John Casey (12 May 1820,

Kilbehenny Kilbehenny (), also Kilbeheny, is a village in County Limerick, Ireland, on the R639 regional road. It is situated on the County Cork border and is within of the County Tipperary border. The village is east of Mitchelstown Mitchelstown ...

County Limerick "Remember Limerick" , image_map = Island_of_Ireland_location_map_Limerick.svg , subdivision_type = Country , subdivision_name = Ireland , subdivision_type1 = Province , subdivision_name1 = Munster , subdivision ...

Ireland Ireland ( ; ga, Éire ; Ulster Scots dialect, Ulster-Scots: ) is an island in the Atlantic Ocean, North Atlantic Ocean, in Northwestern Europe, north-western Europe. It is separated from Great Britain to its east by the North Channel (Grea ...

– 3 January 1891,

Dublin Dublin (; , or ) is the capital and largest city of Republic of Ireland, Ireland. On a bay at the mouth of the River Liffey, it is in the Provinces of Ireland, province of Leinster, bordered on the south by the Dublin Mountains, a part of th ...

) was a respected

Irish Irish may refer to: Common meanings * Someone or something of, from, or related to: ** Ireland, an island situated off the north-western coast of continental Europe ***Éire, Irish language name for the isle ** Northern Ireland, a constituent unit ...

geometer A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

. He is most famous for

Casey's theorem In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey. Formulation of the theorem Let \,O be a circle of radius \,R. Let \,O_1, O_2 ...

on a circle that is tangent to four other circles, an extension of

Ptolemy's theorem In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician ...

. However, he contributed several novel proofs and perspectives on

Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small ...

. He and

Émile Lemoine Émile Michel Hyacinthe Lemoine (; 22 November 1840 – 21 February 1912) was a French civil engineer and a mathematician, a geometer in particular. He was educated at a variety of institutions, including the Prytanée National Militaire and, mo ...

are considered to be the co-founders of the modern geometry of the circle and the triangle.

Biography

He was born at Kilbehenny in Limerick, Ireland and educated locally at Mitchelstown, before becoming a teacher under the Board of National Education. He later became headmaster of the Central Model Schools in Kilkenny City. He subsequently entered

Trinity College Dublin , name_Latin = Collegium Sanctae et Individuae Trinitatis Reginae Elizabethae juxta Dublin , motto = ''Perpetuis futuris temporibus duraturam'' (Latin) , motto_lang = la , motto_English = It will last i ...

in 1858, where he was elected a Scholar in 1861 and was awarded the degree of BA in 1862. He was then Mathematics Master at Kingston School (1862–1873), Professor of Higher Mathematics and Mathematical Physics at the newly founded

Catholic University of Ireland The Catholic University of Ireland (CUI; ga, Ollscoil Chaitliceach na hÉireann) was a private Catholic university in Dublin, Ireland. It was founded in 1851 following the Synod of Thurles in 1850, and in response to the Queen's University o ...

(1873–1881) and Lecturer in Mathematics at its successor, the University College Dublin (1881–1891).

Honours and awards

In 1869, the

University of Dublin The University of Dublin ( ga, Ollscoil Átha Cliath), corporately designated the Chancellor, Doctors and Masters of the University of Dublin, is a university located in Dublin, Ireland. It is the degree-awarding body for Trinity College Dubl ...

awarded Casey the Honorary Degree of Doctor of Laws. 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 science, natural knowledge, incl ...

in June 1875. He was elected to the

Royal Irish Academy The Royal Irish Academy (RIA; ga, Acadamh Ríoga na hÉireann), based in Dublin, is an academic body that promotes study in the sciences, humanities and social sciences. It is Ireland's premier List of Irish learned societies, learned socie ...

and in 1880 became a member of its council. In 1878 the Academy conferred upon him the much coveted Cunningham Gold Medal. His work was also acknowledged by the Norwegian Government, among others. He was elected a member of the Societe Mathematique de France in 1884 and received the honorary degree of Doctor of Laws from the

Royal University of Ireland The Royal University of Ireland was founded in accordance with the ''University Education (Ireland) Act 1879'' as an examining and degree-awarding university based on the model of the University of London. A Royal Charter was issued on 27 Apri ...

in 1885.

Major works

* 1880
''On Cubic Transformations''
* 1881
On Cyclides and Sphero-quartics
from

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, ...

* 1882
The First Six Books of the Elements of Euclid
link from

Project Gutenberg Project Gutenberg (PG) is a Virtual volunteering, volunteer effort to digitize and archive cultural works, as well as to "encourage the creation and distribution of eBooks." It was founded in 1971 by American writer Michael S. Hart and is the ...

* 1885
A Treatise on the Analytic Geometry of the Point, Line, Circle and Conic SectionsSecond edition, 1893
links from Internet Archive * 188
A Sequel to the First Six Books of Euclid, 4th edition
link from Internet Archive * 1886: ''A Treatise on Elementary Trigonometry'' (Dublin, 1886) * 1888
''A Treatise on Plane Trigonometry containing an account of the Hyperbolic Functions''
* 1889
A Treatise on Spherical Geometry''
link from Internet Archive

References

Sources

* ''Irish Monthly'' (1891), XIX, 106, 152 * ''Proc. Royal Society'' (1891), XLIX, 30, p. xxiv.

External links