Die Lineale Ausdehnungslehre ein neuer Zweig der Mathematik: Dargestellt und durch Anwendungen auf die ubrigen Zweige der Mathematik, wie auch auf die Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erlautert

The Prussian schoolmaster Hermann Grassmann (1809-77) taught a range of subjects including mathematics, science and Latin and wrote several secondary-school textbooks. Although he was never appointed to a university post, he devoted much energy to mathematical research and developed revolutionary new insights. Die lineale Ausdehnungslehre, published in 1844, is an astonishing work which was not understood by the mathematicians of its time but which anticipated developments that took a century to come to fruition - vector spaces, dimension, exterior products and many other ideas. Admired rather than read by the next generation, it was only fully appreciated by mathematicians such as Peano and Whitehead.