James Gregory
FRS (November 1638 – October 1675) was a Scottish mathematician and
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
. His surname is sometimes spelt as Gregorie, the original Scottish spelling. He described an early practical design for the
reflecting telescope
A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternati ...
– the
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. James Gregory was a contemporary of Isaac Newton. Both oft ...
– and made advances in
trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
, discovering
infinite series
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, math ...
representations for several trigonometric functions.
In his book ''Geometriae Pars Universalis'' (1668)
Gregory gave both the first published statement and proof of the
fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem), for which he was acknowledged by
Isaac Barrow
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; in particular, for proof of the fundamental theorem ...
.
Biography
Gregory was born in 1638. His mother Janet was the daughter of
Jean and David Anderson and his father was John Gregory, an
Episcopalian
Anglicanism is a Western Christian tradition that has developed from the practices, liturgy, and identity of the Church of England following the English Reformation, in the context of the Protestant Reformation in Europe. It is one of the ...
Church of Scotland minister
A Church of Scotland congregation is led by its minister and elders. Both of these terms are also used in other Christian denominations: see Minister (Christianity) and Elder (Christianity). This article discusses the specific understanding ...
, James was youngest of their three children and he was born in the
manse
A manse () is a clergy house inhabited by, or formerly inhabited by, a minister, usually used in the context of Presbyterian, Methodist, Baptist and other Christian traditions.
Ultimately derived from the Latin ''mansus'', "dwelling", from ' ...
at
Drumoak
Drumoak (, gd, Druim M'Aodhaig, ) is a village situated between Peterculter and Banchory in North Deeside, Aberdeenshire, Scotland. Drumoak is proximate to the River Dee, with Park Bridge, named for the local Park Estate, being a local crossin ...
,
Aberdeenshire
Aberdeenshire ( sco, Aiberdeenshire; gd, Siorrachd Obar Dheathain) is one of the 32 council areas of Scotland.
It takes its name from the County of Aberdeen which has substantially different boundaries. The Aberdeenshire Council area inclu ...
, and was initially educated at home by his mother, Janet Anderson (~1600–1668). It was his mother who endowed Gregory with his appetite for
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 ...
, her uncle –
Alexander Anderson (1582–1619) – having been a pupil and editor of French mathematician
Viète. After his father's death in 1651 his elder brother David took over responsibility for his education. He attended
Aberdeen Grammar School
Aberdeen Grammar School is a state secondary school in Aberdeen, Scotland. It is one of thirteen secondary schools run by the Aberdeen City Council educational department.
It is the oldest school in the city and one of the oldest grammar school ...
, and then
Marischal College
Marischal College ( ) is a large granite building on Broad Street in the centre of Aberdeen in north-east Scotland, and since 2011 has acted as the headquarters of Aberdeen City Council. However, the building was constructed for and is on lon ...
from 1653–1657, graduating AM in 1657.
In 1663 he went to London, meeting
John Collins and fellow Scot
Robert Moray
Sir Robert Moray (alternative spellings: Murrey, Murray) FRS (1608 or 1609 – 4 July 1673) was a Scottish soldier, statesman, diplomat, judge, spy, and natural philosopher. He was well known to Charles I and Charles II, and to the French ...
, one of the founders of the
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
. In 1664 he departed for the
University of Padua
The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from ...
, in the
Venetian Republic
The Republic of Venice ( vec, Repùblega de Venèsia) or Venetian Republic ( vec, Repùblega Vèneta, links=no), traditionally known as La Serenissima ( en, Most Serene Republic of Venice, italics=yes; vec, Serenìsima Repùblega de Venèsia ...
, passing through
Flanders
Flanders (, ; Dutch: ''Vlaanderen'' ) is the Flemish-speaking northern portion of Belgium and one of the communities, regions and language areas of Belgium. However, there are several overlapping definitions, including ones related to cultu ...
, 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
Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemati ...
, before travelling to
St Andrews
St Andrews ( la, S. Andrea(s); sco, Saunt Aundraes; gd, Cill Rìmhinn) is a town on the east coast of Fife in Scotland, southeast of Dundee and northeast of Edinburgh. St Andrews had a recorded population of 16,800 , making it Fife's fourt ...
in late 1668 to take up his post as the first
Regius Professor of Mathematics at the
University of St Andrews
(Aien aristeuein)
, motto_lang = grc
, mottoeng = Ever to ExcelorEver to be the Best
, established =
, type = Public research university
Ancient university
, endowment ...
, a position created for him by
Charles II, probably upon the request of Robert Moray. There at the
University of St Andrews
(Aien aristeuein)
, motto_lang = grc
, mottoeng = Ever to ExcelorEver to be the Best
, established =
, type = Public research university
Ancient university
, endowment ...
