps earlier, he established the theorem that,the result being true only if θ lie between −(1/4)π and (1/4)π.
This formula was later used to calculate digits of π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
, although more efficient formulas were later discovered.
James Gregory discovered the diffraction grating
Diffraction grating
In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as...
by passing sunlight
Sunlight
Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...
through a bird feather
Feather
Feathers are one of the epidermal growths that form the distinctive outer covering, or plumage, on birds and some non-avian theropod dinosaurs. They are considered the most complex integumentary structures found in vertebrates, and indeed a premier example of a complex evolutionary novelty. They...
and observing the diffraction pattern produced. In particular he observed the splitting of sunlight into its component colours – this occurred a year after Newton had done the same with a prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...
and the phenomenon was still highly controversial.
Gregory, an enthusiastic supporter of Newton, later had much friendly correspondence with him and incorporated his ideas into his own teaching, ideas which at that time were controversial and considered quite revolutionary.
The crater Gregory
Gregory (lunar crater)
Gregory is a lunar crater on the far side of the Moon. It is located to the southeast of the crater Ibn Firnas, and north-northeast of Bečvář. About one crater diameter to the north is the smaller Morozov....
on the Moon is named after him. He was the uncle of mathematician David Gregory.
See also
- Possible transmission of Kerala mathematics to Europe
- James Gregory Telescope, St AndrewsJames Gregory TelescopeThe James Gregory Telescope was constructed in 1962 by the University of St Andrews. It is of a Schmidt-Cassegrain design and is fitted with a CCD camera...