Köchel catalogue son's earlier works; Mozart's catalogue of his own compositions (begun in February 1784 with K. 449) allows relatively precise dating of many of his later works. The catalogue included the opening bars of each piece, known as an incipit. Köchel divided the corpus into a main chronology of 626 works, and five appendices ("" in German, abbreviated to "Anh.") The appendices (Anh. I-V) included: Since Köchel published his original catalogue in 1863 (now referred to as K), the dating of Mozart's compositions has been subject to constant revision. Many more pieces have since been found, re-dated, re-attributed and re-numbered, requiring
19th century in science later in the 19th century by the German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed Riemannian geometry, which unifies and vastly generalizes the three types of geometry. The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton in Ireland developed noncommutative algebra. The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were