, he laid the first meridian line across the floor of his lab in 1673, which was 200 years prior to the Greenwich Meridian being established, and thus "arguably making St Andrews the place where time began".
He was successively professor at the
University of St Andrews
(Aien aristeuein)
, motto_lang = grc
, mottoeng = Ever to ExcelorEver to be the Best
, established =
, type = Public research university
Ancient university
, endowment ...
and the
University of Edinburgh
The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1 ...
.
He had married Mary, daughter of
George Jameson, painter, and widow of John Burnet of Elrick, Aberdeen; their son James was Professor of Physics at
King's College, Aberdeen
King's College in Old Aberdeen, Scotland, the full title of which is The University and King's College of Aberdeen (''Collegium Regium Abredonense''), is a formerly independent university founded in 1495 and now an integral part of the Univer ...
. He was the grandfather of
John Gregory (FRS 1756); uncle of
David Gregorie (FRS 1692) and brother of
David Gregory (1627–1720), a physician and inventor.
About a year after assuming the Chair of Mathematics at
Edinburgh
Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...
, 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.
Published works
''Optica Promota''
In the ''Optica Promota'', published in 1663, Gregory described his design for a
reflecting telescope
A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternati ...
, the "
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. James Gregory was a contemporary of Isaac Newton. Both oft ...
". He also described the method for using the
transit of Venus
frameless, upright=0.5
A transit of Venus across the Sun takes place when the planet Venus passes directly between the Sun and a superior planet, becoming visible against (and hence obscuring a small portion of) the solar disk. During a tr ...
to measure the distance of the Earth from the Sun, which was later advocated by
Edmund Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.
From an observatory he constructed on Saint Helena in 1676–77, Hal ...
and adopted as the basis of the first effective measurement of the
Astronomical Unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...
.
''Vera Circuli et Hyperbolae Quadratura''
Before he left Padua, Gregory published ''Vera Circuli et Hyperbolae Quadratura'' (1667) in which he approximated the areas of the
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
and
hyperbola
In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, ca ...
with convergent series:
:
ames Gregory
Ames may refer to:
Places United States
* Ames, Arkansas, a place in Arkansas
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* Ames, Iowa, the most populous city bearing this name
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* Ames, Nebraska
* Ames, New York
* Ames, ...
cannot be denied the authorship of many curious theorems on the relation of the circle to
inscribed
{{unreferenced, date=August 2012
An inscribed triangle of a circle
In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "figure F is inscribed in figu ...
and
circumscribed polygons, and their relation to each other. By means of these theorems he gives with infinitely less trouble than by the usual calculations, … the measure of the circle and hyperbola (and consequently the construction of
logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 ...
s) to more than twenty decimal places. Following the example of
Huygens, he also gave constructions of straight lines equal to the
arcs of the circle, and whose error is still less.
"The first 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, ...
and the discovery of the
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...
can both be attributed to him."
The book 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
A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternati ...
which has come to be known by his name, the Gregorian telescope. Gregory pointed out that a reflecting telescope with a
parabolic mirror
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface gener ...
would correct
spherical aberration
In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strik ...
as well as the
chromatic aberration
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ...
seen in
refracting telescope
A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens as its objective to form an image (also referred to a dioptric telescope). The refracting telescope design was originally used in spyglasses an ...
s. In his design he also placed a concave
secondary mirror
A secondary mirror (or secondary) is the second deflecting or focusing mirror element in a reflecting telescope. Light gathered by the primary mirror is directed towards a focal point typically past the location of the secondary. Secondary mirro ...
with an elliptical surface past the focal point of the parabolic
primary mirror
A primary mirror (or primary) is the principal light-gathering surface (the objective) of a reflecting telescope.
Description
The primary mirror of a reflecting telescope is a spherical or parabolic shaped disks of polished reflective meta ...
, reflecting the image back through a hole in the primary mirror where it could be conveniently viewed. 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 FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
, the Oxford physicist who eventually built the telescope 10 years later, and Sir
Robert Moray
Sir Robert Moray (alternative spellings: Murrey, Murray) FRS (1608 or 1609 – 4 July 1673) was a Scottish soldier, statesman, diplomat, judge, spy, and natural philosopher. He was well known to Charles I and Charles II, and to the French ...
,
polymath
A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
and founding member of the
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
.
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
A radio telescope is a specialized antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency p ...
such as
Arecibo, which features a "Gregorian dome".
Mathematics
The following excerpt is from the ''
Pantologia
''Pantologia'' is an English encyclopedia, published in 12 volumes, 8vo in 1813, with 370 plates (some coloured). Its full title page was ''A New Cyclopedia, comprehending a complete series of Essays, Treatises and Systems, alphabetically arrange ...
