In 1619 Sir Henry Savile founded a chair of Geometry and a Chair of Astronomy at the University of Oxford.

Savile required that the professor of geometry teach the whole of Euclid's Elements, Apollonius'sConics and the complete works of Archimedes. His course notes had to be deposited in the University Library. He was also required to show the practical applications of mathematics, teach arithmetic, mechanics and the theory of music.

Klein's synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm (1872), profoundly influenced mathematical development.

Weierstrass led a seminar on Lobachevsky's geometry in 1870 which was attended by Klein and, two years later, after Klein and Lie had discussed these new generalisations of geometry in Paris, Klein produced his general view of geometry as the properties invariant under the action of some group of transformations in the Erlanger Programm.

After [Thales, etc.] Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrational and the construction of the cosmic figures.

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