Euclid
Euclid (; – "Eukleídēs", ; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His "Elements" is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the "Elements", Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.
John Casey (mathematician)
John Casey (12 May 1820, Kilbehenny, Co. Limerick, Ireland – 3 January 1891, Dublin) was a respected Irish geometer. He is most famous for Casey's theorem on a circle that is tangent to four other circles, an extension of the problem of Apollonius. However, he contributed several novel proofs and perspectives on Euclidean geometry. He and Émile Lemoine are considered to be the co-founders of the modern geometry of the circle and the triangle.
He was born in Kilbehenny, 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 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 (1873–1881) and Lecturer in Mathematics at University College, Dublin (1881–1891).