. A new (cabinet) cyclopædia'' (1813)
Mr. James Gregory was a man of a very acute and penetrating genius. ...The most brilliant part of his character was that of his mathematical genius as an inventor, which was of the first order; as will appear by... his inventions and discoveries hich include
Ij ( fa, ايج, also Romanized as Īj; also known as Hich and Īch) is a village in Golabar Rural District, in the Central District of Ijrud County, Zanjan Province, Iran
Iran, officially the Islamic Republic of Iran, and also ...
quadrature of the circle and hyperbola, by an infinite converging series; his method for the transformation of curves; a geometrical demonstration of Lord Brouncker's series for squaring the hyperbola—his demonstration that the meridian line is analogous to a scale of logarithmic tangents of the half complements of the latitude; he also invented and demonstrated geometrically, by help of the hyperbola, a very simple converging series for making the logarithms; he sent to Mr. Collins the solution of the famous Keplerian problem by an infinite series; he discovered a method of drawing 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 to curves geometrically, without any previous calculations; a rule for the direct and inverse method of tangents, which stands upon the same principle (of exhaustions) with that of fluxions, and differs not much from it in the manner of application; a series for the length of the arc of a circle from the tangent, and vice versa; as also for the secant and logarithmic tangent and secant, and vice versa. These, with others, for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some received from him of Newton's, in which he followed the elegant example of this author, in delivering his series in simple terms, independent of each other.
Other work
In a letter of 1671 to
John Collins, Gregory gives the
power series
In mathematics, a power series (in one variable) is an infinite series of the form
\sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots
where ''an'' represents the coefficient of the ''n''th term and ''c'' is a con ...
expansion of seven functions
:
There is evidence that he discovered the method of taking higher derivatives in order to compute a power series, which was not discovered by Taylor until 1715, but did not publish his results, thinking he had only rediscovered "Mr. Newton's universal method," which was based on a different technique.
James Gregory discovered the
diffraction grating
In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structur ...
by passing
sunlight
Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when ...
through a bird
feather
Feathers are epidermal growths that form a distinctive outer covering, or plumage, on both avian (bird) and some non-avian dinosaurs and other archosaurs. They are the most complex integumentary structures found in vertebrates and a premie ...
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.
A round wheel is unsuitable for irregular surfaces, and Gregory devised an appropriate "adaptable wheel" using a ''Gregory transformation''.
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.
Works
* 1663 �
''Optica promota''(The advance of optics), link from
Google Books
Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical ...
.
* 1667 �
Vera circuli et hyperbolae quadratura(''The true squaring of the circle and hyperbola'') via
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
* 1668 �
''Exercitationes geometricae''(Geometrical exercises), link from Google Books.
* 1668 – ''Geometriae pars universalis'' (The universal part of geometry)
See also
*
James Gregory Telescope, St Andrews
*
Gregor telescope at the
Teide Observatory
Teide Observatory ( es, Observatorio del Teide), IAU code 954, is an astronomical observatory on Mount Teide at , located on Tenerife, Spain. It has been operated by the Instituto de Astrofísica de Canarias since its inauguration in 1964. It bec ...
*
Thomas Reid
Thomas Reid (; 7 May ( O.S. 26 April) 1710 – 7 October 1796) was a religiously trained Scottish philosopher. He was the founder of the Scottish School of Common Sense and played an integral role in the Scottish Enlightenment. In 1783 he wa ...
*
Deans Court
References
Further reading
* Herbert Westren Turnbull (1939) ''James Gregory; Tercentenary Memorial Volume'',
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
*
*
External links
*
*
James Gregory's Euclidean Proof of the Fundamental Theorem of Calculusa
ConvergenceJames Gregory Public Lectures on Religion and Science, University of St AndrewsJames Gregory's "''Optica Promota''" (English translation)* James Gregory (1663)
ttp://lhldigital.lindahall.org/cdm/ref/collection/color/id/29647 ''Optica promota''– digital facsimile from the
Linda Hall Library
The Linda Hall Library is a privately endowed American library of science, engineering and technology located in Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest independently funded public library of scien ...
{{DEFAULTSORT:Gregory, James
1638 births
1675 deaths
People from Kincardine and Mearns
17th-century astronomers
17th-century Scottish mathematicians
Academics of the University of Edinburgh
Academics of the University of St Andrews
Scottish astronomers
Scottish inventors
Alumni of the University of Aberdeen
Fellows of the Royal Society
People educated at Aberdeen Grammar School
British scientific instrument makers
Scottish Episcopalians
University of Padua alumni
British geometers